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<a href="hamiltonian__path_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2021 Google LLC</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#ifndef OR_TOOLS_GRAPH_HAMILTONIAN_PATH_H_</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#define OR_TOOLS_GRAPH_HAMILTONIAN_PATH_H_</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// Solves the Shortest Hamiltonian Path Problem using a complete algorithm.</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// The algorithm was first described in</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">// M. Held, R.M. Karp, A dynamic programming approach to sequencing problems,</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// J. SIAM 10 (1962) 196-210</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">//</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">// The Shortest Hamiltonian Path Problem (SHPP) is similar to the Traveling</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// Salesperson Problem (TSP).</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// You have to visit all the cities, starting from a given one and you</span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">// do not need to return to your starting point. With the TSP, you can start</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">// anywhere, but you have to return to your start location.</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">//</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// By complete we mean that the algorithm guarantees to compute the optimal</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// solution. The algorithm uses dynamic programming. Its time complexity is</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// O(n^2 * 2^(n-1)), where n is the number of nodes to be visited, and '^'</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// denotes exponentiation. Its space complexity is O(n * 2 ^ (n - 1)).</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">//</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// Note that the naive implementation of the SHPP</span></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// exploring all permutations without memorizing intermediate results would</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// have a complexity of (n - 1)! (factorial of (n - 1) ), which is much higher</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// than n^2 * 2^(n-1). To convince oneself of this, just use Stirling's</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// formula: n! ~ sqrt(2 * pi * n)*( n / exp(1)) ^ n.</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// Because of these complexity figures, the algorithm is not practical for</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// problems with more than 20 nodes.</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">//</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// Here is how the algorithm works:</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// Let us denote the nodes to be visited by their indices 0 .. n - 1</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// Let us pick 0 as the starting node.</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// Let d(i,j) denote the distance (or cost) from i to j.</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// f(S, j) where S is a set of nodes and j is a node in S is defined as follows:</span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// f(S, j) = min (i in S \ {j}, f(S \ {j}, i) + cost(i, j))</span></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// (j is an element of S)</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// Note that this formulation, from the original Held-Karp paper is a bit</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// different, but equivalent to the one used in Caseau and Laburthe, Solving</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// Small TSPs with Constraints, 1997, ICLP</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// f(S, j) = min (i in S, f(S \ {i}, i) + cost(i, j))</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// (j is not an element of S)</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">//</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// The advantage of the Held and Karp formulation is that it enables:</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// - to build the dynamic programming lattice layer by layer starting from the</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// subsets with cardinality 1, and increasing the cardinality.</span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// - to traverse the dynamic programming lattice using sequential memory</span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// accesses, making the algorithm cache-friendly, and faster, despite the large</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// amount of computation needed to get the position when f(S, j) is stored.</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// - TODO(user): implement pruning procedures on top of the Held-Karp algorithm.</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">//</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// The set S can be represented by an integer where bit i corresponds to</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// element i in the set. In the following S denotes the integer corresponding</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// to set S.</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">//</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// The dynamic programming iteration is implemented in the method Solve.</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// The optimal value of the Hamiltonian path starting at 0 is given by</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// min (i in S, f(2 ^ n - 1, i))</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// The optimal value of the Traveling Salesman tour is given by f(2 ^ n, 0).</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// (There is actually no need to duplicate the first node, as all the paths</span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// are computed from node 0.)</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">//</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// To implement dynamic programming, we store the preceding results of</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// computing f(S,j) in an array M[Offset(S,j)]. See the comments about</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// LatticeMemoryManager::BaseOffset() to see how this is computed.</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment">//</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// Keywords: Traveling Salesman, Hamiltonian Path, Dynamic Programming,</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// Held, Karp.</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="preprocessor">#include <math.h></span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="preprocessor">#include <stddef.h></span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="preprocessor">#include <algorithm></span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="preprocessor">#include <cmath></span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="preprocessor">#include <cstdint></span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="preprocessor">#include <limits></span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="preprocessor">#include <memory></span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="preprocessor">#include <stack></span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="preprocessor">#include <type_traits></span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="preprocessor">#include <utility></span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="preprocessor">#include <vector></span></div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> </div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="preprocessor">#include "<a class="code" href="integral__types_8h.html">ortools/base/integral_types.h</a>"</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="preprocessor">#include "<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>"</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="preprocessor">#include "<a class="code" href="bitset_8h.html">ortools/util/bitset.h</a>"</span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="preprocessor">#include "<a class="code" href="saturated__arithmetic_8h.html">ortools/util/saturated_arithmetic.h</a>"</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="preprocessor">#include "<a class="code" href="vector__or__function_8h.html">ortools/util/vector_or_function.h</a>"</span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> </div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// TODO(user): Move the Set-related classbelow to util/bitset.h</span></div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// Iterates over the elements of a set represented as an unsigned integer,</span></div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// starting from the smallest element. (See the class Set<Integer> below.)</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Set></div><div class="line"><a name="l00105"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_element_iterator.html"> 105</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_element_iterator.html">ElementIterator</a> {</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00107"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_element_iterator.html#a0a290cf047b502171a3d1770cd194c52"> 107</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1_element_iterator.html#a0a290cf047b502171a3d1770cd194c52">ElementIterator</a>(<a class="code" href="classoperations__research_1_1_set.html">Set</a> set) : current_set_(set) {}</div><div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_element_iterator.html#aefcf46820145a241c215f2e82b69d5f5"> 108</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_element_iterator.html#aefcf46820145a241c215f2e82b69d5f5">operator!=</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_element_iterator.html">ElementIterator</a>& other)<span class="keyword"> const </span>{</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">return</span> current_set_ != other.current_set_;</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  }</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> </div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="comment">// Returns the smallest element in the current_set_.</span></div><div class="line"><a name="l00113"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_element_iterator.html#a9cf56c599b564897633c67574e2e460b"> 113</a></span>  <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_element_iterator.html#a9cf56c599b564897633c67574e2e460b">operator*</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> current_set_.<a class="code" href="classoperations__research_1_1_set.html#abb2b3831b27fd81d60fb39ad01e108a3">SmallestElement</a>(); }</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="comment">// Advances the iterator by removing its smallest element.</span></div><div class="line"><a name="l00116"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_element_iterator.html#a6eb44ef439441ada8ffaaf6ee33a9c40"> 116</a></span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_element_iterator.html">ElementIterator</a>& <a class="code" href="classoperations__research_1_1_element_iterator.html#a6eb44ef439441ada8ffaaf6ee33a9c40">operator++</a>() {</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  current_set_ = current_set_.<a class="code" href="classoperations__research_1_1_set.html#a5865d6398576a8e71b0f346e79c583e7">RemoveSmallestElement</a>();</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  }</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span> </div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="comment">// The current position of the iterator. Stores the set consisting of the</span></div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// not-yet iterated elements.</span></div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <a class="code" href="classoperations__research_1_1_set.html">Set</a> current_set_;</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span> };</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span> </div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Integer></div><div class="line"><a name="l00128"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html"> 128</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_set.html">Set</a> {</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="comment">// Make this visible to classes using this class.</span></div><div class="line"><a name="l00131"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#aabbec0d4f2a126cbdd6c1bce67b7cc8b"> 131</a></span>  <span class="keyword">typedef</span> Integer <a class="code" href="classoperations__research_1_1_set.html#aabbec0d4f2a126cbdd6c1bce67b7cc8b">IntegerType</a>;</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span> </div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="comment">// Useful constants.</span></div><div class="line"><a name="l00134"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a7f72b10501772e497164805b53e2ec80"> 134</a></span>  <span class="keyword">static</span> constexpr Integer <a class="code" href="classoperations__research_1_1_set.html#a7f72b10501772e497164805b53e2ec80">One</a> = static_cast<Integer>(1);</div><div class="line"><a name="l00135"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#ac2fa078fad730b08d36dc600a24e21a1"> 135</a></span>  <span class="keyword">static</span> constexpr Integer <a class="code" href="classoperations__research_1_1_set.html#ac2fa078fad730b08d36dc600a24e21a1">Zero</a> = static_cast<Integer>(0);</div><div class="line"><a name="l00136"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a062c0acf17a051b885ad211acad31079"> 136</a></span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_set.html#a062c0acf17a051b885ad211acad31079">MaxCardinality</a> = 8 * <span class="keyword">sizeof</span>(Integer); <span class="comment">// NOLINT</span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> </div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="comment">// Construct a set from an Integer.</span></div><div class="line"><a name="l00139"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361"> 139</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(Integer n) : value_(n) {</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  static_assert(<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">std::is_integral<Integer>::value</a>, <span class="stringliteral">"Integral type required"</span>);</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  static_assert(<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">std::is_unsigned<Integer>::value</a>, <span class="stringliteral">"Unsigned type required"</span>);</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  }</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span> </div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="comment">// Returns the integer corresponding to the set.</span></div><div class="line"><a name="l00145"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a983cf4555b2577512febcc3aa327a3c8"> 145</a></span>  Integer <a class="code" href="classoperations__research_1_1_set.html#a983cf4555b2577512febcc3aa327a3c8">value</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> value_; }</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div><div class="line"><a name="l00147"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#ae7cd733dab92b86a3aaac89c4d49503f"> 147</a></span>  <span class="keyword">static</span> <a class="code" href="classoperations__research_1_1_set.html">Set</a> <a class="code" href="classoperations__research_1_1_set.html#ae7cd733dab92b86a3aaac89c4d49503f">FullSet</a>(Integer card) {</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">return</span> card == 0 ? <a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(0) : <a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(~<a class="code" href="classoperations__research_1_1_set.html#ac2fa078fad730b08d36dc600a24e21a1">Zero</a> >> (<a class="code" href="classoperations__research_1_1_set.html#a062c0acf17a051b885ad211acad31079">MaxCardinality</a> - card));</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  }</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span> </div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="comment">// Returns the singleton set with 'n' as its only element.</span></div><div class="line"><a name="l00152"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#abbfaa99a45c4a90475cb2f5138f9a162"> 152</a></span>  <span class="keyword">static</span> <a class="code" href="classoperations__research_1_1_set.html">Set</a> <a class="code" href="classoperations__research_1_1_set.html#abbfaa99a45c4a90475cb2f5138f9a162">Singleton</a>(Integer n) { <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(<a class="code" href="classoperations__research_1_1_set.html#a7f72b10501772e497164805b53e2ec80">One</a> << n); }</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> </div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">// Returns a set equal to the calling object, with element n added.</span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">// If n is already in the set, no operation occurs.</span></div><div class="line"><a name="l00156"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#afe05ca596cfc024da65cf61a79812a2f"> 156</a></span>  <a class="code" href="classoperations__research_1_1_set.html">Set</a> <a class="code" href="classoperations__research_1_1_set.html#afe05ca596cfc024da65cf61a79812a2f">AddElement</a>(<span class="keywordtype">int</span> n)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(value_ | (<a class="code" href="classoperations__research_1_1_set.html#a7f72b10501772e497164805b53e2ec80">One</a> << n)); }</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span> </div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="comment">// Returns a set equal to the calling object, with element n removed.</span></div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="comment">// If n is not in the set, no operation occurs.</span></div><div class="line"><a name="l00160"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a190d6e916c3a1a06e2eff670e8b52da8"> 160</a></span>  <a class="code" href="classoperations__research_1_1_set.html">Set</a> <a class="code" href="classoperations__research_1_1_set.html#a190d6e916c3a1a06e2eff670e8b52da8">RemoveElement</a>(<span class="keywordtype">int</span> n)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(value_ & ~(<a class="code" href="classoperations__research_1_1_set.html#a7f72b10501772e497164805b53e2ec80">One</a> << n)); }</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> </div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="comment">// Returns true if the calling set contains element n.</span></div><div class="line"><a name="l00163"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a0faec65dbf29460ec59dfa75d0536efb"> 163</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_set.html#a0faec65dbf29460ec59dfa75d0536efb">Contains</a>(<span class="keywordtype">int</span> n)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> ((<a class="code" href="classoperations__research_1_1_set.html#a7f72b10501772e497164805b53e2ec80">One</a> << n) & value_) != 0; }</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span> </div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="comment">// Returns true if 'other' is included in the calling set.</span></div><div class="line"><a name="l00166"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a9c628cec54eb559f322c284c096f1837"> 166</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_set.html#a9c628cec54eb559f322c284c096f1837">Includes</a>(<a class="code" href="classoperations__research_1_1_set.html">Set</a> other)<span class="keyword"> const </span>{</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keywordflow">return</span> (value_ & other.value_) == other.value_;</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  }</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span> </div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">// Returns the number of elements in the set. Uses the 32-bit version for</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="comment">// types that have 32-bits or less. Specialized for uint64_t.</span></div><div class="line"><a name="l00172"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a879ebf910431019a01f98d0865749c8d"> 172</a></span>  <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_set.html#a879ebf910431019a01f98d0865749c8d">Cardinality</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#a4841d3c6b072a22ba2b2fe43d6c03298">BitCount32</a>(value_); }</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> </div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="comment">// Returns the index of the smallest element in the set. Uses the 32-bit</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="comment">// version for types that have 32-bits or less. Specialized for uint64_t.