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<a href="min__cost__flow_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span></div>
<div class="line"><a id="l00003" 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 id="l00004" 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 id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
<div class="line"><a id="l00006" 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 id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
<div class="line"><a id="l00008" 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 id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an &quot;AS IS&quot; BASIS,</span></div>
<div class="line"><a id="l00010" 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 id="l00011" 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 id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// An implementation of a cost-scaling push-relabel algorithm for</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">// the min-cost flow problem.</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">//</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">// In the following, we consider a graph G = (V,E) where V denotes the set</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">// of nodes (vertices) in the graph, E denotes the set of arcs (edges).</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment">// n = |V| denotes the number of nodes in the graph, and m = |E| denotes the</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">// number of arcs in the graph.</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">//</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">// With each arc (v,w) is associated a nonnegative capacity u(v,w)</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">// (where &#39;u&#39; stands for &quot;upper bound&quot;) and a unit cost c(v,w). With</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">// each node v is associated a quantity named supply(v), which</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">// represents a supply of fluid (if &gt;0) or a demand (if &lt;0).</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// Furthermore, no fluid is created in the graph so</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// sum_{v in V} supply(v) = 0.</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">//</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// A flow is a function from E to R such that:</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// a) f(v,w) &lt;= u(v,w) for all (v,w) in E (capacity constraint).</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// b) f(v,w) = -f(w,v) for all (v,w) in E (flow antisymmetry constraint).</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// c) sum on v f(v,w) + supply(w) = 0 (flow conservation).</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">//</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// The cost of a flow is sum on (v,w) in E ( f(v,w) * c(v,w) ) [Note:</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">// It can be confusing to beginners that the cost is actually double</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// the amount that it might seem at first because of flow</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// antisymmetry.]</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">//</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// The problem to solve: find a flow of minimum cost such that all the</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// fluid flows from the supply nodes to the demand nodes.</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">//</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// The principles behind this algorithm are the following:</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// 1/ handle pseudo-flows instead of flows and refine pseudo-flows until an</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// epsilon-optimal minimum-cost flow is obtained,</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// 2/ deal with epsilon-optimal pseudo-flows.</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">//</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// 1/ A pseudo-flow is like a flow, except that a node&#39;s outflow minus</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// its inflow can be different from its supply. If it is the case at a</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">// given node v, it is said that there is an excess (or deficit) at</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// node v. A deficit is denoted by a negative excess and inflow =</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// outflow + excess.</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// (Look at ortools/graph/max_flow.h to see that the definition</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// of preflow is more restrictive than the one for pseudo-flow in that a preflow</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// only allows non-negative excesses, i.e., no deficit.)</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">// More formally, a pseudo-flow is a function f such that:</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">// a) f(v,w) &lt;= u(v,w) for all (v,w) in E (capacity constraint).</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment">// b) f(v,w) = -f(w,v) for all (v,w) in E (flow antisymmetry constraint).</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">//</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment">// For each v in E, we also define the excess at node v, the algebraic sum of</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// all the incoming preflows at this node, added together with the supply at v.</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment">// excess(v) = sum on u f(u,v) + supply(v)</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment">//</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment">// The goal of the algorithm is to obtain excess(v) = 0 for all v in V, while</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment">// consuming capacity on some arcs, at the lowest possible cost.</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment">//</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">// 2/ Internally to the algorithm and its analysis (but invisibly to</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment">// the client), each node has an associated &quot;price&quot; (or potential), in</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment">// addition to its excess. It is formally a function from E to R (the</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="comment">// set of real numbers.). For a given price function p, the reduced</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="comment">// cost of an arc (v,w) is:</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="comment">// c_p(v,w) = c(v,w) + p(v) - p(w)</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="comment">// (c(v,w) is the cost of arc (v,w).) For those familiar with linear</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="comment">// programming, the price function can be viewed as a set of dual</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="comment">// variables.</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="comment">//</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment">// For a constant epsilon &gt;= 0, a pseudo-flow f is said to be epsilon-optimal</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="comment">// with respect to a price function p if for every residual arc (v,w) in E,</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="comment">// c_p(v,w) &gt;= -epsilon.</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment">//</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="comment">// A flow f is optimal if and only if there exists a price function p such that</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="comment">// no arc is admissible with respect to f and p.</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="comment">//</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment">// If the arc costs are integers, and epsilon &lt; 1/n, any epsilon-optimal flow</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="comment">// is optimal. The integer cost case is handled by multiplying all the arc costs</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="comment">// and the initial value of epsilon by (n+1). When epsilon reaches 1, and</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><span class="comment">// the solution is epsilon-optimal, it means: for all residual arc (v,w) in E,</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="comment">// (n+1) * c_p(v,w) &gt;= -1, thus c_p(v,w) &gt;= -1/(n+1) &gt;= 1/n, and the</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="comment">// solution is optimal.</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="comment">//</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="comment">// A node v is said to be *active* if excess(v) &gt; 0.</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span><span class="comment">// In this case the following operations can be applied to it:</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="comment">// - if there are *admissible* incident arcs, i.e. arcs which are not saturated,</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="comment">// and whose reduced costs are negative, a PushFlow operation can</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="comment">// be applied. It consists in sending as much flow as both the excess at the</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="comment">// node and the capacity of the arc permit.</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment">// - if there are no admissible arcs, the active node considered is relabeled,</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">// This is implemented in Discharge, which itself calls PushFlow and Relabel.</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment">//</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="comment">// Discharge itself is called by Refine. Refine first saturates all the</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment">// admissible arcs, then builds a stack of active nodes. It then applies</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="comment">// Discharge for each active node, possibly adding new ones in the process,</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="comment">// until no nodes are active. In that case an epsilon-optimal flow is obtained.</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="comment">//</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="comment">// Optimize iteratively calls Refine, while epsilon &gt; 1, and divides epsilon by</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="comment">// alpha (set by default to 5) before each iteration.</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span><span class="comment">//</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="comment">// The algorithm starts with epsilon = C, where C is the maximum absolute value</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="comment">// of the arc costs. In the integer case which we are dealing with, since all</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="comment">// costs are multiplied by (n+1), the initial value of epsilon is (n+1)*C.</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="comment">// The algorithm terminates when epsilon = 1, and Refine() has been called.</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="comment">// In this case, a minimum-cost flow is obtained.</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="comment">//</span></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span><span class="comment">// The complexity of the algorithm is O(n^2*m*log(n*C)) where C is the value of</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span><span class="comment">// the largest arc cost in the graph.</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span><span class="comment">//</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span><span class="comment">// IMPORTANT:</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span><span class="comment">// The algorithm is not able to detect the infeasibility of a problem (i.e.,</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="comment">// when a bottleneck in the network prohibits sending all the supplies.)</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment">// Worse, it could in some cases loop forever. This is why feasibility checking</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="comment">// is enabled by default (FLAGS_min_cost_flow_check_feasibility=true.)</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="comment">// Feasibility checking is implemented using a max-flow, which has a much lower</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="comment">// complexity. The impact on performance is negligible, while the risk of being</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span><span class="comment">// caught in an endless loop is removed. Note that using the feasibility checker</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="comment">// roughly doubles the memory consumption.</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span><span class="comment">//</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><span class="comment">// The starting reference for this class of algorithms is:</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span><span class="comment">// A.V. Goldberg and R.E. Tarjan, &quot;Finding Minimum-Cost Circulations by</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span><span class="comment">// Successive Approximation.&quot; Mathematics of Operations Research, Vol. 15,</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span><span class="comment">// 1990:430-466.</span></div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span><span class="comment">// http://portal.acm.org/citation.cfm?id=92225</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span><span class="comment">//</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span><span class="comment">// Implementation issues are tackled in:</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span><span class="comment">// A.V. Goldberg, &quot;An Efficient Implementation of a Scaling Minimum-Cost Flow</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span><span class="comment">// Algorithm,&quot; Journal of Algorithms, (1997) 22:1-29</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span><span class="comment">// http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.258</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span><span class="comment">//</span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="comment">// A.V. Goldberg and M. Kharitonov, &quot;On Implementing Scaling Push-Relabel</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span><span class="comment">// Algorithms for the Minimum-Cost Flow Problem&quot;, Network flows and matching:</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span><span class="comment">// First DIMACS implementation challenge, DIMACS Series in Discrete Mathematics</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span><span class="comment">// and Theoretical Computer Science, (1993) 12:157-198.</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="comment">// ftp://dimacs.rutgers.edu/pub/netflow/submit/papers/Goldberg-mincost/scalmin.ps</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="comment">// and in:</span></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="comment">// U. Bunnagel, B. Korte, and J. Vygen. “Efficient implementation of the</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="comment">// Goldberg-Tarjan minimum-cost flow algorithm.” Optimization Methods and</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><span class="comment">// Software (1998) vol. 10, no. 2:157-174.</span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span><span class="comment">// http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.9897</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span><span class="comment">//</span></div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span><span class="comment">// We have tried as much as possible in this implementation to keep the</span></div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="comment">// notations and namings of the papers cited above, except for &#39;demand&#39; or</span></div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span><span class="comment">// &#39;balance&#39; which have been replaced by &#39;supply&#39;, with the according sign</span></div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span><span class="comment">// changes to better accommodate with the API of the rest of our tools. A demand</span></div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span><span class="comment">// is denoted by a negative supply.</span></div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span><span class="comment">//</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span><span class="comment">// TODO(user): See whether the following can bring any improvements on real-life</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="comment">// problems.</span></div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span><span class="comment">// R.K. Ahuja, A.V. Goldberg, J.B. Orlin, and R.E. Tarjan, &quot;Finding minimum-cost</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span><span class="comment">// flows by double scaling,&quot; Mathematical Programming, (1992) 53:243-266.</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span><span class="comment">// http://www.springerlink.com/index/gu7404218u6kt166.pdf</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span><span class="comment">//</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span><span class="comment">// An interesting general reference on network flows is:</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span><span class="comment">// R. K. Ahuja, T. L. Magnanti, J. B. Orlin, &quot;Network Flows: Theory, Algorithms,</span></div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span><span class="comment">// and Applications,&quot; Prentice Hall, 1993, ISBN: 978-0136175490,</span></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span><span class="comment">// http://www.amazon.com/dp/013617549X</span></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span><span class="comment">//</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span><span class="comment">// Keywords: Push-relabel, min-cost flow, network, graph, Goldberg, Tarjan,</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span><span class="comment">// Dinic, Dinitz.</span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> </div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span><span class="preprocessor">#ifndef OR_TOOLS_GRAPH_MIN_COST_FLOW_H_</span></div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span><span class="preprocessor">#define OR_TOOLS_GRAPH_MIN_COST_FLOW_H_</span></div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> </div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span><span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="preprocessor">#include &lt;stack&gt;</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span><span class="preprocessor">#include &lt;string&gt;</span></div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span><span class="preprocessor">#include &quot;ortools/base/integral_types.h&quot;</span></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span><span class="preprocessor">#include &quot;ortools/base/logging.h&quot;</span></div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span><span class="preprocessor">#include &quot;ortools/base/macros.h&quot;</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span><span class="preprocessor">#include &quot;<a class="code" href="ebert__graph_8h.html">ortools/graph/ebert_graph.h</a>&quot;</span></div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span><span class="preprocessor">#include &quot;<a class="code" href="graph_8h.html">ortools/graph/graph.h</a>&quot;</span></div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span><span class="preprocessor">#include &quot;ortools/util/stats.h&quot;</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span><span class="preprocessor">#include &quot;ortools/util/zvector.h&quot;</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> </div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> </div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span><span class="comment">// Forward declaration.</span></div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> Graph, <span class="keyword">typename</span> ArcFlowType, <span class="keyword">typename</span> ArcScaledCostType&gt;</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span><span class="keyword">class </span>GenericMinCostFlow;</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> </div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span><span class="comment">// Different statuses for a solved problem.</span></div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span><span class="comment">// We use a base class to share it between our different interfaces.</span></div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow_base.html"> 193</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1_min_cost_flow_base.html">MinCostFlowBase</a> {</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70b"> 195</a></span> <span class="keyword">enum</span> <a class="code hl_enumeration" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70b">Status</a> {</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba0e6873a155f86a4695f463bf8601d05f"> 196</a></span> <a class="code hl_enumvalue" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba0e6873a155f86a4695f463bf8601d05f">NOT_SOLVED</a>,</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba2579881e7c83261bc21bafb5a5c92cad"> 197</a></span> <a class="code hl_enumvalue" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba2579881e7c83261bc21bafb5a5c92cad">OPTIMAL</a>,</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba03f919221217f95d21a593a7120165e1"> 198</a></span> <a class="code hl_enumvalue" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba03f919221217f95d21a593a7120165e1">FEASIBLE</a>,</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba2884fa43446c0cbc9c7a9b74d41d7483"> 199</a></span> <a class="code hl_enumvalue" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba2884fa43446c0cbc9c7a9b74d41d7483">INFEASIBLE</a>,</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba6a2175a75814f119266396a0e9681718"> 200</a></span> <a class="code hl_enumvalue" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba6a2175a75814f119266396a0e9681718">UNBALANCED</a>,</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70bac76ecfd837bdc6d4150bb02c403356e4"> 201</a></span> <a class="code hl_enumvalue" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70bac76ecfd837bdc6d4150bb02c403356e4">BAD_RESULT</a>,</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <a class="code hl_enumvalue" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70bac4a203c4d1b6ee01ef2494cf7bc90e88">BAD_COST_RANGE</a></div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70bac4a203c4d1b6ee01ef2494cf7bc90e88"> 203</a></span> };</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span>};</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> </div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span><span class="comment">// A simple and efficient min-cost flow interface. This is as fast as</span></div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span><span class="comment">// GenericMinCostFlow&lt;ReverseArcStaticGraph&gt;, which is the fastest, but is uses</span></div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span><span class="comment">// more memory in order to hide the somewhat involved construction of the</span></div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span><span class="comment">// static graph.</span></div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span><span class="comment">//</span></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span><span class="comment">// TODO(user): If the need arises, extend this interface to support warm start</span></div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span><span class="comment">// and incrementality between solves. Note that this is already supported by the</span></div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span><span class="comment">// GenericMinCostFlow&lt;&gt; interface.</span></div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html"> 214</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1_simple_min_cost_flow.html">SimpleMinCostFlow</a> : <span class="keyword">public</span> <a class="code hl_class" href="classoperations__research_1_1_min_cost_flow_base.html">MinCostFlowBase</a> {</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="comment">// By default, the constructor takes no size. New node indices are created</span></div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="comment">// lazily by AddArcWithCapacityAndUnitCost() or SetNodeSupply() such that the</span></div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="comment">// set of valid nodes will always be [0, NumNodes()).