</span></div><div class="line"><a name="l00176"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#abb2b3831b27fd81d60fb39ad01e108a3"> 176</a></span>  <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_set.html#abb2b3831b27fd81d60fb39ad01e108a3">SmallestElement</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#aeaca21c840bf285f12127938231369b9">LeastSignificantBitPosition32</a>(value_); }</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span> </div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="comment">// Returns a set equal to the calling object, with its smallest</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="comment">// element removed.</span></div><div class="line"><a name="l00180"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a5865d6398576a8e71b0f346e79c583e7"> 180</a></span>  <a class="code" href="classoperations__research_1_1_set.html">Set</a> <a class="code" href="classoperations__research_1_1_set.html#a5865d6398576a8e71b0f346e79c583e7">RemoveSmallestElement</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(value_ & (value_ - 1)); }</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="comment">// Returns the rank of an element in a set. For the set 11100, ElementRank(4)</span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="comment">// would return 2. (Ranks start at zero).</span></div><div class="line"><a name="l00184"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a33392f61ea41062250f3664a055cd3bf"> 184</a></span>  <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_set.html#a33392f61ea41062250f3664a055cd3bf">ElementRank</a>(<span class="keywordtype">int</span> n)<span class="keyword"> const </span>{</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code" href="classoperations__research_1_1_set.html#a0faec65dbf29460ec59dfa75d0536efb">Contains</a>(n)) << <span class="stringliteral">"n = "</span> << n << <span class="stringliteral">", value_ = "</span> << value_;</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_set.html#a31dd4f4c450a217b20db6d8389d71a4e">SingletonRank</a>(<a class="code" href="classoperations__research_1_1_set.html#abbfaa99a45c4a90475cb2f5138f9a162">Singleton</a>(n));</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  }</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span> </div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="comment">// Returns the set consisting of the smallest element of the calling object.</span></div><div class="line"><a name="l00190"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a64f741970505f1dea6a662c3b1776c74"> 190</a></span>  <a class="code" href="classoperations__research_1_1_set.html">Set</a> <a class="code" href="classoperations__research_1_1_set.html#a64f741970505f1dea6a662c3b1776c74">SmallestSingleton</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(value_ & -value_); }</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> </div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="comment">// Returns the rank of the singleton's element in the calling Set.</span></div><div class="line"><a name="l00193"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a31dd4f4c450a217b20db6d8389d71a4e"> 193</a></span>  <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_set.html#a31dd4f4c450a217b20db6d8389d71a4e">SingletonRank</a>(<a class="code" href="classoperations__research_1_1_set.html">Set</a> singleton)<span class="keyword"> const </span>{</div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(singleton.<a class="code" href="classoperations__research_1_1_set.html#a983cf4555b2577512febcc3aa327a3c8">value</a>(), singleton.<a class="code" href="classoperations__research_1_1_set.html#a64f741970505f1dea6a662c3b1776c74">SmallestSingleton</a>().<a class="code" href="classoperations__research_1_1_set.html#a983cf4555b2577512febcc3aa327a3c8">value</a>());</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(value_ & (singleton.value_ - 1)).Cardinality();</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  }</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span> </div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="comment">// STL iterator-related member functions.</span></div><div class="line"><a name="l00199"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a191fa6bb5261ddd97d311ccc1d90fe7c"> 199</a></span>  <a class="code" href="classoperations__research_1_1_element_iterator.html">ElementIterator<Set></a> <a class="code" href="classoperations__research_1_1_set.html#a191fa6bb5261ddd97d311ccc1d90fe7c">begin</a>()<span class="keyword"> const </span>{</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_element_iterator.html">ElementIterator<Set></a>(<a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(value_));</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  }</div><div class="line"><a name="l00202"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a67d03a6e5178376e21bdfa720680e447"> 202</a></span>  <a class="code" href="classoperations__research_1_1_element_iterator.html">ElementIterator<Set></a> <a class="code" href="classoperations__research_1_1_set.html#a67d03a6e5178376e21bdfa720680e447">end</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_element_iterator.html">ElementIterator<Set></a>(<a class="code" href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">Set</a>(0)); }</div><div class="line"><a name="l00203"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a3382ddf3a1f05b9ded21ddb7b0013f78"> 203</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_set.html#a3382ddf3a1f05b9ded21ddb7b0013f78">operator!=</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_set.html">Set</a>& other)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> value_ != other.value_; }</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> </div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="comment">// The Integer representing the set.</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  Integer value_;</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span> };</div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span> </div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="keyword">template</span> <></div><div class="line"><a name="l00211"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#ab1a611fb9b161c503e676197ce82dcc1"> 211</a></span> <span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_set.html#abb2b3831b27fd81d60fb39ad01e108a3">Set<uint64_t>::SmallestElement</a>()<span class="keyword"> const </span>{</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#ae13fcb4162a4180395806f43237c44b2">LeastSignificantBitPosition64</a>(value_);</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span> }</div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span> </div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keyword">template</span> <></div><div class="line"><a name="l00216"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set.html#a4549c2beac5748836f490f1a9691aad2"> 216</a></span> <span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_set.html#a879ebf910431019a01f98d0865749c8d">Set<uint64_t>::Cardinality</a>()<span class="keyword"> const </span>{</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#abc979832d72da1ae793ba6d28ae46672">BitCount64</a>(value_);</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span> }</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span> </div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="comment">// An iterator for sets of increasing corresponding values that have the same</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="comment">// cardinality. For example, the sets with cardinality 3 will be listed as</span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="comment">// ...00111, ...01011, ...01101, ...1110, etc...</span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="keyword">template</span> <<span class="keyword">typename</span> SetRange></div><div class="line"><a name="l00224"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_iterator.html"> 224</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_set_range_iterator.html">SetRangeIterator</a> {</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="comment">// Make the parameter types visible to SetRangeWithCardinality.</span></div><div class="line"><a name="l00227"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_iterator.html#a0e4b89b4bb1b1a5bb3c799938380aeb0"> 227</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SetRange::SetType <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a0e4b89b4bb1b1a5bb3c799938380aeb0">SetType</a>;</div><div class="line"><a name="l00228"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_iterator.html#a4ee741618ffbec86b3a2a280c61ca3f0"> 228</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SetType::IntegerType <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a4ee741618ffbec86b3a2a280c61ca3f0">IntegerType</a>;</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span> </div><div class="line"><a name="l00230"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_iterator.html#ad82623d8471ab5eb30f4e19bc89796b9"> 230</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html#ad82623d8471ab5eb30f4e19bc89796b9">SetRangeIterator</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a0e4b89b4bb1b1a5bb3c799938380aeb0">SetType</a> set) : current_set_(set) {}</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span> </div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="comment">// STL iterator-related methods.</span></div><div class="line"><a name="l00233"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_iterator.html#a8f6ae547a7aba92b9e4fe92a8713085a"> 233</a></span>  <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a0e4b89b4bb1b1a5bb3c799938380aeb0">SetType</a> <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a8f6ae547a7aba92b9e4fe92a8713085a">operator*</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> current_set_; }</div><div class="line"><a name="l00234"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_iterator.html#a9a69c0a346336b270178d60cd6da6404"> 234</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a9a69c0a346336b270178d60cd6da6404">operator!=</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html">SetRangeIterator</a>& other)<span class="keyword"> const </span>{</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">return</span> current_set_ != other.current_set_;</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  }</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span> </div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">// Computes the next set with the same cardinality using Gosper's hack.</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">// ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-239.pdf ITEM 175</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="comment">// Also translated in C https://www.cl.cam.ac.uk/~am21/hakmemc.html</span></div><div class="line"><a name="l00241"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_iterator.html#ab199aaba95428b8647f6bfdd83ecb68c"> 241</a></span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html">SetRangeIterator</a>& <a class="code" href="classoperations__research_1_1_set_range_iterator.html#ab199aaba95428b8647f6bfdd83ecb68c">operator++</a>() {</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a4ee741618ffbec86b3a2a280c61ca3f0">IntegerType</a> c = current_set_.SmallestSingleton().value();</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a4ee741618ffbec86b3a2a280c61ca3f0">IntegerType</a> <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> = current_set_.value();</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a4ee741618ffbec86b3a2a280c61ca3f0">IntegerType</a> r = c + current_set_.value();</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="comment">// Dividing by c as in HAKMEMC can be avoided by taking into account</span></div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="comment">// that c is the smallest singleton of current_set_, and using a shift.</span></div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a4ee741618ffbec86b3a2a280c61ca3f0">IntegerType</a> shift = current_set_.SmallestElement();</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  current_set_ = r == 0 ? <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a0e4b89b4bb1b1a5bb3c799938380aeb0">SetType</a>(0) : <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a0e4b89b4bb1b1a5bb3c799938380aeb0">SetType</a>(((r ^ <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>) >> (shift + 2)) | r);</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  }</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span> </div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="comment">// The current set of iterator.</span></div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <a class="code" href="classoperations__research_1_1_set_range_iterator.html#a0e4b89b4bb1b1a5bb3c799938380aeb0">SetType</a> current_set_;</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span> };</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span> </div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Set></div><div class="line"><a name="l00258"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_with_cardinality.html"> 258</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_set_range_with_cardinality.html">SetRangeWithCardinality</a> {</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00260"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_with_cardinality.html#ac04647d141301b9671da400a7add8e37"> 260</a></span>  <span class="keyword">typedef</span> <a class="code" href="classoperations__research_1_1_set.html">Set</a> <a class="code" href="classoperations__research_1_1_set_range_with_cardinality.html#ac04647d141301b9671da400a7add8e37">SetType</a>;</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="comment">// The end_ set is the first set with cardinality card, that does not fit</span></div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="comment">// in max_card bits. Thus, its bit at position max_card is set, and the</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="comment">// rightmost (card - 1) bits are set.</span></div><div class="line"><a name="l00264"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_with_cardinality.html#ac227945449c4f8144b6c92afd6ae2156"> 264</a></span>  <a class="code" href="classoperations__research_1_1_set_range_with_cardinality.html#ac227945449c4f8144b6c92afd6ae2156">SetRangeWithCardinality</a>(<span class="keywordtype">int</span> card, <span class="keywordtype">int</span> max_card)</div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  : begin_(<a class="code" href="classoperations__research_1_1_set.html">Set</a>::FullSet(card)),</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  end_(<a class="code" href="classoperations__research_1_1_set.html">Set</a>::FullSet(card - 1).AddElement(max_card)) {</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <a class="code" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(0, card);</div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <a class="code" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(0, max_card);</div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(card, begin_.<a class="code" href="classoperations__research_1_1_set.html#a879ebf910431019a01f98d0865749c8d">Cardinality</a>());</div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(card, end_.<a class="code" href="classoperations__research_1_1_set.html#a879ebf910431019a01f98d0865749c8d">Cardinality</a>());</div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  }</div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span> </div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="comment">// STL iterator-related methods.</span></div><div class="line"><a name="l00274"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_with_cardinality.html#a24d9704faf4d419fdabbde6a716e181d"> 274</a></span>  <a class="code" href="classoperations__research_1_1_set_range_iterator.html">SetRangeIterator<SetRangeWithCardinality></a> <a class="code" href="classoperations__research_1_1_set_range_with_cardinality.html#a24d9704faf4d419fdabbde6a716e181d">begin</a>()<span class="keyword"> const </span>{</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html">SetRangeIterator<SetRangeWithCardinality></a>(begin_);</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  }</div><div class="line"><a name="l00277"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_set_range_with_cardinality.html#af7124add76feb58bf035c3375fe140f9"> 277</a></span>  <a class="code" href="classoperations__research_1_1_set_range_iterator.html">SetRangeIterator<SetRangeWithCardinality></a> <a class="code" href="classoperations__research_1_1_set_range_with_cardinality.html#af7124add76feb58bf035c3375fe140f9">end</a>()<span class="keyword"> const </span>{</div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_set_range_iterator.html">SetRangeIterator<SetRangeWithCardinality></a>(end_);</div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  }</div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span> </div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="comment">// Keep the beginning and end of the iterator.</span></div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <a class="code" href="classoperations__research_1_1_set_range_with_cardinality.html#ac04647d141301b9671da400a7add8e37">SetType</a> begin_;</div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <a class="code" href="classoperations__research_1_1_set_range_with_cardinality.html#ac04647d141301b9671da400a7add8e37">SetType</a> end_;</div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span> };</div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span> </div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment">// The Dynamic Programming (DP) algorithm memorizes the values f(set, node) for</span></div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="comment">// node in set, for all the subsets of cardinality <= max_card_.</span></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="comment">// LatticeMemoryManager manages the storage of f(set, node) so that the</span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="comment">// DP iteration access memory in increasing addresses.</span></div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Set, <span class="keyword">typename</span> CostType></div><div class="line"><a name="l00292"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_lattice_memory_manager.html"> 292</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_lattice_memory_manager.html">LatticeMemoryManager</a> {</div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00294"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_lattice_memory_manager.html#a03b88bdfd0b2fcc7e14106cbd425629a"> 294</a></span>  <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#a03b88bdfd0b2fcc7e14106cbd425629a">LatticeMemoryManager</a>() : max_card_(0) {}</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span> </div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="comment">// Reserves memory and fills in the data necessary to access memory.</span></div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#a9614dfea1a66f5d18799a058adc57a95">Init</a>(<span class="keywordtype">int</span> max_card);</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span> </div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="comment">// Returns the offset in memory for f(s, node), with node contained in s.</span></div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  uint64_t <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#a1958048f654b22c744e32dfbcdbeb416">Offset</a>(<a class="code" href="classoperations__research_1_1_set.html">Set</a> s, <span class="keywordtype">int</span> node) <span class="keyword">const</span>;</div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span> </div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="comment">// Returns the base offset in memory for f(s, node), with node contained in s.</span></div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="comment">// This is useful in the Dynamic Programming iterations.</span></div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="comment">// Note(user): inlining this function gains about 5%.</span></div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="comment">// TODO(user): Investigate how to compute BaseOffset(card - 1, s \ { n })</span></div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="comment">// from BaseOffset(card, n) to speed up the DP iteration.</span></div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keyword">inline</span> uint64_t <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#af4a801d214f8a294a6abf462ac12e80a">BaseOffset</a>(<span class="keywordtype">int</span> card, <a class="code" href="classoperations__research_1_1_set.html">Set</a> s) <span class="keyword">const</span>;</div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span> </div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="comment">// Returns the offset delta for a set of cardinality 'card', to which</span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">// node 'removed_node' is replaced by 'added_node' at 'rank'</span></div><div class="line"><a name="l00311"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_lattice_memory_manager.html#a6789c7b14fc935d7e3d03e1376cb79d8"> 311</a></span>  uint64_t <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#a6789c7b14fc935d7e3d03e1376cb79d8">OffsetDelta</a>(<span class="keywordtype">int</span> card, <span class="keywordtype">int</span> added_node, <span class="keywordtype">int</span> removed_node,</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordtype">int</span> rank)<span class="keyword"> const </span>{</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keywordflow">return</span> card *</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  (binomial_coefficients_[added_node][rank] - <span class="comment">// delta for added_node</span></div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  binomial_coefficients_[removed_node][rank]); <span class="comment">// for removed_node.</span></div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  }</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span> </div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="comment">// Memorizes the value = f(s, node) at the correct offset.</span></div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="comment">// This is favored in all other uses than the Dynamic Programming iterations.</span></div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#a4c59c8afdecf1f9d139609ffe9f172ca">SetValue</a>(<a class="code" href="classoperations__research_1_1_set.html">Set</a> s, <span class="keywordtype">int</span> node, CostType <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span> </div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="comment">// Memorizes 'value' at 'offset'. This is useful in the Dynamic Programming</span></div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="comment">// iterations where we want to avoid compute the offset of a pair (set, node).</span></div><div class="line"><a name="l00324"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_lattice_memory_manager.html#a91814684a688a3264fc8f29972969d61"> 324</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#a91814684a688a3264fc8f29972969d61">SetValueAtOffset</a>(uint64_t offset, CostType <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>) {</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  memory_[offset] = <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>;</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  }</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span> </div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="comment">// Returns the memorized value f(s, node) with node in s.</span></div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="comment">// This is favored in all other uses than the Dynamic Programming iterations.</span></div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  CostType <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#aab77eae51a0b3e7781df913213ff4372">Value</a>(<a class="code" href="classoperations__research_1_1_set.html">Set</a> s, <span class="keywordtype">int</span> node) <span class="keyword">const</span>;</div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span> </div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="comment">// Returns the memorized value at 'offset'.</span></div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="comment">// This is useful in the Dynamic Programming iterations.</span></div><div class="line"><a name="l00334"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_lattice_memory_manager.html#afc715a6711310680640765eb66822f8b"> 334</a></span>  CostType <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#afc715a6711310680640765eb66822f8b">ValueAtOffset</a>(uint64_t offset)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> memory_[offset]; }</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span> </div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="comment">// Returns true if the values used to manage memory are set correctly.</span></div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  <span class="comment">// This is intended to only be used in a DCHECK.</span></div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="keywordtype">bool</span> CheckConsistency() <span class="keyword">const</span>;</div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span> </div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="comment">// The maximum cardinality of the set on which the lattice is going to be</span></div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="comment">// used. This is equal to the number of nodes in the TSP.</span></div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keywordtype">int</span> max_card_;</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span> </div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="comment">// binomial_coefficients_[n][k] contains (n choose k).</span></div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  std::vector<std::vector<uint64_t>> binomial_coefficients_;</div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span> </div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="comment">// base_offset_[card] contains the base offset for all f(set, node) with</span></div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="comment">// card(set) == card.</span></div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  std::vector<int64_t> base_offset_;</div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span> </div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="comment">// memory_[Offset(set, node)] contains the costs of the partial path</span></div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="comment">// f(set, node).</span></div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  std::vector<CostType> memory_;</div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span> };</div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Set, <span class="keyword">typename</span> CostType></div><div class="line"><a name="l00358"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_lattice_memory_manager.html#a9614dfea1a66f5d18799a058adc57a95"> 358</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#a9614dfea1a66f5d18799a058adc57a95">LatticeMemoryManager<Set, CostType>::Init</a>(<span class="keywordtype">int</span> max_card) {</div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <a class="code" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(0, max_card);</div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <a class="code" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(<a class="code" href="classoperations__research_1_1_set.html#a062c0acf17a051b885ad211acad31079">Set::MaxCardinality</a>, max_card);</div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="keywordflow">if</span> (max_card <= max_card_) <span class="keywordflow">return</span>;</div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  max_card_ = max_card;</div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  binomial_coefficients_.resize(max_card_ + 1);</div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span> </div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="comment">// Initialize binomial_coefficients_ using Pascal's triangle recursion.</span></div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n <= max_card_; ++n) {</div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  binomial_coefficients_[n].resize(n + 2);</div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  binomial_coefficients_[n][0] = 1;</div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 1; k <= n; ++k) {</div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  binomial_coefficients_[n][k] = binomial_coefficients_[n - 1][k - 1] +</div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  binomial_coefficients_[n - 1][k];</div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  }</div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="comment">// Extend to (n, n + 1) to minimize branchings in LatticeMemoryManager().</span></div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <span class="comment">// This also makes the recurrence above work for k = n.</span></div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  binomial_coefficients_[n][n + 1] = 0;</div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  }</div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  base_offset_.resize(max_card_ + 1);</div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  base_offset_[0] = 0;</div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="comment">// There are k * binomial_coefficients_[max_card_][k] f(S,j) values to store</span></div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="comment">// for each group of f(S,j), with card(S) = k. Update base_offset[k]</span></div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="comment">// accordingly.</span></div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < max_card_; ++k) {</div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  base_offset_[k + 1] =</div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  base_offset_[k] + k * binomial_coefficients_[max_card_][k];</div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  }</div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  memory_.resize(0);</div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  memory_.shrink_to_fit();</div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  memory_.resize(max_card_ * (1 << (max_card_ - 1)));</div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(CheckConsistency());</div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span> }</div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span> </div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Set, <span class="keyword">typename</span> CostType></div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span> <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html">LatticeMemoryManager<Set, CostType>::CheckConsistency</a>()<span class="keyword"> const </span>{</div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n <= max_card_; ++n) {</div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  int64_t sum = 0;</div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k <= n; ++k) {</div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  sum += binomial_coefficients_[n][k];</div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  }</div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(1 << n, sum);</div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  }</div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(0, base_offset_[1]);</div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(max_card_ * (1 << (max_card_ - 1)),</div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  base_offset_[max_card_] + max_card_);</div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span> }</div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span> </div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Set, <span class="keyword">typename</span> CostType></div><div class="line"><a name="l00408"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_lattice_memory_manager.html#af4a801d214f8a294a6abf462ac12e80a"> 408</a></span> uint64_t <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#af4a801d214f8a294a6abf462ac12e80a">LatticeMemoryManager<Set, CostType>::BaseOffset</a>(<span class="keywordtype">int</span> card,</div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <a class="code" href="classoperations__research_1_1_set.html">Set</a> set)<span class="keyword"> const </span>{</div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <a class="code" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(0, card);</div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(set.<a class="code" href="classoperations__research_1_1_set.html#a879ebf910431019a01f98d0865749c8d">Cardinality</a>(), card);</div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  uint64_t local_offset = 0;</div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  <span class="keywordtype">int</span> node_rank = 0;</div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> node : set) {</div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  <span class="comment">// There are binomial_coefficients_[node][node_rank + 1] sets which have</span></div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  <span class="comment">// node at node_rank.</span></div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  local_offset += binomial_coefficients_[node][node_rank + 1];</div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  ++node_rank;</div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  }</div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(card, node_rank);</div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="comment">// Note(user): It is possible to get rid of base_offset_[card] by using a 2-D</span></div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  <span class="comment">// array. It would also make it possible to free all the memory but the layer</span></div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  <span class="comment">// being constructed and the preceding one, if another lattice of paths is</span></div><div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="comment">// constructed.</span></div><div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="comment">// TODO(user): Evaluate the interest of the above.</span></div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  <span class="comment">// There are 'card' f(set, j) to store. That is why we need to multiply</span></div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  <span class="comment">// local_offset by card before adding it to the corresponding base_offset_.</span></div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <span class="keywordflow">return</span> base_offset_[card] + card * local_offset;</div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span> }</div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span> </div><div class="line"><a name="l00431"></a><span class="lineno"> 431</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Set, <span class="keyword">typename</span> CostType></div><div class="line"><a name="l00432"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_lattice_memory_manager.html#a1958048f654b22c744e32dfbcdbeb416"> 432</a></span> uint64_t <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#a1958048f654b22c744e32dfbcdbeb416">LatticeMemoryManager<Set, CostType>::Offset</a>(<a class="code" href="classoperations__research_1_1_set.html">Set</a> set, <span class="keywordtype">int</span> node)<span class="keyword"> const </span>{</div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(set.<a class="code" href="classoperations__research_1_1_set.html#a0faec65dbf29460ec59dfa75d0536efb">Contains</a>(node));</div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  <span class="keywordflow">return</span> BaseOffset(set.<a class="code" href="classoperations__research_1_1_set.html#a879ebf910431019a01f98d0865749c8d">Cardinality</a>(), set) + set.<a class="code" href="classoperations__research_1_1_set.html#a33392f61ea41062250f3664a055cd3bf">ElementRank</a>(node);</div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span> }</div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span> </div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Set, <span class="keyword">typename</span> CostType></div><div class="line"><a name="l00438"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_lattice_memory_manager.html#aab77eae51a0b3e7781df913213ff4372"> 438</a></span> CostType <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#aab77eae51a0b3e7781df913213ff4372">LatticeMemoryManager<Set, CostType>::Value</a>(<a class="code" href="classoperations__research_1_1_set.html">Set</a> set, <span class="keywordtype">int</span> node)<span class="keyword"> const </span>{</div><div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(set.<a class="code" href="classoperations__research_1_1_set.html#a0faec65dbf29460ec59dfa75d0536efb">Contains</a>(node));</div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="keywordflow">return</span> ValueAtOffset(Offset(set, node));</div><div class="line"><a name="l00441"></a><span class="lineno"> 441</span> }</div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span> </div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Set, <span class="keyword">typename</span> CostType></div><div class="line"><a name="l00444"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_lattice_memory_manager.html#a4c59c8afdecf1f9d139609ffe9f172ca"> 444</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html#a4c59c8afdecf1f9d139609ffe9f172ca">LatticeMemoryManager<Set, CostType>::SetValue</a>(<a class="code" href="classoperations__research_1_1_set.html">Set</a> set, <span class="keywordtype">int</span> node,</div><div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  CostType <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>) {</div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(set.<a class="code" href="classoperations__research_1_1_set.html#a0faec65dbf29460ec59dfa75d0536efb">Contains</a>(node));</div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  SetValueAtOffset(Offset(set, node), <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span> }</div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span> </div><div class="line"><a name="l00450"></a><span class="lineno"> 450</span> <span class="comment">// Deprecated type.</span></div><div class="line"><a name="l00451"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#ae8625c5e71962a0f99954d34dab9f92d"> 451</a></span> <span class="keyword">typedef</span> <span class="keywordtype">int</span> <a class="code" href="namespaceoperations__research.html#ae8625c5e71962a0f99954d34dab9f92d">PathNodeIndex</a>;</div><div class="line"><a name="l00452"></a><span class="lineno"> 452</span> </div><div class="line"><a name="l00453"></a><span class="lineno"> 453</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00454"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html"> 454</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver</a> {</div><div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="comment">// HamiltonianPathSolver computes a minimum Hamiltonian path starting at node</span></div><div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  <span class="comment">// 0 over a graph defined by a cost matrix. The cost function need not be</span></div><div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="comment">// symmetric.</span></div><div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="comment">// When the Hamiltonian path is closed, it's a Hamiltonian cycle,</span></div><div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="comment">// i.e. the algorithm solves the Traveling Salesman Problem.</span></div><div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="comment">// Example:</span></div><div class="line"><a name="l00461"></a><span class="lineno"> 461</span> </div><div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <span class="comment">// std::vector<std::vector<int>> cost_mat;</span></div><div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <span class="comment">// ... fill in cost matrix</span></div><div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="comment">// HamiltonianPathSolver<int, std::vector<std::vector<int>>></span></div><div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="comment">// mhp(cost_mat); // no computation done</span></div><div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <span class="comment">// printf("%d\n", mhp.TravelingSalesmanCost()); // computation done and</span></div><div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="comment">// stored</span></div><div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="comment">// In 2010, 26 was the maximum solvable with 24 Gigs of RAM, and it took</span></div><div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <span class="comment">// several minutes. With this 2014 version of the code, one may go a little</span></div><div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  <span class="comment">// higher, but considering the complexity of the algorithm (n*2^n), and that</span></div><div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="comment">// there are very good ways to solve TSP with more than 32 cities,</span></div><div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="comment">// we limit ourselves to 32 cites.</span></div><div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  <span class="comment">// This is why we define the type NodeSet to be 32-bit wide.</span></div><div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="comment">// TODO(user): remove this limitation by using pruning techniques.