</span></div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="comment">//</span></div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="comment">// You may pre-reserve the internal data structures with a given expected</span></div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="comment">// number of nodes and arcs, to potentially gain performance.</span></div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#a6d65a7ab08c98b332781f187776683e5"> 222</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#a6d65a7ab08c98b332781f187776683e5">SimpleMinCostFlow</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> reserve_num_nodes = 0,</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> reserve_num_arcs = 0);</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="comment">// Adds a directed arc from tail to head to the underlying graph with</span></div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="comment">// a given capacity and cost per unit of flow.</span></div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="comment">// * Node indices and the capacity must be non-negative (&gt;= 0).</span></div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="comment">// * The unit cost can take any integer value (even negative).</span></div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="comment">// * Self-looping and duplicate arcs are supported.</span></div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="comment">// * After the method finishes, NumArcs() == the returned ArcIndex + 1.</span></div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#a20e10ea36c32c30c5130f300f1ffde2e"> 231</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#a20e10ea36c32c30c5130f300f1ffde2e">AddArcWithCapacityAndUnitCost</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> tail, <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> head,</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> capacity,</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> unit_cost);</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> </div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="comment">// Sets the supply of the given node. The node index must be non-negative (&gt;=</span></div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="comment">// 0). Nodes implicitly created will have a default supply set to 0. A demand</span></div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="comment">// is modeled as a negative supply.</span></div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#a7cd2dc0776a9f339b56ffac996a7df8c"> 238</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#a7cd2dc0776a9f339b56ffac996a7df8c">SetNodeSupply</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node, <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> supply);</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> </div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="comment">// Solves the problem, and returns the problem status. This function</span></div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="comment">// requires that the sum of all node supply minus node demand is zero and</span></div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="comment">// that the graph has enough capacity to send all supplies and serve all</span></div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="comment">// demands. Otherwise, it will return INFEASIBLE.</span></div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#acc2868367f8fd38360a8b5b56cf71bdc"> 244</a></span> <a class="code hl_enumeration" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70b">Status</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#acc2868367f8fd38360a8b5b56cf71bdc">Solve</a>() {</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keywordflow">return</span> SolveWithPossibleAdjustment(SupplyAdjustment::DONT_ADJUST);</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> }</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> </div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="comment">// Same as Solve(), but does not have the restriction that the supply</span></div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="comment">// must match the demand or that the graph has enough capacity to serve</span></div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="comment">// all the demand or use all the supply. This will compute a maximum-flow</span></div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="comment">// with minimum cost. The value of the maximum-flow will be given by</span></div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="comment">// MaximumFlow().</span></div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#a296c6f72aa7e3127a851efabcf109a2b"> 253</a></span> <a class="code hl_enumeration" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70b">Status</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#a296c6f72aa7e3127a851efabcf109a2b">SolveMaxFlowWithMinCost</a>() {</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="keywordflow">return</span> SolveWithPossibleAdjustment(SupplyAdjustment::ADJUST);</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> }</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> </div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <span class="comment">// Returns the cost of the minimum-cost flow found by the algorithm when</span></div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <span class="comment">// the returned Status is OPTIMAL.</span></div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#ad39ce7ee10c34a3ce1f69f179aa4f1e9"> 259</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#ad39ce7ee10c34a3ce1f69f179aa4f1e9">OptimalCost</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="comment">// Returns the total flow of the minimum-cost flow found by the algorithm</span></div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="comment">// when the returned Status is OPTIMAL.</span></div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#a3351fc1eb1dce4a7f6b937db874b5de1"> 263</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#a3351fc1eb1dce4a7f6b937db874b5de1">MaximumFlow</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> </div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> <span class="comment">// Returns the flow on arc, this only make sense for a successful Solve().</span></div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="comment">//</span></div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> <span class="comment">// Note: It is possible that there is more than one optimal solution. The</span></div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="comment">// algorithm is deterministic so it will always return the same solution for</span></div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> <span class="comment">// a given problem. However, there is no guarantee of this from one code</span></div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="comment">// version to the next (but the code does not change often).</span></div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#a2a420ad8221c326064736ccf148d2f93"> 271</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#a2a420ad8221c326064736ccf148d2f93">Flow</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> </div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="comment">// Accessors for the user given data. The implementation will crash if &quot;arc&quot;</span></div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="comment">// is not in [0, NumArcs()) or &quot;node&quot; is not in [0, NumNodes()).</span></div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#a3be0f6fcc44bc6a4a1e976c1e60b31d0"> 275</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#a3be0f6fcc44bc6a4a1e976c1e60b31d0">NumNodes</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#a7898be8b7efbfe53a58fcf621cf41315"> 276</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#a7898be8b7efbfe53a58fcf621cf41315">NumArcs</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#ab49dbdb731f80e626e575bdf66835f46"> 277</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#ab49dbdb731f80e626e575bdf66835f46">Tail</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#aa5f729a6274027e5e5478e4bd76603ca"> 278</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#aa5f729a6274027e5e5478e4bd76603ca">Head</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#a9dcd8610149406a1593d2a0725290482"> 279</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#a9dcd8610149406a1593d2a0725290482">Capacity</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#aafd4139404e4f42af650481c3ff10cc7"> 280</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#aafd4139404e4f42af650481c3ff10cc7">Supply</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_simple_min_cost_flow.html#a1057f1a98821c9237d75967b575f3829"> 281</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> <a class="code hl_function" href="classoperations__research_1_1_simple_min_cost_flow.html#a1057f1a98821c9237d75967b575f3829">UnitCost</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> </div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keyword">private</span>:</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> typedef ::util::ReverseArcStaticGraph&lt;NodeIndex, ArcIndex&gt; <a class="code hl_class" href="classutil_1_1_reverse_arc_static_graph.html">Graph</a>;</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="keyword">enum</span> SupplyAdjustment { ADJUST, DONT_ADJUST };</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> </div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <span class="comment">// Applies the permutation in arc_permutation_ to the given arc index.</span></div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> PermutedArc(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc);</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="comment">// Solves the problem, potentially applying supply and demand adjustment,</span></div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <span class="comment">// and returns the problem status.</span></div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <a class="code hl_enumeration" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70b">Status</a> SolveWithPossibleAdjustment(SupplyAdjustment adjustment);</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <span class="keywordtype">void</span> ResizeNodeVectors(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node);</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> </div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> std::vector&lt;NodeIndex&gt; arc_tail_;</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> std::vector&lt;NodeIndex&gt; arc_head_;</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> std::vector&lt;FlowQuantity&gt; arc_capacity_;</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> std::vector&lt;FlowQuantity&gt; node_supply_;</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> std::vector&lt;CostValue&gt; arc_cost_;</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> std::vector&lt;ArcIndex&gt; arc_permutation_;</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> std::vector&lt;FlowQuantity&gt; arc_flow_;</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> optimal_cost_;</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> maximum_flow_;</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> </div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_class" href="classoperations__research_1_1_simple_min_cost_flow.html">SimpleMinCostFlow</a>);</div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span>};</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> </div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span><span class="comment">// Generic MinCostFlow that works with StarGraph and all the graphs handling</span></div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span><span class="comment">// reverse arcs from graph.h, see the end of min_cost_flow.cc for the exact</span></div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span><span class="comment">// types this class is compiled for.</span></div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span><span class="comment">//</span></div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span><span class="comment">// One can greatly decrease memory usage by using appropriately small integer</span></div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span><span class="comment">// types:</span></div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span><span class="comment">// - For the Graph&lt;&gt; types, i.e. NodeIndexType and ArcIndexType, see graph.h.