</span></div><div class="line"><a name="l00476"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a346635bd62f6d557d98e490ff2f3f306"> 476</a></span>  <span class="keyword">typedef</span> uint32_t <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a346635bd62f6d557d98e490ff2f3f306">Integer</a>;</div><div class="line"><a name="l00477"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a03106785fd757b213975f94d4b780709"> 477</a></span>  <span class="keyword">typedef</span> <a class="code" href="classoperations__research_1_1_set.html">Set<Integer></a> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a03106785fd757b213975f94d4b780709">NodeSet</a>;</div><div class="line"><a name="l00478"></a><span class="lineno"> 478</span> </div><div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a9c8cdf78154ae6a73f4a272cb8d1ac4a">HamiltonianPathSolver</a>(CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>);</div><div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a9c8cdf78154ae6a73f4a272cb8d1ac4a">HamiltonianPathSolver</a>(<span class="keywordtype">int</span> num_nodes, CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>);</div><div class="line"><a name="l00481"></a><span class="lineno"> 481</span> </div><div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  <span class="comment">// Replaces the cost matrix while avoiding re-allocating memory.</span></div><div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a19edb994fca04e71736cf3a8d62d7a73">ChangeCostMatrix</a>(CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>);</div><div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a19edb994fca04e71736cf3a8d62d7a73">ChangeCostMatrix</a>(<span class="keywordtype">int</span> num_nodes, CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>);</div><div class="line"><a name="l00485"></a><span class="lineno"> 485</span> </div><div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  <span class="comment">// Returns the cost of the Hamiltonian path from 0 to end_node.</span></div><div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  CostType <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a0b31a8637cf8c0fb125444577e6ad92b">HamiltonianCost</a>(<span class="keywordtype">int</span> end_node);</div><div class="line"><a name="l00488"></a><span class="lineno"> 488</span> </div><div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="comment">// Returns the shortest Hamiltonian path from 0 to end_node.</span></div><div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  std::vector<int> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a8acc60c87190fac89379315aa08ce7a5">HamiltonianPath</a>(<span class="keywordtype">int</span> end_node);</div><div class="line"><a name="l00491"></a><span class="lineno"> 491</span> </div><div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  <span class="comment">// Returns the end-node that yields the shortest Hamiltonian path of</span></div><div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="comment">// all shortest Hamiltonian path from 0 to end-node (end-node != 0).</span></div><div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#ad20cbbfc6081d40231920c3c9543f97e">BestHamiltonianPathEndNode</a>();</div><div class="line"><a name="l00495"></a><span class="lineno"> 495</span> </div><div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  <span class="comment">// Deprecated API. Stores HamiltonianPath(BestHamiltonianPathEndNode()) into</span></div><div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  <span class="comment">// *path.</span></div><div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a8acc60c87190fac89379315aa08ce7a5">HamiltonianPath</a>(std::vector<PathNodeIndex>* path);</div><div class="line"><a name="l00499"></a><span class="lineno"> 499</span> </div><div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  <span class="comment">// Returns the cost of the TSP tour.</span></div><div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  CostType <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#ab558649a26fef3a74f0909ef5af45e90">TravelingSalesmanCost</a>();</div><div class="line"><a name="l00502"></a><span class="lineno"> 502</span> </div><div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="comment">// Returns the TSP tour in the vector pointed to by the argument.</span></div><div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  std::vector<int> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a326a998ed18bedda49bd2cab5cbd4079">TravelingSalesmanPath</a>();</div><div class="line"><a name="l00505"></a><span class="lineno"> 505</span> </div><div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="comment">// Deprecated API.</span></div><div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a326a998ed18bedda49bd2cab5cbd4079">TravelingSalesmanPath</a>(std::vector<PathNodeIndex>* path);</div><div class="line"><a name="l00508"></a><span class="lineno"> 508</span> </div><div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="comment">// Returns true if there won't be precision issues.</span></div><div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="comment">// This is always true for integers, but not for floating-point types.</span></div><div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a5daed8b7f3c98c693f32dff60adeb4cc">IsRobust</a>();</div><div class="line"><a name="l00512"></a><span class="lineno"> 512</span> </div><div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <span class="comment">// Returns true if the cost matrix verifies the triangle inequality.</span></div><div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a44af6c2df0188e77ceeec78a190ecf3f">VerifiesTriangleInequality</a>();</div><div class="line"><a name="l00515"></a><span class="lineno"> 515</span> </div><div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <span class="comment">// Saturated arithmetic helper class.</span></div><div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> T,</div><div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="keywordtype">bool</span> = <span class="keyword">true</span> <span class="comment">/* Dummy parameter to allow specialization */</span>></div><div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <span class="comment">// Returns the saturated addition of a and b. It is specialized below for</span></div><div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <span class="comment">// int32_t and int64_t.</span></div><div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <span class="keyword">struct </span>SaturatedArithmetic {</div><div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  <span class="keyword">static</span> T Add(T <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, T <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) { <span class="keywordflow">return</span> <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> + <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>; }</div><div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="keyword">static</span> T Sub(T <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, T <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) { <span class="keywordflow">return</span> <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> - <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>; }</div><div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  };</div><div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keyword">template</span> <<span class="keywordtype">bool</span> Dummy></div><div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  <span class="keyword">struct </span>SaturatedArithmetic<int64_t, Dummy> {</div><div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <span class="keyword">static</span> int64_t Add(int64_t <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, int64_t <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) { <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#a111f44b9b9cf67a8e8d83794ac9f5291">CapAdd</a>(<a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>); }</div><div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <span class="keyword">static</span> int64_t Sub(int64_t <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, int64_t <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) { <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research.html#a4a43d435871f16c321861fa5de32df82">CapSub</a>(<a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>); }</div><div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  };</div><div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="comment">// TODO(user): implement this natively in saturated_arithmetic.h</span></div><div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  <span class="keyword">template</span> <<span class="keywordtype">bool</span> Dummy></div><div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  <span class="keyword">struct </span>SaturatedArithmetic<int32_t, Dummy> {</div><div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  <span class="keyword">static</span> int32_t Add(int32_t <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, int32_t <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) {</div><div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="keyword">const</span> int64_t a64 = <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>;</div><div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <span class="keyword">const</span> int64_t b64 = <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>;</div><div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <span class="keyword">const</span> int64_t min_int32 = <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits<int32_t>::min</a>();</div><div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  <span class="keyword">const</span> int64_t max_int32 = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits<int32_t>::max</a>();</div><div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  <span class="keywordflow">return</span> static_cast<int32_t>(</div><div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(min_int32, <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(max_int32, a64 + b64)));</div><div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  }</div><div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  <span class="keyword">static</span> int32_t Sub(int32_t <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, int32_t <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) {</div><div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  <span class="keyword">const</span> int64_t a64 = <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>;</div><div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  <span class="keyword">const</span> int64_t b64 = <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>;</div><div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  <span class="keyword">const</span> int64_t min_int32 = <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits<int32_t>::min</a>();</div><div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  <span class="keyword">const</span> int64_t max_int32 = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits<int32_t>::max</a>();</div><div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  <span class="keywordflow">return</span> static_cast<int32_t>(</div><div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(min_int32, <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(max_int32, a64 - b64)));</div><div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  }</div><div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  };</div><div class="line"><a name="l00551"></a><span class="lineno"> 551</span> </div><div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> T></div><div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  <span class="keyword">using</span> Saturated = SaturatedArithmetic<T>;</div><div class="line"><a name="l00554"></a><span class="lineno"> 554</span> </div><div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="comment">// Returns the cost value between two nodes.</span></div><div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  CostType Cost(<span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j) { <span class="keywordflow">return</span> cost_(i, j); }</div><div class="line"><a name="l00557"></a><span class="lineno"> 557</span> </div><div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="comment">// Does all the Dynamic Progamming iterations.</span></div><div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  <span class="keywordtype">void</span> Solve();</div><div class="line"><a name="l00560"></a><span class="lineno"> 560</span> </div><div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  <span class="comment">// Computes a path by looking at the information in mem_.</span></div><div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  std::vector<int> ComputePath(CostType <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>, <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a03106785fd757b213975f94d4b780709">NodeSet</a> set, <span class="keywordtype">int</span> end);</div><div class="line"><a name="l00563"></a><span class="lineno"> 563</span> </div><div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  <span class="comment">// Returns true if the path covers all nodes, and its cost is equal to cost.</span></div><div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="keywordtype">bool</span> PathIsValid(<span class="keyword">const</span> std::vector<int>& path, CostType <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>);</div><div class="line"><a name="l00566"></a><span class="lineno"> 566</span> </div><div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  <span class="comment">// Cost function used to build Hamiltonian paths.</span></div><div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  MatrixOrFunction<CostType, CostFunction, true> cost_;</div><div class="line"><a name="l00569"></a><span class="lineno"> 569</span> </div><div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  <span class="comment">// The number of nodes in the problem.</span></div><div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  <span class="keywordtype">int</span> num_nodes_;</div><div class="line"><a name="l00572"></a><span class="lineno"> 572</span> </div><div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  <span class="comment">// The cost of the computed TSP path.</span></div><div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  CostType tsp_cost_;</div><div class="line"><a name="l00575"></a><span class="lineno"> 575</span> </div><div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  <span class="comment">// The cost of the computed Hamiltonian path.</span></div><div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  std::vector<CostType> hamiltonian_costs_;</div><div class="line"><a name="l00578"></a><span class="lineno"> 578</span> </div><div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  <span class="keywordtype">bool</span> robust_;</div><div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  <span class="keywordtype">bool</span> triangle_inequality_ok_;</div><div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  <span class="keywordtype">bool</span> robustness_checked_;</div><div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  <span class="keywordtype">bool</span> triangle_inequality_checked_;</div><div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  <span class="keywordtype">bool</span> solved_;</div><div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  std::vector<int> tsp_path_;</div><div class="line"><a name="l00585"></a><span class="lineno"> 585</span> </div><div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  <span class="comment">// The vector of smallest Hamiltonian paths starting at 0, indexed by their</span></div><div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  <span class="comment">// end nodes.</span></div><div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  std::vector<std::vector<int>> hamiltonian_paths_;</div><div class="line"><a name="l00589"></a><span class="lineno"> 589</span> </div><div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  <span class="comment">// The end node that gives the smallest Hamiltonian path. The smallest</span></div><div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  <span class="comment">// Hamiltonian path starting at 0 of all</span></div><div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  <span class="comment">// is hamiltonian_paths_[best_hamiltonian_path_end_node_].</span></div><div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  <span class="keywordtype">int</span> best_hamiltonian_path_end_node_;</div><div class="line"><a name="l00594"></a><span class="lineno"> 594</span> </div><div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  LatticeMemoryManager<NodeSet, CostType> mem_;</div><div class="line"><a name="l00596"></a><span class="lineno"> 596</span> };</div><div class="line"><a name="l00597"></a><span class="lineno"> 597</span> </div><div class="line"><a name="l00598"></a><span class="lineno"> 598</span> <span class="comment">// Utility function to simplify building a HamiltonianPathSolver from a functor.</span></div><div class="line"><a name="l00599"></a><span class="lineno"> 599</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00600"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a715b0dbb9f0903ab629b8c6da1b35b45"> 600</a></span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction></a> <a class="code" href="namespaceoperations__research.html#a715b0dbb9f0903ab629b8c6da1b35b45">MakeHamiltonianPathSolver</a>(</div><div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  <span class="keywordtype">int</span> num_nodes, CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>) {</div><div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction></a>(num_nodes,</div><div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  std::move(<a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>));</div><div class="line"><a name="l00604"></a><span class="lineno"> 604</span> }</div><div class="line"><a name="l00605"></a><span class="lineno"> 605</span> </div><div class="line"><a name="l00606"></a><span class="lineno"> 606</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00607"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a9c8cdf78154ae6a73f4a272cb8d1ac4a"> 607</a></span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html#a9c8cdf78154ae6a73f4a272cb8d1ac4a">HamiltonianPathSolver<CostType, CostFunction>::HamiltonianPathSolver</a>(</div><div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>)</div><div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  : <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver</a><CostType, CostFunction>(<a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>.size(), <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>) {}</div><div class="line"><a name="l00610"></a><span class="lineno"> 610</span> </div><div class="line"><a name="l00611"></a><span class="lineno"> 611</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00612"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#acc36ec0dcfa554cf72acb4ddb64c066c"> 612</a></span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction>::HamiltonianPathSolver</a>(</div><div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  <span class="keywordtype">int</span> num_nodes, CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>)</div><div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  : cost_(std::move(<a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>)),</div><div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  num_nodes_(num_nodes),</div><div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  tsp_cost_(0),</div><div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  hamiltonian_costs_(0),</div><div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  robust_(true),</div><div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  triangle_inequality_ok_(true),</div><div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  robustness_checked_(false),</div><div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  triangle_inequality_checked_(false),</div><div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  solved_(false) {</div><div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  <a class="code" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(NodeSet::MaxCardinality, num_nodes_);</div><div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  <a class="code" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>(cost_.Check());</div><div class="line"><a name="l00625"></a><span class="lineno"> 625</span> }</div><div class="line"><a name="l00626"></a><span class="lineno"> 626</span> </div><div class="line"><a name="l00627"></a><span class="lineno"> 627</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00628"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a19edb994fca04e71736cf3a8d62d7a73"> 628</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction>::ChangeCostMatrix</a>(</div><div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>) {</div><div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  ChangeCostMatrix(<a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>.size(), <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>);</div><div class="line"><a name="l00631"></a><span class="lineno"> 631</span> }</div><div class="line"><a name="l00632"></a><span class="lineno"> 632</span> </div><div class="line"><a name="l00633"></a><span class="lineno"> 633</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00634"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a25f9e15b1f7c966c06f9a3e308d93436"> 634</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction>::ChangeCostMatrix</a>(</div><div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  <span class="keywordtype">int</span> num_nodes, CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>) {</div><div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  robustness_checked_ = <span class="keyword">false</span>;</div><div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  triangle_inequality_checked_ = <span class="keyword">false</span>;</div><div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  solved_ = <span class="keyword">false</span>;</div><div class="line"><a name="l00639"></a><span class="lineno"> 639</span>  cost_.Reset(<a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>);</div><div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  num_nodes_ = num_nodes;</div><div class="line"><a name="l00641"></a><span class="lineno"> 641</span>  <a class="code" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(NodeSet::MaxCardinality, num_nodes_);</div><div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  <a class="code" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>(cost_.Check());</div><div class="line"><a name="l00643"></a><span class="lineno"> 643</span> }</div><div class="line"><a name="l00644"></a><span class="lineno"> 644</span> </div><div class="line"><a name="l00645"></a><span class="lineno"> 645</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00646"></a><span class="lineno"> 646</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#af904018d9a1c9983624b1ce0331f2bf5">HamiltonianPathSolver<CostType, CostFunction>::Solve</a>() {</div><div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  <span class="keywordflow">if</span> (solved_) <span class="keywordflow">return</span>;</div><div class="line"><a name="l00648"></a><span class="lineno"> 648</span>  <span class="keywordflow">if</span> (num_nodes_ == 0) {</div><div class="line"><a name="l00649"></a><span class="lineno"> 649</span>  tsp_cost_ = 0;</div><div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  tsp_path_ = {0};</div><div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  hamiltonian_paths_.resize(1);</div><div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  hamiltonian_costs_.resize(1);</div><div class="line"><a name="l00653"></a><span class="lineno"> 653</span>  best_hamiltonian_path_end_node_ = 0;</div><div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  hamiltonian_costs_[0] = 0;</div><div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  hamiltonian_paths_[0] = {0};</div><div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  <span class="keywordflow">return</span>;</div><div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  }</div><div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  mem_.Init(num_nodes_);</div><div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  <span class="comment">// Initialize the first layer of the search lattice, taking into account</span></div><div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  <span class="comment">// that base_offset_[1] == 0. (This is what the DCHECK_EQ is for).</span></div><div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> dest = 0; dest < num_nodes_; ++dest) {</div><div class="line"><a name="l00662"></a><span class="lineno"> 662</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(dest, mem_.BaseOffset(1, NodeSet::Singleton(dest)));</div><div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  mem_.SetValueAtOffset(dest, Cost(0, dest));</div><div class="line"><a name="l00664"></a><span class="lineno"> 664</span>  }</div><div class="line"><a name="l00665"></a><span class="lineno"> 665</span> </div><div class="line"><a name="l00666"></a><span class="lineno"> 666</span>  <span class="comment">// Populate the dynamic programming lattice layer by layer, by iterating</span></div><div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  <span class="comment">// on cardinality.</span></div><div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> card = 2; card <= num_nodes_; ++card) {</div><div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  <span class="comment">// Iterate on sets of same cardinality.</span></div><div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  <span class="keywordflow">for</span> (NodeSet set :</div><div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  SetRangeWithCardinality<Set<uint32_t>>(card, num_nodes_)) {</div><div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  <span class="comment">// Using BaseOffset and maintaining the node ranks, to reduce the</span></div><div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  <span class="comment">// computational effort for accessing the data.</span></div><div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  <span class="keyword">const</span> uint64_t set_offset = mem_.BaseOffset(card, set);</div><div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  <span class="comment">// The first subset on which we'll iterate is set.RemoveSmallestElement().</span></div><div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  <span class="comment">// Compute its offset. It will be updated incrementaly. This saves about</span></div><div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  <span class="comment">// 30-35% of computation time.</span></div><div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  uint64_t subset_offset =</div><div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  mem_.BaseOffset(card - 1, set.RemoveSmallestElement());</div><div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  <span class="keywordtype">int</span> prev_dest = set.SmallestElement();</div><div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  <span class="keywordtype">int</span> dest_rank = 0;</div><div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> dest : set) {</div><div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  CostType min_cost = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits<CostType>::max</a>();</div><div class="line"><a name="l00684"></a><span class="lineno"> 684</span>  <span class="keyword">const</span> NodeSet subset = set.RemoveElement(dest);</div><div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  <span class="comment">// We compute the offset for subset from the preceding iteration</span></div><div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  <span class="comment">// by taking into account that prev_dest is now in subset, and</span></div><div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  <span class="comment">// that dest is now removed from subset.</span></div><div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  subset_offset += mem_.OffsetDelta(card - 1, prev_dest, dest, dest_rank);</div><div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  <span class="keywordtype">int</span> src_rank = 0;</div><div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> src : subset) {</div><div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  min_cost = <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(</div><div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  min_cost, Saturated<CostType>::Add(</div><div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  Cost(src, dest),</div><div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  mem_.ValueAtOffset(subset_offset + src_rank)));</div><div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  ++src_rank;</div><div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  }</div><div class="line"><a name="l00697"></a><span class="lineno"> 697</span>  prev_dest = dest;</div><div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  mem_.SetValueAtOffset(set_offset + dest_rank, min_cost);</div><div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  ++dest_rank;</div><div class="line"><a name="l00700"></a><span class="lineno"> 700</span>  }</div><div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  }</div><div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  }</div><div class="line"><a name="l00703"></a><span class="lineno"> 703</span> </div><div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  <span class="keyword">const</span> NodeSet full_set = NodeSet::FullSet(num_nodes_);</div><div class="line"><a name="l00705"></a><span class="lineno"> 705</span> </div><div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  <span class="comment">// Get the cost of the tsp from node 0. It is the path that leaves 0 and goes</span></div><div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  <span class="comment">// through all other nodes, and returns at 0, with minimal cost.</span></div><div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  tsp_cost_ = mem_.Value(full_set, 0);</div><div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  tsp_path_ = ComputePath(tsp_cost_, full_set, 0);</div><div class="line"><a name="l00710"></a><span class="lineno"> 710</span> </div><div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  hamiltonian_paths_.resize(num_nodes_);</div><div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  hamiltonian_costs_.resize(num_nodes_);</div><div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  <span class="comment">// Compute the cost of the Hamiltonian paths starting from node 0, going</span></div><div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  <span class="comment">// through all the other nodes, and ending at end_node. Compute the minimum</span></div><div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  <span class="comment">// one along the way.</span></div><div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  CostType min_hamiltonian_cost = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits<CostType>::max</a>();</div><div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  <span class="keyword">const</span> NodeSet hamiltonian_set = full_set.RemoveElement(0);</div><div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> end_node : hamiltonian_set) {</div><div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  <span class="keyword">const</span> CostType <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a> = mem_.Value(hamiltonian_set, end_node);</div><div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  hamiltonian_costs_[end_node] = <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>;</div><div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  <span class="keywordflow">if</span> (<a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a> <= min_hamiltonian_cost) {</div><div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  min_hamiltonian_cost = <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>;</div><div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  best_hamiltonian_path_end_node_ = end_node;</div><div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  }</div><div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  <a class="code" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(tsp_cost_, Saturated<CostType>::Add(<a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>, Cost(end_node, 0)));</div><div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  <span class="comment">// Get the Hamiltonian paths.</span></div><div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  hamiltonian_paths_[end_node] =</div><div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  ComputePath(hamiltonian_costs_[end_node], hamiltonian_set, end_node);</div><div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  }</div><div class="line"><a name="l00730"></a><span class="lineno"> 730</span> </div><div class="line"><a name="l00731"></a><span class="lineno"> 731</span>  solved_ = <span class="keyword">true</span>;</div><div class="line"><a name="l00732"></a><span class="lineno"> 732</span> }</div><div class="line"><a name="l00733"></a><span class="lineno"> 733</span> </div><div class="line"><a name="l00734"></a><span class="lineno"> 734</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00735"></a><span class="lineno"> 735</span> std::vector<int> HamiltonianPathSolver<CostType, CostFunction>::ComputePath(</div><div class="line"><a name="l00736"></a><span class="lineno"> 736</span>  CostType <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>, NodeSet set, <span class="keywordtype">int</span> end_node) {</div><div class="line"><a name="l00737"></a><span class="lineno"> 737</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(set.Contains(end_node));</div><div class="line"><a name="l00738"></a><span class="lineno"> 738</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> path_size = set.Cardinality() + 1;</div><div class="line"><a name="l00739"></a><span class="lineno"> 739</span>  std::vector<int> path(path_size, 0);</div><div class="line"><a name="l00740"></a><span class="lineno"> 740</span>  NodeSet subset = set.RemoveElement(end_node);</div><div class="line"><a name="l00741"></a><span class="lineno"> 741</span>  path[path_size - 1] = end_node;</div><div class="line"><a name="l00742"></a><span class="lineno"> 742</span>  <span class="keywordtype">int</span> dest = end_node;</div><div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  CostType current_cost = <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>;</div><div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> rank = path_size - 2; rank >= 0; --rank) {</div><div class="line"><a name="l00745"></a><span class="lineno"> 745</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> src : subset) {</div><div class="line"><a name="l00746"></a><span class="lineno"> 746</span>  <span class="keyword">const</span> CostType partial_cost = mem_.Value(subset, src);</div><div class="line"><a name="l00747"></a><span class="lineno"> 747</span>  <span class="keyword">const</span> CostType incumbent_cost =</div><div class="line"><a name="l00748"></a><span class="lineno"> 748</span>  Saturated<CostType>::Add(partial_cost, Cost(src, dest));</div><div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  <span class="comment">// Take precision into account when CosttType is float or double.</span></div><div class="line"><a name="l00750"></a><span class="lineno"> 750</span>  <span class="comment">// There is no visible penalty in the case CostType is an integer type.</span></div><div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  <span class="keywordflow">if</span> (std::abs(Saturated<CostType>::Sub(current_cost, incumbent_cost)) <=</div><div class="line"><a name="l00752"></a><span class="lineno"> 752</span>  std::numeric_limits<CostType>::epsilon() * current_cost) {</div><div class="line"><a name="l00753"></a><span class="lineno"> 753</span>  subset = subset.RemoveElement(src);</div><div class="line"><a name="l00754"></a><span class="lineno"> 754</span>  current_cost = partial_cost;</div><div class="line"><a name="l00755"></a><span class="lineno"> 755</span>  path[rank] = src;</div><div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  dest = src;</div><div class="line"><a name="l00757"></a><span class="lineno"> 757</span>  <span class="keywordflow">break</span>;</div><div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  }</div><div class="line"><a name="l00759"></a><span class="lineno"> 759</span>  }</div><div class="line"><a name="l00760"></a><span class="lineno"> 760</span>  }</div><div class="line"><a name="l00761"></a><span class="lineno"> 761</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(0, subset.value());</div><div class="line"><a name="l00762"></a><span class="lineno"> 762</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(PathIsValid(path, <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>));</div><div class="line"><a name="l00763"></a><span class="lineno"> 763</span>  <span class="keywordflow">return</span> path;</div><div class="line"><a name="l00764"></a><span class="lineno"> 764</span> }</div><div class="line"><a name="l00765"></a><span class="lineno"> 765</span> </div><div class="line"><a name="l00766"></a><span class="lineno"> 766</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00767"></a><span class="lineno"> 767</span> <span class="keywordtype">bool</span> HamiltonianPathSolver<CostType, CostFunction>::PathIsValid(</div><div class="line"><a name="l00768"></a><span class="lineno"> 768</span>  <span class="keyword">const</span> std::vector<int>& path, CostType <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>) {</div><div class="line"><a name="l00769"></a><span class="lineno"> 769</span>  NodeSet coverage(0);</div><div class="line"><a name="l00770"></a><span class="lineno"> 770</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> node : path) {</div><div class="line"><a name="l00771"></a><span class="lineno"> 771</span>  coverage = coverage.AddElement(node);</div><div class="line"><a name="l00772"></a><span class="lineno"> 772</span>  }</div><div class="line"><a name="l00773"></a><span class="lineno"> 773</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(NodeSet::FullSet(num_nodes_).<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>(), coverage.value());</div><div class="line"><a name="l00774"></a><span class="lineno"> 774</span>  CostType check_cost = 0;</div><div class="line"><a name="l00775"></a><span class="lineno"> 775</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < path.size() - 1; ++i) {</div><div class="line"><a name="l00776"></a><span class="lineno"> 776</span>  check_cost =</div><div class="line"><a name="l00777"></a><span class="lineno"> 777</span>  Saturated<CostType>::Add(check_cost, Cost(path[i], path[i + 1]));</div><div class="line"><a name="l00778"></a><span class="lineno"> 778</span>  }</div><div class="line"><a name="l00779"></a><span class="lineno"> 779</span>  <a class="code" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(std::abs(Saturated<CostType>::Sub(<a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>, check_cost)),</div><div class="line"><a name="l00780"></a><span class="lineno"> 780</span>  std::numeric_limits<CostType>::epsilon() * <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>)</div><div class="line"><a name="l00781"></a><span class="lineno"> 781</span>  << <span class="stringliteral">"cost = "</span> << <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a> << <span class="stringliteral">" check_cost = "</span> << check_cost;</div><div class="line"><a name="l00782"></a><span class="lineno"> 782</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00783"></a><span class="lineno"> 783</span> }</div><div class="line"><a name="l00784"></a><span class="lineno"> 784</span> </div><div class="line"><a name="l00785"></a><span class="lineno"> 785</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00786"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a5daed8b7f3c98c693f32dff60adeb4cc"> 786</a></span> <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction>::IsRobust</a>() {</div><div class="line"><a name="l00787"></a><span class="lineno"> 787</span>  <span class="keywordflow">if</span> (std::numeric_limits<CostType>::is_integer) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00788"></a><span class="lineno"> 788</span>  <span class="keywordflow">if</span> (robustness_checked_) <span class="keywordflow">return</span> robust_;</div><div class="line"><a name="l00789"></a><span class="lineno"> 789</span>  CostType min_cost = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits<CostType>::max</a>();</div><div class="line"><a name="l00790"></a><span class="lineno"> 790</span>  CostType max_cost = <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits<CostType>::min</a>();</div><div class="line"><a name="l00791"></a><span class="lineno"> 791</span> </div><div class="line"><a name="l00792"></a><span class="lineno"> 792</span>  <span class="comment">// We compute the min and max for the cost matrix.</span></div><div class="line"><a name="l00793"></a><span class="lineno"> 793</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_nodes_; ++i) {</div><div class="line"><a name="l00794"></a><span class="lineno"> 794</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < num_nodes_; ++j) {</div><div class="line"><a name="l00795"></a><span class="lineno"> 795</span>  <span class="keywordflow">if</span> (i == j) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00796"></a><span class="lineno"> 796</span>  min_cost = <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(min_cost, Cost(i, j));</div><div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  max_cost = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(max_cost, Cost(i, j));</div><div class="line"><a name="l00798"></a><span class="lineno"> 798</span>  }</div><div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  }</div><div class="line"><a name="l00800"></a><span class="lineno"> 800</span>  <span class="comment">// We determine if the range of the cost matrix is going to</span></div><div class="line"><a name="l00801"></a><span class="lineno"> 801</span>  <span class="comment">// make the algorithm not robust because of precision issues.