</span></div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span><span class="comment">// - ArcFlowType is used for the *per-arc* flow quantity. It must be signed, and</span></div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span><span class="comment">// large enough to hold the maximum arc capacity and its negation.</span></div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span><span class="comment">// - ArcScaledCostType is used for a per-arc scaled cost. It must be signed</span></div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span><span class="comment">// and large enough to hold the maximum unit cost of an arc times</span></div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span><span class="comment">// (num_nodes + 1).</span></div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span><span class="comment">//</span></div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span><span class="comment">// Note that the latter two are different than FlowQuantity and CostValue, which</span></div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span><span class="comment">// are used for global, aggregated values and may need to be larger.</span></div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span><span class="comment">//</span></div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span><span class="comment">// TODO(user): Avoid using the globally defined type CostValue and FlowQuantity.</span></div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span><span class="comment">// Also uses the Arc*Type where there is no risk of overflow in more places.</span></div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> <a class="code hl_typedef" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>, <span class="keyword">typename</span> ArcFlowType = <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a>,</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> <span class="keyword">typename</span> ArcScaledCostType = <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a>&gt;</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html"> 327</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1_generic_min_cost_flow.html">GenericMinCostFlow</a> : <span class="keyword">public</span> <a class="code hl_class" href="classoperations__research_1_1_min_cost_flow_base.html">MinCostFlowBase</a> {</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a4ddaeee9414a17257bb052c459325caf"> 329</a></span> <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">Graph::NodeIndex</a> <a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a4ddaeee9414a17257bb052c459325caf">NodeIndex</a>;</div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48"> 330</a></span> <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">Graph::ArcIndex</a> <a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a>;</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a0d012d3907b8306ddfc1a7089342fbe2"> 331</a></span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Graph::OutgoingArcIterator <a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a0d012d3907b8306ddfc1a7089342fbe2">OutgoingArcIterator</a>;</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Graph::OutgoingOrOppositeIncomingArcIterator</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a277838ded7171a604a67babdbea05988"> 333</a></span> <a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a277838ded7171a604a67babdbea05988">OutgoingOrOppositeIncomingArcIterator</a>;</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#ad2ab85b2912dbf12804d3d1ddea9ec15"> 334</a></span> <span class="keyword">typedef</span> ZVector&lt;ArcIndex&gt; <a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#ad2ab85b2912dbf12804d3d1ddea9ec15">ArcIndexArray</a>;</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> </div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <span class="comment">// Initialize a MinCostFlow instance on the given graph. The graph does not</span></div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> <span class="comment">// need to be fully built yet, but its capacity reservation is used to</span></div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> <span class="comment">// initialize the memory of this class.</span></div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a34e6d785d3dc22ee8d54bad8f1cf6cc2"> 339</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a34e6d785d3dc22ee8d54bad8f1cf6cc2">GenericMinCostFlow</a>(<span class="keyword">const</span> <a class="code hl_typedef" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>* <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a88421a0f6fd8896906a4a4b86f41ca4f">graph</a>);</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> </div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> <span class="comment">// Returns the graph associated to the current object.</span></div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a88421a0f6fd8896906a4a4b86f41ca4f"> 342</a></span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>* <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a88421a0f6fd8896906a4a4b86f41ca4f">graph</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> graph_; }</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> </div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> <span class="comment">// Returns the status of last call to Solve(). NOT_SOLVED is returned if</span></div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> <span class="comment">// Solve() has never been called or if the problem has been modified in such a</span></div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> <span class="comment">// way that the previous solution becomes invalid.</span></div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#adb1490a44086db009cdb51f854a02a65"> 347</a></span> <a class="code hl_enumeration" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70b">Status</a> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#adb1490a44086db009cdb51f854a02a65">status</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> status_; }</div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> </div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> <span class="comment">// Sets the supply corresponding to node. A demand is modeled as a negative</span></div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> <span class="comment">// supply.</span></div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a7cd2dc0776a9f339b56ffac996a7df8c"> 351</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a7cd2dc0776a9f339b56ffac996a7df8c">SetNodeSupply</a>(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a4ddaeee9414a17257bb052c459325caf">NodeIndex</a> node, <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> supply);</div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> </div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> <span class="comment">// Sets the unit cost for the given arc.</span></div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#ab7f4041c8667d63761aecb9657823945"> 354</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#ab7f4041c8667d63761aecb9657823945">SetArcUnitCost</a>(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> arc, ArcScaledCostType unit_cost);</div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> </div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> <span class="comment">// Sets the capacity for the given arc.</span></div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#aeb6622ffa760bc9403144736f8ac4ad4"> 357</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#aeb6622ffa760bc9403144736f8ac4ad4">SetArcCapacity</a>(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> arc, ArcFlowType new_capacity);</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> </div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> <span class="comment">// Sets the flow for the given arc. Note that new_flow must be smaller than</span></div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> <span class="comment">// the capacity of the arc.</span></div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a89b020eea8abc71434d63071a1e38527"> 361</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a89b020eea8abc71434d63071a1e38527">SetArcFlow</a>(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> arc, ArcFlowType new_flow);</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> </div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> <span class="comment">// Solves the problem, returning true if a min-cost flow could be found.</span></div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a942f29030f08426e7e318204e987e2f7"> 364</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a942f29030f08426e7e318204e987e2f7">Solve</a>();</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> </div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="comment">// Checks for feasibility, i.e., that all the supplies and demands can be</span></div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> <span class="comment">// matched without exceeding bottlenecks in the network.</span></div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> <span class="comment">// If infeasible_supply_node (resp. infeasible_demand_node) are not NULL,</span></div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> <span class="comment">// they are populated with the indices of the nodes where the initial supplies</span></div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <span class="comment">// (resp. demands) are too large. Feasible values for the supplies and</span></div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <span class="comment">// demands are accessible through FeasibleSupply.</span></div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> <span class="comment">// Note that CheckFeasibility is called by Solve() when the flag</span></div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> <span class="comment">// min_cost_flow_check_feasibility is set to true (which is the default.)</span></div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a92607deae80e69a2a63cc2d8f5205bd5"> 374</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a92607deae80e69a2a63cc2d8f5205bd5">CheckFeasibility</a>(std::vector&lt;NodeIndex&gt;* <span class="keyword">const</span> infeasible_supply_node,</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> std::vector&lt;NodeIndex&gt;* <span class="keyword">const</span> infeasible_demand_node);</div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> </div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> <span class="comment">// Makes the min-cost flow problem solvable by truncating supplies and</span></div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> <span class="comment">// demands to a level acceptable by the network. There may be several ways to</span></div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> <span class="comment">// do it. In our case, the levels are computed from the result of the max-flow</span></div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> <span class="comment">// algorithm run in CheckFeasibility().</span></div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> <span class="comment">// MakeFeasible returns false if CheckFeasibility() was not called before.</span></div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a3051a4b6d1a5a9fb5444f6d5a295a95c"> 382</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a3051a4b6d1a5a9fb5444f6d5a295a95c">MakeFeasible</a>();</div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> </div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> <span class="comment">// Returns the cost of the minimum-cost flow found by the algorithm.</span></div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#aa9b606016d2b0a38fed1e5c8acd818ed"> 385</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#aa9b606016d2b0a38fed1e5c8acd818ed">GetOptimalCost</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> total_flow_cost_; }</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> </div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> <span class="comment">// Returns the flow on the given arc using the equations given in the</span></div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> <span class="comment">// comment on residual_arc_capacity_.</span></div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a2a420ad8221c326064736ccf148d2f93"> 389</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a2a420ad8221c326064736ccf148d2f93">Flow</a>(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> </div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="comment">// Returns the capacity of the given arc.</span></div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a9dcd8610149406a1593d2a0725290482"> 392</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a9dcd8610149406a1593d2a0725290482">Capacity</a>(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> </div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> <span class="comment">// Returns the unscaled cost for the given arc.</span></div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a1057f1a98821c9237d75967b575f3829"> 395</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a1057f1a98821c9237d75967b575f3829">UnitCost</a>(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> </div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> <span class="comment">// Returns the supply at a given node. Demands are modelled as negative</span></div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> <span class="comment">// supplies.</span></div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#aafd4139404e4f42af650481c3ff10cc7"> 399</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#aafd4139404e4f42af650481c3ff10cc7">Supply</a>(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a4ddaeee9414a17257bb052c459325caf">NodeIndex</a> node) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> </div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <span class="comment">// Returns the initial supply at a given node.</span></div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a84859dfe0d913de5132fd421bf5d002d"> 402</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a84859dfe0d913de5132fd421bf5d002d">InitialSupply</a>(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a4ddaeee9414a17257bb052c459325caf">NodeIndex</a> node) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> </div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> <span class="comment">// Returns the largest supply (if &gt; 0) or largest demand in absolute value</span></div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> <span class="comment">// (if &lt; 0) admissible at node. If the problem is not feasible, some of these</span></div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <span class="comment">// values will be smaller (in absolute value) than the initial supplies</span></div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> <span class="comment">// and demand given as input.</span></div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a27a137ef3b0fb7f787eb460dcfd52591"> 408</a></span> <a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a27a137ef3b0fb7f787eb460dcfd52591">FeasibleSupply</a>(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a4ddaeee9414a17257bb052c459325caf">NodeIndex</a> node) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> </div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> <span class="comment">// Whether to use the UpdatePrices() heuristic.</span></div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#ae01fa6e52a98aee14eea54a935012ed0"> 411</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#ae01fa6e52a98aee14eea54a935012ed0">SetUseUpdatePrices</a>(<span class="keywordtype">bool</span> value) { use_price_update_ = value; }</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> </div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="comment">// Whether to check the feasibility of the problem with a max-flow, prior to</span></div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> <span class="comment">// solving it. This uses about twice as much memory, but detects infeasible</span></div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> <span class="comment">// problems (where the flow can&#39;t be satisfied) and makes Solve() return</span></div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> <span class="comment">// INFEASIBLE. If you disable this check, you will spare memory but you must</span></div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> <span class="comment">// make sure that your problem is feasible, otherwise the code can loop</span></div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> <span class="comment">// forever.</span></div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_generic_min_cost_flow.html#a74d8ec554b2414ab5f84d8d394b443ca"> 419</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a74d8ec554b2414ab5f84d8d394b443ca">SetCheckFeasibility</a>(<span class="keywordtype">bool</span> value) { check_feasibility_ = value; }</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> </div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <span class="keyword">private</span>:</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> <span class="comment">// Returns true if the given arc is admissible i.e. if its residual capacity</span></div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> <span class="comment">// is strictly positive, and its reduced cost strictly negative, i.e., pushing</span></div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> <span class="comment">// more flow into it will result in a reduction of the total cost.</span></div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> <span class="keywordtype">bool</span> IsAdmissible(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> <span class="keywordtype">bool</span> FastIsAdmissible(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc, <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> tail_potential) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> </div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> <span class="comment">// Returns true if node is active, i.e., if its supply is positive.</span></div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> <span class="keywordtype">bool</span> IsActive(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> </div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> <span class="comment">// Returns the reduced cost for a given arc.</span></div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> ReducedCost(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> FastReducedCost(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc, <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> tail_potential) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> </div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> <span class="comment">// Returns the first incident arc of a given node.</span></div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> <a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> GetFirstOutgoingOrOppositeIncomingArc(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> </div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> <span class="comment">// Checks the consistency of the input, i.e., whether the sum of the supplies</span></div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> <span class="comment">// for all nodes is equal to zero. To be used in a DCHECK.</span></div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> <span class="keywordtype">bool</span> CheckInputConsistency() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> </div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> <span class="comment">// Checks whether the result is valid, i.e. whether for each arc,</span></div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> <span class="comment">// residual_arc_capacity_[arc] == 0 || ReducedCost(arc) &gt;= -epsilon_.</span></div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> <span class="comment">// (A solution is epsilon-optimal if ReducedCost(arc) &gt;= -epsilon.)</span></div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> <span class="comment">// To be used in a DCHECK.</span></div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> <span class="keywordtype">bool</span> CheckResult() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> </div>
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> <span class="comment">// Checks that the cost range fits in the range of int64_t&#39;s.</span></div>
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> <span class="comment">// To be used in a DCHECK.</span></div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> <span class="keywordtype">bool</span> CheckCostRange() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> </div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> <span class="comment">// Checks the relabel precondition (to be used in a DCHECK):</span></div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> <span class="comment">// - The node must be active, or have a 0 excess (relaxation for the Push</span></div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> <span class="comment">// Look-Ahead heuristic).</span></div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> <span class="comment">// - The node must have no admissible arcs.</span></div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> <span class="keywordtype">bool</span> CheckRelabelPrecondition(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> </div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> <span class="comment">// Returns context concatenated with information about a given arc</span></div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> <span class="comment">// in a human-friendly way.</span></div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> std::string DebugString(<span class="keyword">const</span> std::string&amp; context, <a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> </div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> <span class="comment">// Resets the first_admissible_arc_ array to the first incident arc of each</span></div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> <span class="comment">// node.</span></div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> <span class="keywordtype">void</span> ResetFirstAdmissibleArcs();</div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> </div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> <span class="comment">// Scales the costs, by multiplying them by (graph_-&gt;num_nodes() + 1).</span></div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> <span class="keywordtype">void</span> ScaleCosts();</div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> </div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> <span class="comment">// Unscales the costs, by dividing them by (graph_-&gt;num_nodes() + 1).</span></div>
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <span class="keywordtype">void</span> UnscaleCosts();</div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> </div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> <span class="comment">// Optimizes the cost by dividing epsilon_ by alpha_ and calling Refine().</span></div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> <span class="keywordtype">void</span> Optimize();</div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span> </div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> <span class="comment">// Saturates the admissible arcs, i.e., push as much flow as possible.</span></div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> <span class="keywordtype">void</span> SaturateAdmissibleArcs();</div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> </div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span> <span class="comment">// Pushes flow on a given arc, i.e., consumes flow on</span></div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> <span class="comment">// residual_arc_capacity_[arc], and consumes -flow on</span></div>
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span> <span class="comment">// residual_arc_capacity_[Opposite(arc)]. Updates node_excess_ at the tail</span></div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> <span class="comment">// and head of the arc accordingly.</span></div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> <span class="keywordtype">void</span> PushFlow(<a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> flow, <a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc);</div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> <span class="keywordtype">void</span> FastPushFlow(<a class="code hl_typedef" href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">FlowQuantity</a> flow, <a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc, <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> tail);</div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> </div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> <span class="comment">// Initializes the stack active_nodes_.</span></div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> <span class="keywordtype">void</span> InitializeActiveNodeStack();</div>
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span> </div>
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span> <span class="comment">// Price update heuristics as described in A.V. Goldberg, &quot;An Efficient</span></div>