</span></div><div class="line"><a name="l00802"></a><span class="lineno"> 802</span>  robust_ =</div><div class="line"><a name="l00803"></a><span class="lineno"> 803</span>  min_cost >= 0 && min_cost > num_nodes_ * max_cost *</div><div class="line"><a name="l00804"></a><span class="lineno"> 804</span>  std::numeric_limits<CostType>::epsilon();</div><div class="line"><a name="l00805"></a><span class="lineno"> 805</span>  robustness_checked_ = <span class="keyword">true</span>;</div><div class="line"><a name="l00806"></a><span class="lineno"> 806</span>  <span class="keywordflow">return</span> robust_;</div><div class="line"><a name="l00807"></a><span class="lineno"> 807</span> }</div><div class="line"><a name="l00808"></a><span class="lineno"> 808</span> </div><div class="line"><a name="l00809"></a><span class="lineno"> 809</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00810"></a><span class="lineno"> 810</span> <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver</a><CostType,</div><div class="line"><a name="l00811"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a44af6c2df0188e77ceeec78a190ecf3f"> 811</a></span>  CostFunction>::VerifiesTriangleInequality() {</div><div class="line"><a name="l00812"></a><span class="lineno"> 812</span>  <span class="keywordflow">if</span> (triangle_inequality_checked_) <span class="keywordflow">return</span> triangle_inequality_ok_;</div><div class="line"><a name="l00813"></a><span class="lineno"> 813</span>  triangle_inequality_ok_ = <span class="keyword">true</span>;</div><div class="line"><a name="l00814"></a><span class="lineno"> 814</span>  triangle_inequality_checked_ = <span class="keyword">true</span>;</div><div class="line"><a name="l00815"></a><span class="lineno"> 815</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < num_nodes_; ++k) {</div><div class="line"><a name="l00816"></a><span class="lineno"> 816</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_nodes_; ++i) {</div><div class="line"><a name="l00817"></a><span class="lineno"> 817</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < num_nodes_; ++j) {</div><div class="line"><a name="l00818"></a><span class="lineno"> 818</span>  <span class="keyword">const</span> CostType detour_cost =</div><div class="line"><a name="l00819"></a><span class="lineno"> 819</span>  Saturated<CostType>::Add(Cost(i, k), Cost(k, j));</div><div class="line"><a name="l00820"></a><span class="lineno"> 820</span>  <span class="keywordflow">if</span> (detour_cost < Cost(i, j)) {</div><div class="line"><a name="l00821"></a><span class="lineno"> 821</span>  triangle_inequality_ok_ = <span class="keyword">false</span>;</div><div class="line"><a name="l00822"></a><span class="lineno"> 822</span>  <span class="keywordflow">return</span> triangle_inequality_ok_;</div><div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  }</div><div class="line"><a name="l00824"></a><span class="lineno"> 824</span>  }</div><div class="line"><a name="l00825"></a><span class="lineno"> 825</span>  }</div><div class="line"><a name="l00826"></a><span class="lineno"> 826</span>  }</div><div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  <span class="keywordflow">return</span> triangle_inequality_ok_;</div><div class="line"><a name="l00828"></a><span class="lineno"> 828</span> }</div><div class="line"><a name="l00829"></a><span class="lineno"> 829</span> </div><div class="line"><a name="l00830"></a><span class="lineno"> 830</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00831"></a><span class="lineno"> 831</span> <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver</a><CostType,</div><div class="line"><a name="l00832"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#ad20cbbfc6081d40231920c3c9543f97e"> 832</a></span>  CostFunction>::BestHamiltonianPathEndNode() {</div><div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  <a class="code" href="namespaceoperations__research_1_1sat.html#af904018d9a1c9983624b1ce0331f2bf5">Solve</a>();</div><div class="line"><a name="l00834"></a><span class="lineno"> 834</span>  <span class="keywordflow">return</span> best_hamiltonian_path_end_node_;</div><div class="line"><a name="l00835"></a><span class="lineno"> 835</span> }</div><div class="line"><a name="l00836"></a><span class="lineno"> 836</span> </div><div class="line"><a name="l00837"></a><span class="lineno"> 837</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00838"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a0b31a8637cf8c0fb125444577e6ad92b"> 838</a></span> CostType <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction>::HamiltonianCost</a>(</div><div class="line"><a name="l00839"></a><span class="lineno"> 839</span>  <span class="keywordtype">int</span> end_node) {</div><div class="line"><a name="l00840"></a><span class="lineno"> 840</span>  <a class="code" href="namespaceoperations__research_1_1sat.html#af904018d9a1c9983624b1ce0331f2bf5">Solve</a>();</div><div class="line"><a name="l00841"></a><span class="lineno"> 841</span>  <span class="keywordflow">return</span> hamiltonian_costs_[end_node];</div><div class="line"><a name="l00842"></a><span class="lineno"> 842</span> }</div><div class="line"><a name="l00843"></a><span class="lineno"> 843</span> </div><div class="line"><a name="l00844"></a><span class="lineno"> 844</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00845"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a8acc60c87190fac89379315aa08ce7a5"> 845</a></span> std::vector<int> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction>::HamiltonianPath</a>(</div><div class="line"><a name="l00846"></a><span class="lineno"> 846</span>  <span class="keywordtype">int</span> end_node) {</div><div class="line"><a name="l00847"></a><span class="lineno"> 847</span>  <a class="code" href="namespaceoperations__research_1_1sat.html#af904018d9a1c9983624b1ce0331f2bf5">Solve</a>();</div><div class="line"><a name="l00848"></a><span class="lineno"> 848</span>  <span class="keywordflow">return</span> hamiltonian_paths_[end_node];</div><div class="line"><a name="l00849"></a><span class="lineno"> 849</span> }</div><div class="line"><a name="l00850"></a><span class="lineno"> 850</span> </div><div class="line"><a name="l00851"></a><span class="lineno"> 851</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00852"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a971732356f9acd6f4806e12ef8bddfb0"> 852</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction>::HamiltonianPath</a>(</div><div class="line"><a name="l00853"></a><span class="lineno"> 853</span>  std::vector<PathNodeIndex>* path) {</div><div class="line"><a name="l00854"></a><span class="lineno"> 854</span>  *path = HamiltonianPath(best_hamiltonian_path_end_node_);</div><div class="line"><a name="l00855"></a><span class="lineno"> 855</span> }</div><div class="line"><a name="l00856"></a><span class="lineno"> 856</span> </div><div class="line"><a name="l00857"></a><span class="lineno"> 857</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00858"></a><span class="lineno"> 858</span> CostType</div><div class="line"><a name="l00859"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#ab558649a26fef3a74f0909ef5af45e90"> 859</a></span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction>::TravelingSalesmanCost</a>() {</div><div class="line"><a name="l00860"></a><span class="lineno"> 860</span>  <a class="code" href="namespaceoperations__research_1_1sat.html#af904018d9a1c9983624b1ce0331f2bf5">Solve</a>();</div><div class="line"><a name="l00861"></a><span class="lineno"> 861</span>  <span class="keywordflow">return</span> tsp_cost_;</div><div class="line"><a name="l00862"></a><span class="lineno"> 862</span> }</div><div class="line"><a name="l00863"></a><span class="lineno"> 863</span> </div><div class="line"><a name="l00864"></a><span class="lineno"> 864</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00865"></a><span class="lineno"> 865</span> std::vector<int></div><div class="line"><a name="l00866"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a326a998ed18bedda49bd2cab5cbd4079"> 866</a></span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction>::TravelingSalesmanPath</a>() {</div><div class="line"><a name="l00867"></a><span class="lineno"> 867</span>  <a class="code" href="namespaceoperations__research_1_1sat.html#af904018d9a1c9983624b1ce0331f2bf5">Solve</a>();</div><div class="line"><a name="l00868"></a><span class="lineno"> 868</span>  <span class="keywordflow">return</span> tsp_path_;</div><div class="line"><a name="l00869"></a><span class="lineno"> 869</span> }</div><div class="line"><a name="l00870"></a><span class="lineno"> 870</span> </div><div class="line"><a name="l00871"></a><span class="lineno"> 871</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00872"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_hamiltonian_path_solver.html#a30e8f070c957fed7c7bf2ebcc5c338b8"> 872</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_hamiltonian_path_solver.html">HamiltonianPathSolver<CostType, CostFunction>::TravelingSalesmanPath</a>(</div><div class="line"><a name="l00873"></a><span class="lineno"> 873</span>  std::vector<PathNodeIndex>* path) {</div><div class="line"><a name="l00874"></a><span class="lineno"> 874</span>  *path = TravelingSalesmanPath();</div><div class="line"><a name="l00875"></a><span class="lineno"> 875</span> }</div><div class="line"><a name="l00876"></a><span class="lineno"> 876</span> </div><div class="line"><a name="l00877"></a><span class="lineno"> 877</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00878"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_pruning_hamiltonian_solver.html"> 878</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html">PruningHamiltonianSolver</a> {</div><div class="line"><a name="l00879"></a><span class="lineno"> 879</span>  <span class="comment">// PruningHamiltonianSolver computes a minimum Hamiltonian path from node 0</span></div><div class="line"><a name="l00880"></a><span class="lineno"> 880</span>  <span class="comment">// over a graph defined by a cost matrix, with pruning. For each search state,</span></div><div class="line"><a name="l00881"></a><span class="lineno"> 881</span>  <span class="comment">// PruningHamiltonianSolver computes the lower bound for the future overall</span></div><div class="line"><a name="l00882"></a><span class="lineno"> 882</span>  <span class="comment">// TSP cost, and stops further search if it exceeds the current best solution.</span></div><div class="line"><a name="l00883"></a><span class="lineno"> 883</span> </div><div class="line"><a name="l00884"></a><span class="lineno"> 884</span>  <span class="comment">// For the heuristics to determine future lower bound over visited nodeset S</span></div><div class="line"><a name="l00885"></a><span class="lineno"> 885</span>  <span class="comment">// and last visited node k, the cost of minimum spanning tree of (V \ S) ∪ {k}</span></div><div class="line"><a name="l00886"></a><span class="lineno"> 886</span>  <span class="comment">// is calculated and added to the current cost(S). The cost of MST is</span></div><div class="line"><a name="l00887"></a><span class="lineno"> 887</span>  <span class="comment">// guaranteed to be smaller than or equal to the cost of Hamiltonian path,</span></div><div class="line"><a name="l00888"></a><span class="lineno"> 888</span>  <span class="comment">// because Hamiltonian path is a spanning tree itself.</span></div><div class="line"><a name="l00889"></a><span class="lineno"> 889</span> </div><div class="line"><a name="l00890"></a><span class="lineno"> 890</span>  <span class="comment">// TODO(user): Use generic map-based cache instead of lattice-based one.</span></div><div class="line"><a name="l00891"></a><span class="lineno"> 891</span>  <span class="comment">// TODO(user): Use SaturatedArithmetic for better precision.</span></div><div class="line"><a name="l00892"></a><span class="lineno"> 892</span> </div><div class="line"><a name="l00893"></a><span class="lineno"> 893</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00894"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a346635bd62f6d557d98e490ff2f3f306"> 894</a></span>  <span class="keyword">typedef</span> uint32_t <a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a346635bd62f6d557d98e490ff2f3f306">Integer</a>;</div><div class="line"><a name="l00895"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a03106785fd757b213975f94d4b780709"> 895</a></span>  <span class="keyword">typedef</span> <a class="code" href="classoperations__research_1_1_set.html">Set<Integer></a> <a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a03106785fd757b213975f94d4b780709">NodeSet</a>;</div><div class="line"><a name="l00896"></a><span class="lineno"> 896</span> </div><div class="line"><a name="l00897"></a><span class="lineno"> 897</span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html">PruningHamiltonianSolver</a>(CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>);</div><div class="line"><a name="l00898"></a><span class="lineno"> 898</span>  <a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html">PruningHamiltonianSolver</a>(<span class="keywordtype">int</span> num_nodes, CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>);</div><div class="line"><a name="l00899"></a><span class="lineno"> 899</span> </div><div class="line"><a name="l00900"></a><span class="lineno"> 900</span>  <span class="comment">// Returns the cost of the Hamiltonian path from 0 to end_node.</span></div><div class="line"><a name="l00901"></a><span class="lineno"> 901</span>  CostType HamiltonianCost(<span class="keywordtype">int</span> end_node);</div><div class="line"><a name="l00902"></a><span class="lineno"> 902</span> </div><div class="line"><a name="l00903"></a><span class="lineno"> 903</span>  <span class="comment">// TODO(user): Add function to return an actual path.</span></div><div class="line"><a name="l00904"></a><span class="lineno"> 904</span>  <span class="comment">// TODO(user): Add functions for Hamiltonian cycle.</span></div><div class="line"><a name="l00905"></a><span class="lineno"> 905</span> </div><div class="line"><a name="l00906"></a><span class="lineno"> 906</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00907"></a><span class="lineno"> 907</span>  <span class="comment">// Returns the cost value between two nodes.</span></div><div class="line"><a name="l00908"></a><span class="lineno"> 908</span>  CostType Cost(<span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j) { <span class="keywordflow">return</span> cost_(i, j); }</div><div class="line"><a name="l00909"></a><span class="lineno"> 909</span> </div><div class="line"><a name="l00910"></a><span class="lineno"> 910</span>  <span class="comment">// Solve and get TSP cost.</span></div><div class="line"><a name="l00911"></a><span class="lineno"> 911</span>  <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#af904018d9a1c9983624b1ce0331f2bf5">Solve</a>(<span class="keywordtype">int</span> end_node);</div><div class="line"><a name="l00912"></a><span class="lineno"> 912</span> </div><div class="line"><a name="l00913"></a><span class="lineno"> 913</span>  <span class="comment">// Compute lower bound for remaining subgraph.</span></div><div class="line"><a name="l00914"></a><span class="lineno"> 914</span>  CostType ComputeFutureLowerBound(NodeSet current_set, <span class="keywordtype">int</span> last_visited);</div><div class="line"><a name="l00915"></a><span class="lineno"> 915</span> </div><div class="line"><a name="l00916"></a><span class="lineno"> 916</span>  <span class="comment">// Cost function used to build Hamiltonian paths.</span></div><div class="line"><a name="l00917"></a><span class="lineno"> 917</span>  <a class="code" href="classoperations__research_1_1_matrix_or_function.html">MatrixOrFunction<CostType, CostFunction, true></a> cost_;</div><div class="line"><a name="l00918"></a><span class="lineno"> 918</span> </div><div class="line"><a name="l00919"></a><span class="lineno"> 919</span>  <span class="comment">// The number of nodes in the problem.</span></div><div class="line"><a name="l00920"></a><span class="lineno"> 920</span>  <span class="keywordtype">int</span> num_nodes_;</div><div class="line"><a name="l00921"></a><span class="lineno"> 921</span> </div><div class="line"><a name="l00922"></a><span class="lineno"> 922</span>  <span class="comment">// The cost of the computed TSP path.</span></div><div class="line"><a name="l00923"></a><span class="lineno"> 923</span>  CostType tsp_cost_;</div><div class="line"><a name="l00924"></a><span class="lineno"> 924</span> </div><div class="line"><a name="l00925"></a><span class="lineno"> 925</span>  <span class="comment">// If already solved.</span></div><div class="line"><a name="l00926"></a><span class="lineno"> 926</span>  <span class="keywordtype">bool</span> solved_;</div><div class="line"><a name="l00927"></a><span class="lineno"> 927</span> </div><div class="line"><a name="l00928"></a><span class="lineno"> 928</span>  <span class="comment">// Memoize for dynamic programming.</span></div><div class="line"><a name="l00929"></a><span class="lineno"> 929</span>  <a class="code" href="classoperations__research_1_1_lattice_memory_manager.html">LatticeMemoryManager<NodeSet, CostType></a> mem_;</div><div class="line"><a name="l00930"></a><span class="lineno"> 930</span> };</div><div class="line"><a name="l00931"></a><span class="lineno"> 931</span> </div><div class="line"><a name="l00932"></a><span class="lineno"> 932</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00933"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a4772bfe5f78a696373e531ba983bc695"> 933</a></span> <a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html">PruningHamiltonianSolver<CostType, CostFunction>::PruningHamiltonianSolver</a>(</div><div class="line"><a name="l00934"></a><span class="lineno"> 934</span>  CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>)</div><div class="line"><a name="l00935"></a><span class="lineno"> 935</span>  : <a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html">PruningHamiltonianSolver</a><CostType, CostFunction>(<a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>.size(), <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>) {}</div><div class="line"><a name="l00936"></a><span class="lineno"> 936</span> </div><div class="line"><a name="l00937"></a><span class="lineno"> 937</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00938"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a5834452c9889879749638cdb31869678"> 938</a></span> <a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a4772bfe5f78a696373e531ba983bc695">PruningHamiltonianSolver<CostType, CostFunction>::PruningHamiltonianSolver</a>(</div><div class="line"><a name="l00939"></a><span class="lineno"> 939</span>  <span class="keywordtype">int</span> num_nodes, CostFunction <a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>)</div><div class="line"><a name="l00940"></a><span class="lineno"> 940</span>  : cost_(std::move(<a class="code" href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a>)),</div><div class="line"><a name="l00941"></a><span class="lineno"> 941</span>  num_nodes_(num_nodes),</div><div class="line"><a name="l00942"></a><span class="lineno"> 942</span>  tsp_cost_(0),</div><div class="line"><a name="l00943"></a><span class="lineno"> 943</span>  solved_(false) {}</div><div class="line"><a name="l00944"></a><span class="lineno"> 944</span> </div><div class="line"><a name="l00945"></a><span class="lineno"> 945</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l00946"></a><span class="lineno"> 946</span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html">PruningHamiltonianSolver<CostType, CostFunction>::Solve</a>(<span class="keywordtype">int</span> end_node) {</div><div class="line"><a name="l00947"></a><span class="lineno"> 947</span>  <span class="keywordflow">if</span> (solved_ || num_nodes_ == 0) <span class="keywordflow">return</span>;</div><div class="line"><a name="l00948"></a><span class="lineno"> 948</span>  <span class="comment">// TODO(user): Use an approximate solution as a base target before solving.</span></div><div class="line"><a name="l00949"></a><span class="lineno"> 949</span> </div><div class="line"><a name="l00950"></a><span class="lineno"> 950</span>  <span class="comment">// TODO(user): Instead of pure DFS, find out the order of sets to compute</span></div><div class="line"><a name="l00951"></a><span class="lineno"> 951</span>  <span class="comment">// to utilize cache as possible.