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span> <span class="comment">// Implementation of a Scaling Minimum-Cost Flow Algorithm,&quot; Journal of</span></div>
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span> <span class="comment">// Algorithms, (1997) 22:1-29</span></div>
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> <span class="comment">// http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.258</span></div>
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> <span class="keywordtype">void</span> UpdatePrices();</div>
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> </div>
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> <span class="comment">// Performs an epsilon-optimization step by saturating admissible arcs</span></div>
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span> <span class="comment">// and discharging the active nodes.</span></div>
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span> <span class="keywordtype">void</span> Refine();</div>
<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span> </div>
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span> <span class="comment">// Discharges an active node by saturating its admissible adjacent arcs,</span></div>
<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span> <span class="comment">// if any, and by relabelling it when it becomes inactive.</span></div>
<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"> 500</span> <span class="keywordtype">void</span> Discharge(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node);</div>
<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span> </div>
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> <span class="comment">// Part of the Push LookAhead heuristic. When we are about to push on the</span></div>
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> <span class="comment">// in_arc, we check that the head (i.e node here) can accept the flow and</span></div>
<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"> 504</span> <span class="comment">// return true if this is the case:</span></div>
<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> <span class="comment">// - Returns true if the node excess is &lt; 0.</span></div>
<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> <span class="comment">// - Returns true if node is an admissible arc at its current potential.</span></div>
<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> <span class="comment">// - If the two conditions above are false, the node can be relabeled. We</span></div>
<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"> 508</span> <span class="comment">// do that and return true if the in_arc is still admissible.</span></div>
<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> <span class="keywordtype">bool</span> LookAhead(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> in_arc, <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> in_tail_potential, <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node);</div>
<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"> 510</span> </div>
<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"> 511</span> <span class="comment">// Relabels node, i.e., decreases its potential while keeping the</span></div>
<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"> 512</span> <span class="comment">// epsilon-optimality of the pseudo flow. See CheckRelabelPrecondition() for</span></div>
<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"> 513</span> <span class="comment">// details on the preconditions.</span></div>
<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span> <span class="keywordtype">void</span> Relabel(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node);</div>
<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"> 515</span> </div>
<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span> <span class="comment">// Handy member functions to make the code more compact.</span></div>
<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> Head(<a class="code hl_typedef" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> graph_-&gt;Head(arc); }</div>
<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span> <a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a4ddaeee9414a17257bb052c459325caf">NodeIndex</a> Tail(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> arc)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> graph_-&gt;Tail(arc); }</div>
<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> <a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> Opposite(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span> <span class="keywordtype">bool</span> IsArcDirect(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span> <span class="keywordtype">bool</span> IsArcValid(<a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">ArcIndex</a> arc) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span> </div>
<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span> <span class="comment">// Pointer to the graph passed as argument.</span></div>
<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>* graph_;</div>
<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span> </div>
<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span> <span class="comment">// An array representing the supply (if &gt; 0) or the demand (if &lt; 0)</span></div>
<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> <span class="comment">// for each node in graph_.</span></div>
<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a03fc0981d2d99da114ccd8b3abc0c6e1">QuantityArray</a> node_excess_;</div>
<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span> </div>
<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> <span class="comment">// An array representing the potential (or price function) for</span></div>
<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span> <span class="comment">// each node in graph_.</span></div>
<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span> <a class="code hl_typedef" href="namespaceoperations__research.html#acbdd6fd1484828a3d5e809c551ba8cf7">CostArray</a> node_potential_;</div>
<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span> </div>
<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> <span class="comment">// An array representing the residual_capacity for each arc in graph_.</span></div>
<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</span> <span class="comment">// Residual capacities enable one to represent the capacity and flow for all</span></div>
<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span> <span class="comment">// arcs in the graph in the following manner.</span></div>
<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"> 537</span> <span class="comment">// For all arcs, residual_arc_capacity_[arc] = capacity[arc] - flow[arc]</span></div>
<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> <span class="comment">// Moreover, for reverse arcs, capacity[arc] = 0 by definition.</span></div>
<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span> <span class="comment">// Also flow[Opposite(arc)] = -flow[arc] by definition.</span></div>
<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> <span class="comment">// Therefore:</span></div>
<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"> 541</span> <span class="comment">// - for a direct arc:</span></div>
<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</span> <span class="comment">// flow[arc] = 0 - flow[Opposite(arc)]</span></div>
<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span> <span class="comment">// = capacity[Opposite(arc)] - flow[Opposite(arc)]</span></div>
<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span> <span class="comment">// = residual_arc_capacity_[Opposite(arc)]</span></div>
<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span> <span class="comment">// - for a reverse arc:</span></div>
<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span> <span class="comment">// flow[arc] = -residual_arc_capacity_[arc]</span></div>
<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"> 547</span> <span class="comment">// Using these facts enables one to only maintain residual_arc_capacity_,</span></div>
<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span> <span class="comment">// instead of both capacity and flow, for each direct and indirect arc. This</span></div>
<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> <span class="comment">// reduces the amount of memory for this information by a factor 2.</span></div>
<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span> <span class="comment">// Note that the sum of the largest capacity of an arc in the graph and of</span></div>
<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span> <span class="comment">// the total flow in the graph mustn&#39;t exceed the largest 64 bit integer</span></div>
<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span> <span class="comment">// to avoid errors. CheckInputConsistency() verifies this constraint.</span></div>
<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span> ZVector&lt;ArcFlowType&gt; residual_arc_capacity_;</div>
<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> </div>
<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span> <span class="comment">// An array representing the first admissible arc for each node in graph_.</span></div>
<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> <a class="code hl_typedef" href="classoperations__research_1_1_generic_min_cost_flow.html#ad2ab85b2912dbf12804d3d1ddea9ec15">ArcIndexArray</a> first_admissible_arc_;</div>
<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</span> </div>
<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> <span class="comment">// A stack used for managing active nodes in the algorithm.</span></div>
<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span> <span class="comment">// Note that the papers cited above recommend the use of a queue, but</span></div>
<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"> 560</span> <span class="comment">// benchmarking so far has not proved it is better.</span></div>
<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> std::stack&lt;NodeIndex&gt; active_nodes_;</div>
<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> </div>
<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span> <span class="comment">// epsilon_ is the tolerance for optimality.</span></div>
<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> epsilon_;</div>
<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span> </div>
<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"> 566</span> <span class="comment">// alpha_ is the factor by which epsilon_ is divided at each iteration of</span></div>
<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> <span class="comment">// Refine().</span></div>
<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> <span class="keyword">const</span> int64_t alpha_;</div>
<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"> 569</span> </div>
<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> <span class="comment">// cost_scaling_factor_ is the scaling factor for cost.</span></div>
<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> cost_scaling_factor_;</div>
<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> </div>
<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span> <span class="comment">// An array representing the scaled unit cost for each arc in graph_.</span></div>
<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"> 574</span> ZVector&lt;ArcScaledCostType&gt; scaled_arc_unit_cost_;</div>
<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span> </div>
<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"> 576</span> <span class="comment">// The total cost of the flow.</span></div>
<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">CostValue</a> total_flow_cost_;</div>
<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> </div>
<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> <span class="comment">// The status of the problem.</span></div>
<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> <a class="code hl_enumeration" href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70b">Status</a> status_;</div>
<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> </div>
<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> <span class="comment">// An array containing the initial excesses (i.e. the supplies) for each</span></div>
<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> <span class="comment">// node. This is used to create the max-flow-based feasibility checker.</span></div>