</span></div><div class="line"><a name="l00952"></a><span class="lineno"> 952</span> </div><div class="line"><a name="l00953"></a><span class="lineno"> 953</span>  mem_.Init(num_nodes_);</div><div class="line"><a name="l00954"></a><span class="lineno"> 954</span>  NodeSet start_set = NodeSet::Singleton(0);</div><div class="line"><a name="l00955"></a><span class="lineno"> 955</span>  std::stack<std::pair<NodeSet, int>> state_stack;</div><div class="line"><a name="l00956"></a><span class="lineno"> 956</span>  state_stack.push(std::make_pair(start_set, 0));</div><div class="line"><a name="l00957"></a><span class="lineno"> 957</span> </div><div class="line"><a name="l00958"></a><span class="lineno"> 958</span>  <span class="keywordflow">while</span> (!state_stack.empty()) {</div><div class="line"><a name="l00959"></a><span class="lineno"> 959</span>  <span class="keyword">const</span> std::pair<NodeSet, int> current = state_stack.top();</div><div class="line"><a name="l00960"></a><span class="lineno"> 960</span>  state_stack.pop();</div><div class="line"><a name="l00961"></a><span class="lineno"> 961</span> </div><div class="line"><a name="l00962"></a><span class="lineno"> 962</span>  <span class="keyword">const</span> NodeSet current_set = current.first;</div><div class="line"><a name="l00963"></a><span class="lineno"> 963</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> last_visited = current.second;</div><div class="line"><a name="l00964"></a><span class="lineno"> 964</span>  <span class="keyword">const</span> CostType current_cost = mem_.Value(current_set, last_visited);</div><div class="line"><a name="l00965"></a><span class="lineno"> 965</span> </div><div class="line"><a name="l00966"></a><span class="lineno"> 966</span>  <span class="comment">// TODO(user): Optimize iterating unvisited nodes.</span></div><div class="line"><a name="l00967"></a><span class="lineno"> 967</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> next_to_visit = 0; next_to_visit < num_nodes_; next_to_visit++) {</div><div class="line"><a name="l00968"></a><span class="lineno"> 968</span>  <span class="comment">// Let's to as much check possible before adding to stack.</span></div><div class="line"><a name="l00969"></a><span class="lineno"> 969</span> </div><div class="line"><a name="l00970"></a><span class="lineno"> 970</span>  <span class="comment">// Skip if this node is already visited.</span></div><div class="line"><a name="l00971"></a><span class="lineno"> 971</span>  <span class="keywordflow">if</span> (current_set.Contains(next_to_visit)) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00972"></a><span class="lineno"> 972</span> </div><div class="line"><a name="l00973"></a><span class="lineno"> 973</span>  <span class="comment">// Skip if the end node is prematurely visited.</span></div><div class="line"><a name="l00974"></a><span class="lineno"> 974</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> next_cardinality = current_set.Cardinality() + 1;</div><div class="line"><a name="l00975"></a><span class="lineno"> 975</span>  <span class="keywordflow">if</span> (next_to_visit == end_node && next_cardinality != num_nodes_) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00976"></a><span class="lineno"> 976</span> </div><div class="line"><a name="l00977"></a><span class="lineno"> 977</span>  <span class="keyword">const</span> NodeSet next_set = current_set.AddElement(next_to_visit);</div><div class="line"><a name="l00978"></a><span class="lineno"> 978</span>  <span class="keyword">const</span> CostType next_cost =</div><div class="line"><a name="l00979"></a><span class="lineno"> 979</span>  current_cost + Cost(last_visited, next_to_visit);</div><div class="line"><a name="l00980"></a><span class="lineno"> 980</span> </div><div class="line"><a name="l00981"></a><span class="lineno"> 981</span>  <span class="comment">// Compare with the best cost found so far, and skip if that is better.</span></div><div class="line"><a name="l00982"></a><span class="lineno"> 982</span>  <span class="keyword">const</span> CostType previous_best = mem_.Value(next_set, next_to_visit);</div><div class="line"><a name="l00983"></a><span class="lineno"> 983</span>  <span class="keywordflow">if</span> (previous_best != 0 && next_cost >= previous_best) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00984"></a><span class="lineno"> 984</span> </div><div class="line"><a name="l00985"></a><span class="lineno"> 985</span>  <span class="comment">// Compute lower bound of Hamiltonian cost, and skip if this is greater</span></div><div class="line"><a name="l00986"></a><span class="lineno"> 986</span>  <span class="comment">// than the best Hamiltonian cost found so far.</span></div><div class="line"><a name="l00987"></a><span class="lineno"> 987</span>  <span class="keyword">const</span> CostType <a class="code" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a> =</div><div class="line"><a name="l00988"></a><span class="lineno"> 988</span>  ComputeFutureLowerBound(next_set, next_to_visit);</div><div class="line"><a name="l00989"></a><span class="lineno"> 989</span>  <span class="keywordflow">if</span> (tsp_cost_ != 0 && next_cost + <a class="code" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a> >= tsp_cost_) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00990"></a><span class="lineno"> 990</span> </div><div class="line"><a name="l00991"></a><span class="lineno"> 991</span>  <span class="comment">// If next is the last node to visit, update tsp_cost_ and skip.</span></div><div class="line"><a name="l00992"></a><span class="lineno"> 992</span>  <span class="keywordflow">if</span> (next_cardinality == num_nodes_) {</div><div class="line"><a name="l00993"></a><span class="lineno"> 993</span>  tsp_cost_ = next_cost;</div><div class="line"><a name="l00994"></a><span class="lineno"> 994</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00995"></a><span class="lineno"> 995</span>  }</div><div class="line"><a name="l00996"></a><span class="lineno"> 996</span> </div><div class="line"><a name="l00997"></a><span class="lineno"> 997</span>  <span class="comment">// Add to the stack, finally.</span></div><div class="line"><a name="l00998"></a><span class="lineno"> 998</span>  mem_.SetValue(next_set, next_to_visit, next_cost);</div><div class="line"><a name="l00999"></a><span class="lineno"> 999</span>  state_stack.push(std::make_pair(next_set, next_to_visit));</div><div class="line"><a name="l01000"></a><span class="lineno"> 1000</span>  }</div><div class="line"><a name="l01001"></a><span class="lineno"> 1001</span>  }</div><div class="line"><a name="l01002"></a><span class="lineno"> 1002</span> </div><div class="line"><a name="l01003"></a><span class="lineno"> 1003</span>  solved_ = <span class="keyword">true</span>;</div><div class="line"><a name="l01004"></a><span class="lineno"> 1004</span> }</div><div class="line"><a name="l01005"></a><span class="lineno"> 1005</span> </div><div class="line"><a name="l01006"></a><span class="lineno"> 1006</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l01007"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a0b31a8637cf8c0fb125444577e6ad92b"> 1007</a></span> CostType <a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a0b31a8637cf8c0fb125444577e6ad92b">PruningHamiltonianSolver<CostType, CostFunction>::HamiltonianCost</a>(</div><div class="line"><a name="l01008"></a><span class="lineno"> 1008</span>  <span class="keywordtype">int</span> end_node) {</div><div class="line"><a name="l01009"></a><span class="lineno"> 1009</span>  <a class="code" href="namespaceoperations__research_1_1sat.html#af904018d9a1c9983624b1ce0331f2bf5">Solve</a>(end_node);</div><div class="line"><a name="l01010"></a><span class="lineno"> 1010</span>  <span class="keywordflow">return</span> tsp_cost_;</div><div class="line"><a name="l01011"></a><span class="lineno"> 1011</span> }</div><div class="line"><a name="l01012"></a><span class="lineno"> 1012</span> </div><div class="line"><a name="l01013"></a><span class="lineno"> 1013</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CostType, <span class="keyword">typename</span> CostFunction></div><div class="line"><a name="l01014"></a><span class="lineno"> 1014</span> CostType</div><div class="line"><a name="l01015"></a><span class="lineno"> 1015</span> <a class="code" href="classoperations__research_1_1_pruning_hamiltonian_solver.html">PruningHamiltonianSolver<CostType, CostFunction>::ComputeFutureLowerBound</a>(</div><div class="line"><a name="l01016"></a><span class="lineno"> 1016</span>  NodeSet current_set, <span class="keywordtype">int</span> last_visited) {</div><div class="line"><a name="l01017"></a><span class="lineno"> 1017</span>  <span class="comment">// TODO(user): Compute MST.</span></div><div class="line"><a name="l01018"></a><span class="lineno"> 1018</span>  <span class="keywordflow">return</span> 0; <span class="comment">// For now, return 0 as future lower bound.</span></div><div class="line"><a name="l01019"></a><span class="lineno"> 1019</span> }</div><div class="line"><a name="l01020"></a><span class="lineno"> 1020</span> } <span class="comment">// namespace operations_research</span></div><div class="line"><a name="l01021"></a><span class="lineno"> 1021</span> </div><div class="line"><a name="l01022"></a><span class="lineno"> 1022</span> <span class="preprocessor">#endif // OR_TOOLS_GRAPH_HAMILTONIAN_PATH_H_</span></div><div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html_a19edb994fca04e71736cf3a8d62d7a73"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html#a19edb994fca04e71736cf3a8d62d7a73">operations_research::HamiltonianPathSolver::ChangeCostMatrix</a></div><div class="ttdeci">void ChangeCostMatrix(CostFunction cost)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00628">hamiltonian_path.h:628</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_lattice_memory_manager_html_a91814684a688a3264fc8f29972969d61"><div class="ttname"><a href="classoperations__research_1_1_lattice_memory_manager.html#a91814684a688a3264fc8f29972969d61">operations_research::LatticeMemoryManager::SetValueAtOffset</a></div><div class="ttdeci">void SetValueAtOffset(uint64_t offset, CostType value)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00324">hamiltonian_path.h:324</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_a3e1cfef60e774a81f30eaddf26a3a274"><div class="ttname"><a href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a></div><div class="ttdeci">#define CHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00495">base/logging.h:495</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a4a43d435871f16c321861fa5de32df82"><div class="ttname"><a href="namespaceoperations__research.html#a4a43d435871f16c321861fa5de32df82">operations_research::CapSub</a></div><div class="ttdeci">int64_t CapSub(int64_t x, int64_t y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00158">saturated_arithmetic.h:158</a></div></div>
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<div class="ttc" id="alldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_a7cc25402ecd7591b4c39934dd656b1f9"><div class="ttname"><a href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a></div><div class="ttdeci">#define CHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00706">base/logging.h:706</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_range_iterator_html_ad82623d8471ab5eb30f4e19bc89796b9"><div class="ttname"><a href="classoperations__research_1_1_set_range_iterator.html#ad82623d8471ab5eb30f4e19bc89796b9">operations_research::SetRangeIterator::SetRangeIterator</a></div><div class="ttdeci">SetRangeIterator(const SetType set)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00230">hamiltonian_path.h:230</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_afe05ca596cfc024da65cf61a79812a2f"><div class="ttname"><a href="classoperations__research_1_1_set.html#afe05ca596cfc024da65cf61a79812a2f">operations_research::Set::AddElement</a></div><div class="ttdeci">Set AddElement(int n) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00156">hamiltonian_path.h:156</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html_a0b31a8637cf8c0fb125444577e6ad92b"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html#a0b31a8637cf8c0fb125444577e6ad92b">operations_research::HamiltonianPathSolver::HamiltonianCost</a></div><div class="ttdeci">CostType HamiltonianCost(int end_node)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00838">hamiltonian_path.h:838</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_lattice_memory_manager_html_afc715a6711310680640765eb66822f8b"><div class="ttname"><a href="classoperations__research_1_1_lattice_memory_manager.html#afc715a6711310680640765eb66822f8b">operations_research::LatticeMemoryManager::ValueAtOffset</a></div><div class="ttdeci">CostType ValueAtOffset(uint64_t offset) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00334">hamiltonian_path.h:334</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_abb2b3831b27fd81d60fb39ad01e108a3"><div class="ttname"><a href="classoperations__research_1_1_set.html#abb2b3831b27fd81d60fb39ad01e108a3">operations_research::Set::SmallestElement</a></div><div class="ttdeci">int SmallestElement() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00176">hamiltonian_path.h:176</a></div></div>
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||
<div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html_ad20cbbfc6081d40231920c3c9543f97e"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html#ad20cbbfc6081d40231920c3c9543f97e">operations_research::HamiltonianPathSolver::BestHamiltonianPathEndNode</a></div><div class="ttdeci">int BestHamiltonianPathEndNode()</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00832">hamiltonian_path.h:832</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a715b0dbb9f0903ab629b8c6da1b35b45"><div class="ttname"><a href="namespaceoperations__research.html#a715b0dbb9f0903ab629b8c6da1b35b45">operations_research::MakeHamiltonianPathSolver</a></div><div class="ttdeci">HamiltonianPathSolver< CostType, CostFunction > MakeHamiltonianPathSolver(int num_nodes, CostFunction cost)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00600">hamiltonian_path.h:600</a></div></div>
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||
<div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html">operations_research::HamiltonianPathSolver</a></div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00454">hamiltonian_path.h:454</a></div></div>
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||
<div class="ttc" id="classoperations__research_1_1_set_html_a67d03a6e5178376e21bdfa720680e447"><div class="ttname"><a href="classoperations__research_1_1_set.html#a67d03a6e5178376e21bdfa720680e447">operations_research::Set::end</a></div><div class="ttdeci">ElementIterator< Set > end() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00202">hamiltonian_path.h:202</a></div></div>
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||
<div class="ttc" id="classoperations__research_1_1_set_range_iterator_html_a0e4b89b4bb1b1a5bb3c799938380aeb0"><div class="ttname"><a href="classoperations__research_1_1_set_range_iterator.html#a0e4b89b4bb1b1a5bb3c799938380aeb0">operations_research::SetRangeIterator::SetType</a></div><div class="ttdeci">SetRange::SetType SetType</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00227">hamiltonian_path.h:227</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_pruning_hamiltonian_solver_html_a4772bfe5f78a696373e531ba983bc695"><div class="ttname"><a href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a4772bfe5f78a696373e531ba983bc695">operations_research::PruningHamiltonianSolver::PruningHamiltonianSolver</a></div><div class="ttdeci">PruningHamiltonianSolver(CostFunction cost)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00933">hamiltonian_path.h:933</a></div></div>
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||
<div class="ttc" id="classoperations__research_1_1_lattice_memory_manager_html_a1958048f654b22c744e32dfbcdbeb416"><div class="ttname"><a href="classoperations__research_1_1_lattice_memory_manager.html#a1958048f654b22c744e32dfbcdbeb416">operations_research::LatticeMemoryManager::Offset</a></div><div class="ttdeci">uint64_t Offset(Set s, int node) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00432">hamiltonian_path.h:432</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_lattice_memory_manager_html_aab77eae51a0b3e7781df913213ff4372"><div class="ttname"><a href="classoperations__research_1_1_lattice_memory_manager.html#aab77eae51a0b3e7781df913213ff4372">operations_research::LatticeMemoryManager::Value</a></div><div class="ttdeci">CostType Value(Set s, int node) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00438">hamiltonian_path.h:438</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1sat_html_af904018d9a1c9983624b1ce0331f2bf5"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#af904018d9a1c9983624b1ce0331f2bf5">operations_research::sat::Solve</a></div><div class="ttdeci">CpSolverResponse Solve(const CpModelProto &model_proto)</div><div class="ttdoc">Solves the given CpModelProto and returns an instance of CpSolverResponse.</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__solver_8cc_source.html#l03470">cp_model_solver.cc:3470</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html_a346635bd62f6d557d98e490ff2f3f306"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html#a346635bd62f6d557d98e490ff2f3f306">operations_research::HamiltonianPathSolver::Integer</a></div><div class="ttdeci">uint32_t Integer</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00476">hamiltonian_path.h:476</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_element_iterator_html_a6eb44ef439441ada8ffaaf6ee33a9c40"><div class="ttname"><a href="classoperations__research_1_1_element_iterator.html#a6eb44ef439441ada8ffaaf6ee33a9c40">operations_research::ElementIterator::operator++</a></div><div class="ttdeci">const ElementIterator & operator++()</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00116">hamiltonian_path.h:116</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_a450e5cf964a0b2c866641c8f4e4b3361"><div class="ttname"><a href="classoperations__research_1_1_set.html#a450e5cf964a0b2c866641c8f4e4b3361">operations_research::Set::Set</a></div><div class="ttdeci">Set(Integer n)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00139">hamiltonian_path.h:139</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_lattice_memory_manager_html"><div class="ttname"><a href="classoperations__research_1_1_lattice_memory_manager.html">operations_research::LatticeMemoryManager</a></div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00292">hamiltonian_path.h:292</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_a879ebf910431019a01f98d0865749c8d"><div class="ttname"><a href="classoperations__research_1_1_set.html#a879ebf910431019a01f98d0865749c8d">operations_research::Set::Cardinality</a></div><div class="ttdeci">int Cardinality() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00172">hamiltonian_path.h:172</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_a983cf4555b2577512febcc3aa327a3c8"><div class="ttname"><a href="classoperations__research_1_1_set.html#a983cf4555b2577512febcc3aa327a3c8">operations_research::Set::value</a></div><div class="ttdeci">Integer value() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00145">hamiltonian_path.h:145</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_pruning_hamiltonian_solver_html_a0b31a8637cf8c0fb125444577e6ad92b"><div class="ttname"><a href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a0b31a8637cf8c0fb125444577e6ad92b">operations_research::PruningHamiltonianSolver::HamiltonianCost</a></div><div class="ttdeci">CostType HamiltonianCost(int end_node)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l01007">hamiltonian_path.h:1007</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_lattice_memory_manager_html_af4a801d214f8a294a6abf462ac12e80a"><div class="ttname"><a href="classoperations__research_1_1_lattice_memory_manager.html#af4a801d214f8a294a6abf462ac12e80a">operations_research::LatticeMemoryManager::BaseOffset</a></div><div class="ttdeci">uint64_t BaseOffset(int card, Set s) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00408">hamiltonian_path.h:408</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_a33392f61ea41062250f3664a055cd3bf"><div class="ttname"><a href="classoperations__research_1_1_set.html#a33392f61ea41062250f3664a055cd3bf">operations_research::Set::ElementRank</a></div><div class="ttdeci">int ElementRank(int n) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00184">hamiltonian_path.h:184</a></div></div>
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<div class="ttc" id="constraint__solver_2table_8cc_html_a9293e4d29cac928301645070dd307683"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a></div><div class="ttdeci">int64_t b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00047">constraint_solver/table.cc:47</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_a9c628cec54eb559f322c284c096f1837"><div class="ttname"><a href="classoperations__research_1_1_set.html#a9c628cec54eb559f322c284c096f1837">operations_research::Set::Includes</a></div><div class="ttdeci">bool Includes(Set other) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00166">hamiltonian_path.h:166</a></div></div>