<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a03fc0981d2d99da114ccd8b3abc0c6e1">QuantityArray</a> initial_node_excess_;</div>
<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> </div>
<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"> 586</span> <span class="comment">// An array containing the best acceptable excesses for each of the</span></div>
<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> <span class="comment">// nodes. These excesses are imposed by the result of the max-flow-based</span></div>
<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> <span class="comment">// feasibility checker for the nodes with an initial supply != 0. For the</span></div>
<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"> 589</span> <span class="comment">// other nodes, the excess is simply 0.</span></div>
<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a03fc0981d2d99da114ccd8b3abc0c6e1">QuantityArray</a> feasible_node_excess_;</div>
<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> </div>
<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> <span class="comment">// Statistics about this class.</span></div>
<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> StatsGroup stats_;</div>
<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> </div>
<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> <span class="comment">// Number of Relabel() since last UpdatePrices().</span></div>
<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> <span class="keywordtype">int</span> num_relabels_since_last_price_update_;</div>
<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> </div>
<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> <span class="comment">// A Boolean which is true when feasibility has been checked.</span></div>
<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> <span class="keywordtype">bool</span> feasibility_checked_;</div>
<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span> </div>
<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</span> <span class="comment">// Whether to use the UpdatePrices() heuristic.</span></div>
<div class="line"><a id="l00602" name="l00602"></a><span class="lineno"> 602</span> <span class="keywordtype">bool</span> use_price_update_;</div>
<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> </div>
<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span> <span class="comment">// Whether to check the problem feasibility with a max-flow.</span></div>
<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> <span class="keywordtype">bool</span> check_feasibility_;</div>
<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span> </div>
<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a34e6d785d3dc22ee8d54bad8f1cf6cc2">GenericMinCostFlow</a>);</div>
<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</span>};</div>
<div class="line"><a id="l00609" name="l00609"></a><span class="lineno"> 609</span> </div>
<div class="line"><a id="l00610" name="l00610"></a><span class="lineno"> 610</span><span class="preprocessor">#if !SWIG</span></div>
<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span> </div>
<div class="line"><a id="l00612" name="l00612"></a><span class="lineno"> 612</span><span class="comment">// Default MinCostFlow instance that uses StarGraph.</span></div>
<div class="line"><a id="l00613" name="l00613"></a><span class="lineno"> 613</span><span class="comment">// New clients should use SimpleMinCostFlow if they can.</span></div>
<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow.html"> 614</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1_min_cost_flow.html">MinCostFlow</a> : <span class="keyword">public</span> <a class="code hl_class" href="classoperations__research_1_1_generic_min_cost_flow.html">GenericMinCostFlow</a>&lt;StarGraph&gt; {</div>
<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"> 615</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_min_cost_flow.html#a6b237a92c15ebe2ebc6cce0e71d91b22"> 616</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1_min_cost_flow.html#a6b237a92c15ebe2ebc6cce0e71d91b22">MinCostFlow</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_ebert_graph.html">StarGraph</a>* <a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a88421a0f6fd8896906a4a4b86f41ca4f">graph</a>) : <a class="code hl_class" href="classoperations__research_1_1_generic_min_cost_flow.html">GenericMinCostFlow</a>(<a class="code hl_function" href="classoperations__research_1_1_generic_min_cost_flow.html#a88421a0f6fd8896906a4a4b86f41ca4f">graph</a>) {}</div>
<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"> 617</span>};</div>
<div class="line"><a id="l00618" name="l00618"></a><span class="lineno"> 618</span> </div>
<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span><span class="preprocessor">#endif </span><span class="comment">// SWIG</span></div>
<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</span> </div>
<div class="line"><a id="l00621" name="l00621"></a><span class="lineno"> 621</span>} <span class="comment">// namespace operations_research</span></div>
<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_GRAPH_MIN_COST_FLOW_H_</span></div>
<div class="ttc" id="aclassoperations__research_1_1_ebert_graph_html"><div class="ttname"><a href="classoperations__research_1_1_ebert_graph.html">operations_research::EbertGraph</a></div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l01187">ebert_graph.h:1189</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html">operations_research::GenericMinCostFlow</a></div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00327">min_cost_flow.h:327</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a0d012d3907b8306ddfc1a7089342fbe2"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a0d012d3907b8306ddfc1a7089342fbe2">operations_research::GenericMinCostFlow::OutgoingArcIterator</a></div><div class="ttdeci">Graph::OutgoingArcIterator OutgoingArcIterator</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00331">min_cost_flow.h:331</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a1057f1a98821c9237d75967b575f3829"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a1057f1a98821c9237d75967b575f3829">operations_research::GenericMinCostFlow::UnitCost</a></div><div class="ttdeci">CostValue UnitCost(ArcIndex arc) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a277838ded7171a604a67babdbea05988"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a277838ded7171a604a67babdbea05988">operations_research::GenericMinCostFlow::OutgoingOrOppositeIncomingArcIterator</a></div><div class="ttdeci">Graph::OutgoingOrOppositeIncomingArcIterator OutgoingOrOppositeIncomingArcIterator</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00333">min_cost_flow.h:333</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a27a137ef3b0fb7f787eb460dcfd52591"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a27a137ef3b0fb7f787eb460dcfd52591">operations_research::GenericMinCostFlow::FeasibleSupply</a></div><div class="ttdeci">FlowQuantity FeasibleSupply(NodeIndex node) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a2a420ad8221c326064736ccf148d2f93"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a2a420ad8221c326064736ccf148d2f93">operations_research::GenericMinCostFlow::Flow</a></div><div class="ttdeci">FlowQuantity Flow(ArcIndex arc) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a3051a4b6d1a5a9fb5444f6d5a295a95c"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a3051a4b6d1a5a9fb5444f6d5a295a95c">operations_research::GenericMinCostFlow::MakeFeasible</a></div><div class="ttdeci">bool MakeFeasible()</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a34e6d785d3dc22ee8d54bad8f1cf6cc2"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a34e6d785d3dc22ee8d54bad8f1cf6cc2">operations_research::GenericMinCostFlow::GenericMinCostFlow</a></div><div class="ttdeci">GenericMinCostFlow(const Graph *graph)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a44aa9e2f47277c91d8064c7126a2ff48"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a44aa9e2f47277c91d8064c7126a2ff48">operations_research::GenericMinCostFlow::ArcIndex</a></div><div class="ttdeci">Graph::ArcIndex ArcIndex</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00330">min_cost_flow.h:330</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a4ddaeee9414a17257bb052c459325caf"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a4ddaeee9414a17257bb052c459325caf">operations_research::GenericMinCostFlow::NodeIndex</a></div><div class="ttdeci">Graph::NodeIndex NodeIndex</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00329">min_cost_flow.h:329</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a74d8ec554b2414ab5f84d8d394b443ca"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a74d8ec554b2414ab5f84d8d394b443ca">operations_research::GenericMinCostFlow::SetCheckFeasibility</a></div><div class="ttdeci">void SetCheckFeasibility(bool value)</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00419">min_cost_flow.h:419</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a7cd2dc0776a9f339b56ffac996a7df8c"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a7cd2dc0776a9f339b56ffac996a7df8c">operations_research::GenericMinCostFlow::SetNodeSupply</a></div><div class="ttdeci">void SetNodeSupply(NodeIndex node, FlowQuantity supply)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a84859dfe0d913de5132fd421bf5d002d"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a84859dfe0d913de5132fd421bf5d002d">operations_research::GenericMinCostFlow::InitialSupply</a></div><div class="ttdeci">FlowQuantity InitialSupply(NodeIndex node) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a88421a0f6fd8896906a4a4b86f41ca4f"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a88421a0f6fd8896906a4a4b86f41ca4f">operations_research::GenericMinCostFlow::graph</a></div><div class="ttdeci">const Graph * graph() const</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00342">min_cost_flow.h:342</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a89b020eea8abc71434d63071a1e38527"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a89b020eea8abc71434d63071a1e38527">operations_research::GenericMinCostFlow::SetArcFlow</a></div><div class="ttdeci">void SetArcFlow(ArcIndex arc, ArcFlowType new_flow)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a92607deae80e69a2a63cc2d8f5205bd5"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a92607deae80e69a2a63cc2d8f5205bd5">operations_research::GenericMinCostFlow::CheckFeasibility</a></div><div class="ttdeci">bool CheckFeasibility(std::vector&lt; NodeIndex &gt; *const infeasible_supply_node, std::vector&lt; NodeIndex &gt; *const infeasible_demand_node)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a942f29030f08426e7e318204e987e2f7"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a942f29030f08426e7e318204e987e2f7">operations_research::GenericMinCostFlow::Solve</a></div><div class="ttdeci">bool Solve()</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_a9dcd8610149406a1593d2a0725290482"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#a9dcd8610149406a1593d2a0725290482">operations_research::GenericMinCostFlow::Capacity</a></div><div class="ttdeci">FlowQuantity Capacity(ArcIndex arc) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_aa9b606016d2b0a38fed1e5c8acd818ed"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#aa9b606016d2b0a38fed1e5c8acd818ed">operations_research::GenericMinCostFlow::GetOptimalCost</a></div><div class="ttdeci">CostValue GetOptimalCost() const</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00385">min_cost_flow.h:385</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_aafd4139404e4f42af650481c3ff10cc7"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#aafd4139404e4f42af650481c3ff10cc7">operations_research::GenericMinCostFlow::Supply</a></div><div class="ttdeci">FlowQuantity Supply(NodeIndex node) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_ab7f4041c8667d63761aecb9657823945"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#ab7f4041c8667d63761aecb9657823945">operations_research::GenericMinCostFlow::SetArcUnitCost</a></div><div class="ttdeci">void SetArcUnitCost(ArcIndex arc, ArcScaledCostType unit_cost)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_ad2ab85b2912dbf12804d3d1ddea9ec15"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#ad2ab85b2912dbf12804d3d1ddea9ec15">operations_research::GenericMinCostFlow::ArcIndexArray</a></div><div class="ttdeci">ZVector&lt; ArcIndex &gt; ArcIndexArray</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00334">min_cost_flow.h:334</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_adb1490a44086db009cdb51f854a02a65"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#adb1490a44086db009cdb51f854a02a65">operations_research::GenericMinCostFlow::status</a></div><div class="ttdeci">Status status() const</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00347">min_cost_flow.h:347</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_ae01fa6e52a98aee14eea54a935012ed0"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#ae01fa6e52a98aee14eea54a935012ed0">operations_research::GenericMinCostFlow::SetUseUpdatePrices</a></div><div class="ttdeci">void SetUseUpdatePrices(bool value)</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00411">min_cost_flow.h:411</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_generic_min_cost_flow_html_aeb6622ffa760bc9403144736f8ac4ad4"><div class="ttname"><a href="classoperations__research_1_1_generic_min_cost_flow.html#aeb6622ffa760bc9403144736f8ac4ad4">operations_research::GenericMinCostFlow::SetArcCapacity</a></div><div class="ttdeci">void SetArcCapacity(ArcIndex arc, ArcFlowType new_capacity)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_base_html"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow_base.html">operations_research::MinCostFlowBase</a></div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00193">min_cost_flow.h:193</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_base_html_a67a0db04d321a74b7e7fcfd3f1a3f70b"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70b">operations_research::MinCostFlowBase::Status</a></div><div class="ttdeci">Status</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00195">min_cost_flow.h:195</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_base_html_a67a0db04d321a74b7e7fcfd3f1a3f70ba03f919221217f95d21a593a7120165e1"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba03f919221217f95d21a593a7120165e1">operations_research::MinCostFlowBase::FEASIBLE</a></div><div class="ttdeci">@ FEASIBLE</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00198">min_cost_flow.h:198</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_base_html_a67a0db04d321a74b7e7fcfd3f1a3f70ba0e6873a155f86a4695f463bf8601d05f"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba0e6873a155f86a4695f463bf8601d05f">operations_research::MinCostFlowBase::NOT_SOLVED</a></div><div class="ttdeci">@ NOT_SOLVED</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00196">min_cost_flow.h:196</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_base_html_a67a0db04d321a74b7e7fcfd3f1a3f70ba2579881e7c83261bc21bafb5a5c92cad"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba2579881e7c83261bc21bafb5a5c92cad">operations_research::MinCostFlowBase::OPTIMAL</a></div><div class="ttdeci">@ OPTIMAL</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00197">min_cost_flow.h:197</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_base_html_a67a0db04d321a74b7e7fcfd3f1a3f70ba2884fa43446c0cbc9c7a9b74d41d7483"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba2884fa43446c0cbc9c7a9b74d41d7483">operations_research::MinCostFlowBase::INFEASIBLE</a></div><div class="ttdeci">@ INFEASIBLE</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00199">min_cost_flow.h:199</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_base_html_a67a0db04d321a74b7e7fcfd3f1a3f70ba6a2175a75814f119266396a0e9681718"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70ba6a2175a75814f119266396a0e9681718">operations_research::MinCostFlowBase::UNBALANCED</a></div><div class="ttdeci">@ UNBALANCED</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00200">min_cost_flow.h:200</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_base_html_a67a0db04d321a74b7e7fcfd3f1a3f70bac4a203c4d1b6ee01ef2494cf7bc90e88"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70bac4a203c4d1b6ee01ef2494cf7bc90e88">operations_research::MinCostFlowBase::BAD_COST_RANGE</a></div><div class="ttdeci">@ BAD_COST_RANGE</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00203">min_cost_flow.h:202</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_base_html_a67a0db04d321a74b7e7fcfd3f1a3f70bac76ecfd837bdc6d4150bb02c403356e4"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow_base.html#a67a0db04d321a74b7e7fcfd3f1a3f70bac76ecfd837bdc6d4150bb02c403356e4">operations_research::MinCostFlowBase::BAD_RESULT</a></div><div class="ttdeci">@ BAD_RESULT</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00201">min_cost_flow.h:201</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_html"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow.html">operations_research::MinCostFlow</a></div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00614">min_cost_flow.h:614</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_min_cost_flow_html_a6b237a92c15ebe2ebc6cce0e71d91b22"><div class="ttname"><a href="classoperations__research_1_1_min_cost_flow.html#a6b237a92c15ebe2ebc6cce0e71d91b22">operations_research::MinCostFlow::MinCostFlow</a></div><div class="ttdeci">MinCostFlow(const StarGraph *graph)</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00616">min_cost_flow.h:616</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html">operations_research::SimpleMinCostFlow</a></div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00214">min_cost_flow.h:214</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_a1057f1a98821c9237d75967b575f3829"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#a1057f1a98821c9237d75967b575f3829">operations_research::SimpleMinCostFlow::UnitCost</a></div><div class="ttdeci">CostValue UnitCost(ArcIndex arc) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_a20e10ea36c32c30c5130f300f1ffde2e"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#a20e10ea36c32c30c5130f300f1ffde2e">operations_research::SimpleMinCostFlow::AddArcWithCapacityAndUnitCost</a></div><div class="ttdeci">ArcIndex AddArcWithCapacityAndUnitCost(NodeIndex tail, NodeIndex head, FlowQuantity capacity, CostValue unit_cost)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_a296c6f72aa7e3127a851efabcf109a2b"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#a296c6f72aa7e3127a851efabcf109a2b">operations_research::SimpleMinCostFlow::SolveMaxFlowWithMinCost</a></div><div class="ttdeci">Status SolveMaxFlowWithMinCost()</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00253">min_cost_flow.h:253</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_a2a420ad8221c326064736ccf148d2f93"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#a2a420ad8221c326064736ccf148d2f93">operations_research::SimpleMinCostFlow::Flow</a></div><div class="ttdeci">FlowQuantity Flow(ArcIndex arc) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_a3351fc1eb1dce4a7f6b937db874b5de1"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#a3351fc1eb1dce4a7f6b937db874b5de1">operations_research::SimpleMinCostFlow::MaximumFlow</a></div><div class="ttdeci">FlowQuantity MaximumFlow() const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_a3be0f6fcc44bc6a4a1e976c1e60b31d0"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#a3be0f6fcc44bc6a4a1e976c1e60b31d0">operations_research::SimpleMinCostFlow::NumNodes</a></div><div class="ttdeci">NodeIndex NumNodes() const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_a6d65a7ab08c98b332781f187776683e5"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#a6d65a7ab08c98b332781f187776683e5">operations_research::SimpleMinCostFlow::SimpleMinCostFlow</a></div><div class="ttdeci">SimpleMinCostFlow(NodeIndex reserve_num_nodes=0, ArcIndex reserve_num_arcs=0)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_a7898be8b7efbfe53a58fcf621cf41315"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#a7898be8b7efbfe53a58fcf621cf41315">operations_research::SimpleMinCostFlow::NumArcs</a></div><div class="ttdeci">ArcIndex NumArcs() const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_a7cd2dc0776a9f339b56ffac996a7df8c"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#a7cd2dc0776a9f339b56ffac996a7df8c">operations_research::SimpleMinCostFlow::SetNodeSupply</a></div><div class="ttdeci">void SetNodeSupply(NodeIndex node, FlowQuantity supply)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_a9dcd8610149406a1593d2a0725290482"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#a9dcd8610149406a1593d2a0725290482">operations_research::SimpleMinCostFlow::Capacity</a></div><div class="ttdeci">FlowQuantity Capacity(ArcIndex arc) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_aa5f729a6274027e5e5478e4bd76603ca"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#aa5f729a6274027e5e5478e4bd76603ca">operations_research::SimpleMinCostFlow::Head</a></div><div class="ttdeci">NodeIndex Head(ArcIndex arc) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_aafd4139404e4f42af650481c3ff10cc7"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#aafd4139404e4f42af650481c3ff10cc7">operations_research::SimpleMinCostFlow::Supply</a></div><div class="ttdeci">FlowQuantity Supply(NodeIndex node) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_ab49dbdb731f80e626e575bdf66835f46"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#ab49dbdb731f80e626e575bdf66835f46">operations_research::SimpleMinCostFlow::Tail</a></div><div class="ttdeci">NodeIndex Tail(ArcIndex arc) const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_acc2868367f8fd38360a8b5b56cf71bdc"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#acc2868367f8fd38360a8b5b56cf71bdc">operations_research::SimpleMinCostFlow::Solve</a></div><div class="ttdeci">Status Solve()</div><div class="ttdef"><b>Definition:</b> <a href="min__cost__flow_8h_source.html#l00244">min_cost_flow.h:244</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_simple_min_cost_flow_html_ad39ce7ee10c34a3ce1f69f179aa4f1e9"><div class="ttname"><a href="classoperations__research_1_1_simple_min_cost_flow.html#ad39ce7ee10c34a3ce1f69f179aa4f1e9">operations_research::SimpleMinCostFlow::OptimalCost</a></div><div class="ttdeci">CostValue OptimalCost() const</div></div>
<div class="ttc" id="aclassutil_1_1_reverse_arc_static_graph_html"><div class="ttname"><a href="classutil_1_1_reverse_arc_static_graph.html">util::ReverseArcStaticGraph</a></div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00549">graph.h:550</a></div></div>
<div class="ttc" id="aebert__graph_8h_html"><div class="ttname"><a href="ebert__graph_8h.html">ebert_graph.h</a></div></div>
<div class="ttc" id="agraph_8h_html"><div class="ttname"><a href="graph_8h.html">graph.h</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdef"><b>Definition:</b> <a href="christofides_8h_source.html#l00043">christofides.h:43</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html_a03fc0981d2d99da114ccd8b3abc0c6e1"><div class="ttname"><a href="namespaceoperations__research.html#a03fc0981d2d99da114ccd8b3abc0c6e1">operations_research::QuantityArray</a></div><div class="ttdeci">ZVector&lt; FlowQuantity &gt; QuantityArray</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00210">ebert_graph.h:210</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html_a1d1a935ab48f768867fc7e8607ca97b4"><div class="ttname"><a href="namespaceoperations__research.html#a1d1a935ab48f768867fc7e8607ca97b4">operations_research::CostValue</a></div><div class="ttdeci">int64_t CostValue</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00204">ebert_graph.h:204</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html_a259d58fc853dd928f2148dbcf1ef25cd"><div class="ttname"><a href="namespaceoperations__research.html#a259d58fc853dd928f2148dbcf1ef25cd">operations_research::FlowQuantity</a></div><div class="ttdeci">int64_t FlowQuantity</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00203">ebert_graph.h:203</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html_a7ffcae041a5d746371436101400cdb6b"><div class="ttname"><a href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">operations_research::NodeIndex</a></div><div class="ttdeci">int32_t NodeIndex</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00201">ebert_graph.h:193</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html_acbdd6fd1484828a3d5e809c551ba8cf7"><div class="ttname"><a href="namespaceoperations__research.html#acbdd6fd1484828a3d5e809c551ba8cf7">operations_research::CostArray</a></div><div class="ttdeci">ZVector&lt; CostValue &gt; CostArray</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00211">ebert_graph.h:211</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html_aecf320bda6e95d1edaf3a546673e3e6b"><div class="ttname"><a href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">operations_research::ArcIndex</a></div><div class="ttdeci">int32_t ArcIndex</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00202">ebert_graph.h:202</a></div></div>
<div class="ttc" id="anamespaceutil_html_a2f76166dbe0c4055a1f256235ad00478"><div class="ttname"><a href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">util::Graph</a></div><div class="ttdeci">ListGraph Graph</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l02361">graph.h:2361</a></div></div>
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