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<div class="ttc" id="integral__types_8h_html"><div class="ttname"><a href="integral__types_8h.html">integral_types.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_abbfaa99a45c4a90475cb2f5138f9a162"><div class="ttname"><a href="classoperations__research_1_1_set.html#abbfaa99a45c4a90475cb2f5138f9a162">operations_research::Set::Singleton</a></div><div class="ttdeci">static Set Singleton(Integer n)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00152">hamiltonian_path.h:152</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_range_iterator_html_a9a69c0a346336b270178d60cd6da6404"><div class="ttname"><a href="classoperations__research_1_1_set_range_iterator.html#a9a69c0a346336b270178d60cd6da6404">operations_research::SetRangeIterator::operator!=</a></div><div class="ttdeci">bool operator!=(const SetRangeIterator &other) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00234">hamiltonian_path.h:234</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_element_iterator_html_a9cf56c599b564897633c67574e2e460b"><div class="ttname"><a href="classoperations__research_1_1_element_iterator.html#a9cf56c599b564897633c67574e2e460b">operations_research::ElementIterator::operator *</a></div><div class="ttdeci">int operator *() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00113">hamiltonian_path.h:113</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_aabbec0d4f2a126cbdd6c1bce67b7cc8b"><div class="ttname"><a href="classoperations__research_1_1_set.html#aabbec0d4f2a126cbdd6c1bce67b7cc8b">operations_research::Set::IntegerType</a></div><div class="ttdeci">Integer IntegerType</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00131">hamiltonian_path.h:131</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a4841d3c6b072a22ba2b2fe43d6c03298"><div class="ttname"><a href="namespaceoperations__research.html#a4841d3c6b072a22ba2b2fe43d6c03298">operations_research::BitCount32</a></div><div class="ttdeci">uint32_t BitCount32(uint32_t n)</div><div class="ttdef"><b>Definition:</b> <a href="bitset_8h_source.html#l00053">bitset.h:53</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_a31dd4f4c450a217b20db6d8389d71a4e"><div class="ttname"><a href="classoperations__research_1_1_set.html#a31dd4f4c450a217b20db6d8389d71a4e">operations_research::Set::SingletonRank</a></div><div class="ttdeci">int SingletonRank(Set singleton) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00193">hamiltonian_path.h:193</a></div></div>
|
||
<div class="ttc" id="alldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_range_with_cardinality_html_af7124add76feb58bf035c3375fe140f9"><div class="ttname"><a href="classoperations__research_1_1_set_range_with_cardinality.html#af7124add76feb58bf035c3375fe140f9">operations_research::SetRangeWithCardinality::end</a></div><div class="ttdeci">SetRangeIterator< SetRangeWithCardinality > end() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00277">hamiltonian_path.h:277</a></div></div>
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||
<div class="ttc" id="namespaceoperations__research_html_a111f44b9b9cf67a8e8d83794ac9f5291"><div class="ttname"><a href="namespaceoperations__research.html#a111f44b9b9cf67a8e8d83794ac9f5291">operations_research::CapAdd</a></div><div class="ttdeci">int64_t CapAdd(int64_t x, int64_t y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00126">saturated_arithmetic.h:126</a></div></div>
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<div class="ttc" id="gscip__solver_8cc_html_a1e2f9a2352c1d9a6cada9544898fceec"><div class="ttname"><a href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a></div><div class="ttdeci">double lower_bound</div><div class="ttdef"><b>Definition:</b> <a href="gscip__solver_8cc_source.html#l00125">gscip_solver.cc:125</a></div></div>
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<div class="ttc" id="vector__or__function_8h_html"><div class="ttname"><a href="vector__or__function_8h.html">vector_or_function.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_set_html_a0faec65dbf29460ec59dfa75d0536efb"><div class="ttname"><a href="classoperations__research_1_1_set.html#a0faec65dbf29460ec59dfa75d0536efb">operations_research::Set::Contains</a></div><div class="ttdeci">bool Contains(int n) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00163">hamiltonian_path.h:163</a></div></div>
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||
<div class="ttc" id="classoperations__research_1_1_set_range_iterator_html_ab199aaba95428b8647f6bfdd83ecb68c"><div class="ttname"><a href="classoperations__research_1_1_set_range_iterator.html#ab199aaba95428b8647f6bfdd83ecb68c">operations_research::SetRangeIterator::operator++</a></div><div class="ttdeci">const SetRangeIterator & operator++()</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00241">hamiltonian_path.h:241</a></div></div>
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||
<div class="ttc" id="classoperations__research_1_1_set_range_iterator_html"><div class="ttname"><a href="classoperations__research_1_1_set_range_iterator.html">operations_research::SetRangeIterator</a></div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00224">hamiltonian_path.h:224</a></div></div>
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||
<div class="ttc" id="classoperations__research_1_1_set_html_a5865d6398576a8e71b0f346e79c583e7"><div class="ttname"><a href="classoperations__research_1_1_set.html#a5865d6398576a8e71b0f346e79c583e7">operations_research::Set::RemoveSmallestElement</a></div><div class="ttdeci">Set RemoveSmallestElement() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00180">hamiltonian_path.h:180</a></div></div>
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||
<div class="ttc" id="classoperations__research_1_1_set_html_ae7cd733dab92b86a3aaac89c4d49503f"><div class="ttname"><a href="classoperations__research_1_1_set.html#ae7cd733dab92b86a3aaac89c4d49503f">operations_research::Set::FullSet</a></div><div class="ttdeci">static Set FullSet(Integer card)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00147">hamiltonian_path.h:147</a></div></div>
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||
<div class="ttc" id="classoperations__research_1_1_set_html_ac2fa078fad730b08d36dc600a24e21a1"><div class="ttname"><a href="classoperations__research_1_1_set.html#ac2fa078fad730b08d36dc600a24e21a1">operations_research::Set::Zero</a></div><div class="ttdeci">static constexpr Integer Zero</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00135">hamiltonian_path.h:135</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html_ab558649a26fef3a74f0909ef5af45e90"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html#ab558649a26fef3a74f0909ef5af45e90">operations_research::HamiltonianPathSolver::TravelingSalesmanCost</a></div><div class="ttdeci">CostType TravelingSalesmanCost()</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00859">hamiltonian_path.h:859</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_html"><div class="ttname"><a href="classoperations__research_1_1_set.html">operations_research::Set</a></div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00128">hamiltonian_path.h:128</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_element_iterator_html"><div class="ttname"><a href="classoperations__research_1_1_element_iterator.html">operations_research::ElementIterator</a></div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00105">hamiltonian_path.h:105</a></div></div>
|
||
<div class="ttc" id="base_2logging_8h_html_aae2dc65d9ea248d54bf39daa986dd295"><div class="ttname"><a href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a></div><div class="ttdeci">#define DCHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00894">base/logging.h:894</a></div></div>
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||
<div class="ttc" id="saturated__arithmetic_8h_html"><div class="ttname"><a href="saturated__arithmetic_8h.html">saturated_arithmetic.h</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_element_iterator_html_a0a290cf047b502171a3d1770cd194c52"><div class="ttname"><a href="classoperations__research_1_1_element_iterator.html#a0a290cf047b502171a3d1770cd194c52">operations_research::ElementIterator::ElementIterator</a></div><div class="ttdeci">ElementIterator(Set set)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00107">hamiltonian_path.h:107</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_lattice_memory_manager_html_a6789c7b14fc935d7e3d03e1376cb79d8"><div class="ttname"><a href="classoperations__research_1_1_lattice_memory_manager.html#a6789c7b14fc935d7e3d03e1376cb79d8">operations_research::LatticeMemoryManager::OffsetDelta</a></div><div class="ttdeci">uint64_t OffsetDelta(int card, int added_node, int removed_node, int rank) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00311">hamiltonian_path.h:311</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_html_a190d6e916c3a1a06e2eff670e8b52da8"><div class="ttname"><a href="classoperations__research_1_1_set.html#a190d6e916c3a1a06e2eff670e8b52da8">operations_research::Set::RemoveElement</a></div><div class="ttdeci">Set RemoveElement(int n) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00160">hamiltonian_path.h:160</a></div></div>
|
||
<div class="ttc" id="routing__flow_8cc_html_a75d7b5e4cab1e156cc7a2c5eba1e16f1"><div class="ttname"><a href="routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1">cost</a></div><div class="ttdeci">int64_t cost</div><div class="ttdef"><b>Definition:</b> <a href="routing__flow_8cc_source.html#l00152">routing_flow.cc:152</a></div></div>
|
||
<div class="ttc" id="base_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html_a9c8cdf78154ae6a73f4a272cb8d1ac4a"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html#a9c8cdf78154ae6a73f4a272cb8d1ac4a">operations_research::HamiltonianPathSolver::HamiltonianPathSolver</a></div><div class="ttdeci">HamiltonianPathSolver(CostFunction cost)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00607">hamiltonian_path.h:607</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_range_with_cardinality_html_a24d9704faf4d419fdabbde6a716e181d"><div class="ttname"><a href="classoperations__research_1_1_set_range_with_cardinality.html#a24d9704faf4d419fdabbde6a716e181d">operations_research::SetRangeWithCardinality::begin</a></div><div class="ttdeci">SetRangeIterator< SetRangeWithCardinality > begin() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00274">hamiltonian_path.h:274</a></div></div>
|
||
<div class="ttc" id="base_2logging_8h_html_ae17f8119c108cf3070bad3449c7e0006"><div class="ttname"><a href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a></div><div class="ttdeci">#define DCHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00889">base/logging.h:889</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html_a326a998ed18bedda49bd2cab5cbd4079"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html#a326a998ed18bedda49bd2cab5cbd4079">operations_research::HamiltonianPathSolver::TravelingSalesmanPath</a></div><div class="ttdeci">std::vector< int > TravelingSalesmanPath()</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00866">hamiltonian_path.h:866</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_html_a191fa6bb5261ddd97d311ccc1d90fe7c"><div class="ttname"><a href="classoperations__research_1_1_set.html#a191fa6bb5261ddd97d311ccc1d90fe7c">operations_research::Set::begin</a></div><div class="ttdeci">ElementIterator< Set > begin() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00199">hamiltonian_path.h:199</a></div></div>
|
||
<div class="ttc" id="base_2logging_8h_html_ae89df3243bbb8341130c7b3f44145ea0"><div class="ttname"><a href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a></div><div class="ttdeci">#define DCHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00890">base/logging.h:890</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_range_with_cardinality_html_ac04647d141301b9671da400a7add8e37"><div class="ttname"><a href="classoperations__research_1_1_set_range_with_cardinality.html#ac04647d141301b9671da400a7add8e37">operations_research::SetRangeWithCardinality::SetType</a></div><div class="ttdeci">Set SetType</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00260">hamiltonian_path.h:260</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_matrix_or_function_html"><div class="ttname"><a href="classoperations__research_1_1_matrix_or_function.html">operations_research::MatrixOrFunction< CostType, CostFunction, true ></a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_pruning_hamiltonian_solver_html"><div class="ttname"><a href="classoperations__research_1_1_pruning_hamiltonian_solver.html">operations_research::PruningHamiltonianSolver</a></div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00878">hamiltonian_path.h:878</a></div></div>
|
||
<div class="ttc" id="namespaceoperations__research_html_ae13fcb4162a4180395806f43237c44b2"><div class="ttname"><a href="namespaceoperations__research.html#ae13fcb4162a4180395806f43237c44b2">operations_research::LeastSignificantBitPosition64</a></div><div class="ttdeci">int LeastSignificantBitPosition64(uint64_t n)</div><div class="ttdef"><b>Definition:</b> <a href="bitset_8h_source.html#l00127">bitset.h:127</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_lattice_memory_manager_html_a9614dfea1a66f5d18799a058adc57a95"><div class="ttname"><a href="classoperations__research_1_1_lattice_memory_manager.html#a9614dfea1a66f5d18799a058adc57a95">operations_research::LatticeMemoryManager::Init</a></div><div class="ttdeci">void Init(int max_card)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00358">hamiltonian_path.h:358</a></div></div>
|
||
<div class="ttc" id="namespaceoperations__research_html_abc979832d72da1ae793ba6d28ae46672"><div class="ttname"><a href="namespaceoperations__research.html#abc979832d72da1ae793ba6d28ae46672">operations_research::BitCount64</a></div><div class="ttdeci">uint64_t BitCount64(uint64_t n)</div><div class="ttdef"><b>Definition:</b> <a href="bitset_8h_source.html#l00042">bitset.h:42</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html_a03106785fd757b213975f94d4b780709"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html#a03106785fd757b213975f94d4b780709">operations_research::HamiltonianPathSolver::NodeSet</a></div><div class="ttdeci">Set< Integer > NodeSet</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00477">hamiltonian_path.h:477</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_range_iterator_html_a8f6ae547a7aba92b9e4fe92a8713085a"><div class="ttname"><a href="classoperations__research_1_1_set_range_iterator.html#a8f6ae547a7aba92b9e4fe92a8713085a">operations_research::SetRangeIterator::operator *</a></div><div class="ttdeci">SetType operator *() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00233">hamiltonian_path.h:233</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html_a5daed8b7f3c98c693f32dff60adeb4cc"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html#a5daed8b7f3c98c693f32dff60adeb4cc">operations_research::HamiltonianPathSolver::IsRobust</a></div><div class="ttdeci">bool IsRobust()</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00786">hamiltonian_path.h:786</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_range_iterator_html_a4ee741618ffbec86b3a2a280c61ca3f0"><div class="ttname"><a href="classoperations__research_1_1_set_range_iterator.html#a4ee741618ffbec86b3a2a280c61ca3f0">operations_research::SetRangeIterator::IntegerType</a></div><div class="ttdeci">SetType::IntegerType IntegerType</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00228">hamiltonian_path.h:228</a></div></div>
|
||
<div class="ttc" id="base_2logging_8h_html_a4395e95bab44e222cb2e77251017a0e2"><div class="ttname"><a href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a></div><div class="ttdeci">#define DCHECK_LE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00892">base/logging.h:892</a></div></div>
|
||
<div class="ttc" id="namespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_html_a3382ddf3a1f05b9ded21ddb7b0013f78"><div class="ttname"><a href="classoperations__research_1_1_set.html#a3382ddf3a1f05b9ded21ddb7b0013f78">operations_research::Set::operator!=</a></div><div class="ttdeci">bool operator!=(const Set &other) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00203">hamiltonian_path.h:203</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_hamiltonian_path_solver_html_a44af6c2df0188e77ceeec78a190ecf3f"><div class="ttname"><a href="classoperations__research_1_1_hamiltonian_path_solver.html#a44af6c2df0188e77ceeec78a190ecf3f">operations_research::HamiltonianPathSolver::VerifiesTriangleInequality</a></div><div class="ttdeci">bool VerifiesTriangleInequality()</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00811">hamiltonian_path.h:811</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_element_iterator_html_aefcf46820145a241c215f2e82b69d5f5"><div class="ttname"><a href="classoperations__research_1_1_element_iterator.html#aefcf46820145a241c215f2e82b69d5f5">operations_research::ElementIterator::operator!=</a></div><div class="ttdeci">bool operator!=(const ElementIterator &other) const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00108">hamiltonian_path.h:108</a></div></div>
|
||
<div class="ttc" id="namespaceoperations__research_html_aeaca21c840bf285f12127938231369b9"><div class="ttname"><a href="namespaceoperations__research.html#aeaca21c840bf285f12127938231369b9">operations_research::LeastSignificantBitPosition32</a></div><div class="ttdeci">int LeastSignificantBitPosition32(uint32_t n)</div><div class="ttdef"><b>Definition:</b> <a href="bitset_8h_source.html#l00182">bitset.h:182</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_range_with_cardinality_html"><div class="ttname"><a href="classoperations__research_1_1_set_range_with_cardinality.html">operations_research::SetRangeWithCardinality</a></div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00258">hamiltonian_path.h:258</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_lattice_memory_manager_html_a03b88bdfd0b2fcc7e14106cbd425629a"><div class="ttname"><a href="classoperations__research_1_1_lattice_memory_manager.html#a03b88bdfd0b2fcc7e14106cbd425629a">operations_research::LatticeMemoryManager::LatticeMemoryManager</a></div><div class="ttdeci">LatticeMemoryManager()</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00294">hamiltonian_path.h:294</a></div></div>
|
||
<div class="ttc" id="bitset_8h_html"><div class="ttname"><a href="bitset_8h.html">bitset.h</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_lattice_memory_manager_html_a4c59c8afdecf1f9d139609ffe9f172ca"><div class="ttname"><a href="classoperations__research_1_1_lattice_memory_manager.html#a4c59c8afdecf1f9d139609ffe9f172ca">operations_research::LatticeMemoryManager::SetValue</a></div><div class="ttdeci">void SetValue(Set s, int node, CostType value)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00444">hamiltonian_path.h:444</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_html_a64f741970505f1dea6a662c3b1776c74"><div class="ttname"><a href="classoperations__research_1_1_set.html#a64f741970505f1dea6a662c3b1776c74">operations_research::Set::SmallestSingleton</a></div><div class="ttdeci">Set SmallestSingleton() const</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00190">hamiltonian_path.h:190</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_pruning_hamiltonian_solver_html_a346635bd62f6d557d98e490ff2f3f306"><div class="ttname"><a href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a346635bd62f6d557d98e490ff2f3f306">operations_research::PruningHamiltonianSolver::Integer</a></div><div class="ttdeci">uint32_t Integer</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00894">hamiltonian_path.h:894</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_range_with_cardinality_html_ac227945449c4f8144b6c92afd6ae2156"><div class="ttname"><a href="classoperations__research_1_1_set_range_with_cardinality.html#ac227945449c4f8144b6c92afd6ae2156">operations_research::SetRangeWithCardinality::SetRangeWithCardinality</a></div><div class="ttdeci">SetRangeWithCardinality(int card, int max_card)</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00264">hamiltonian_path.h:264</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_set_html_a062c0acf17a051b885ad211acad31079"><div class="ttname"><a href="classoperations__research_1_1_set.html#a062c0acf17a051b885ad211acad31079">operations_research::Set::MaxCardinality</a></div><div class="ttdeci">static const int MaxCardinality</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00136">hamiltonian_path.h:136</a></div></div>
|
||
<div class="ttc" id="classoperations__research_1_1_pruning_hamiltonian_solver_html_a03106785fd757b213975f94d4b780709"><div class="ttname"><a href="classoperations__research_1_1_pruning_hamiltonian_solver.html#a03106785fd757b213975f94d4b780709">operations_research::PruningHamiltonianSolver::NodeSet</a></div><div class="ttdeci">Set< Integer > NodeSet</div><div class="ttdef"><b>Definition:</b> <a href="hamiltonian__path_8h_source.html#l00895">hamiltonian_path.h:895</a></div></div>
|
||
<div class="ttc" id="demon__profiler_8cc_html_ac072af30c4ffbc834bb4c681f6ecb514"><div class="ttname"><a href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a></div><div class="ttdeci">int64_t value</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00044">demon_profiler.cc:44</a></div></div>
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