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237 lines
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<div class="title">bellman_ford.cc</div> </div>
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<a href="bellman__ford_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include <functional></span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#include <memory></span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include <utility></span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  </div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "<a class="code" href="integral__types_8h.html">ortools/base/integral_types.h</a>"</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include "<a class="code" href="shortestpaths_8h.html">ortools/graph/shortestpaths.h</a>"</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  </div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00023"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bellman_ford.html"> 23</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_bellman_ford.html">BellmanFord</a> {</div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00025"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bellman_ford.html#ad437d1ef7c1ace92a552ef6de9cae7f1"> 25</a></span>  <span class="keyword">static</span> constexpr int64_t <a class="code" href="classoperations__research_1_1_bellman_ford.html#ad437d1ef7c1ace92a552ef6de9cae7f1">kInfinity</a> = <a class="code" href="integral__types_8h.html#a808bd435380aa1e2bbd6f13ac7759897">kint64max</a> / 2;</div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  </div>
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<div class="line"><a name="l00027"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bellman_ford.html#a56ced16ea2e109c940af9336b0ad99d7"> 27</a></span>  <a class="code" href="classoperations__research_1_1_bellman_ford.html#a56ced16ea2e109c940af9336b0ad99d7">BellmanFord</a>(<span class="keywordtype">int</span> node_count, <span class="keywordtype">int</span> start_node,</div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  std::function<int64_t(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph,</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  int64_t disconnected_distance)</div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  : node_count_(node_count),</div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  start_node_(start_node),</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  graph_(std::move(graph)),</div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  disconnected_distance_(disconnected_distance),</div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  distance_(new int64_t[node_count_]),</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  predecessor_(new int[node_count_]) {}</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_bellman_ford.html#a48b9f284876a7bfaa4d6841cac33554e">ShortestPath</a>(<span class="keywordtype">int</span> end_node, std::vector<int>* <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>);</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  </div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keywordtype">void</span> Initialize();</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordtype">void</span> Update();</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordtype">bool</span> Check() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordtype">void</span> FindPath(<span class="keywordtype">int</span> dest, std::vector<int>* <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  </div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> node_count_;</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> start_node_;</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  std::function<int64_t(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph_;</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keyword">const</span> int64_t disconnected_distance_;</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  std::unique_ptr<int64_t[]> distance_;</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  std::unique_ptr<int[]> predecessor_;</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> };</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  </div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="keywordtype">void</span> BellmanFord::Initialize() {</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < node_count_; i++) {</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  distance_[i] = <a class="code" href="integral__types_8h.html#a808bd435380aa1e2bbd6f13ac7759897">kint64max</a> / 2;</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  predecessor_[i] = -1;</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  }</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  distance_[start_node_] = 0;</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> }</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  </div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="keywordtype">void</span> BellmanFord::Update() {</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < node_count_ - 1; i++) {</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> u = 0; u < node_count_; u++) {</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> v = 0; v < node_count_; v++) {</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">const</span> int64_t graph_u_v = graph_(u, v);</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">if</span> (graph_u_v != disconnected_distance_) {</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">const</span> int64_t other_distance = distance_[u] + graph_u_v;</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">if</span> (distance_[v] > other_distance) {</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  distance_[v] = other_distance;</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  predecessor_[v] = u;</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  }</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  }</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  }</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  }</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  }</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> }</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  </div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="keywordtype">bool</span> BellmanFord::Check()<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> u = 0; u < node_count_; u++) {</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> v = 0; v < node_count_; v++) {</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> graph_u_v = graph_(u, v);</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordflow">if</span> (graph_u_v != disconnected_distance_) {</div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordflow">if</span> (distance_[v] > distance_[u] + graph_u_v) {</div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  }</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  }</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  }</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  }</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> }</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  </div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="keywordtype">void</span> BellmanFord::FindPath(<span class="keywordtype">int</span> dest, std::vector<int>* <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keywordtype">int</span> j = dest;</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>->push_back(j);</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">while</span> (predecessor_[j] != -1) {</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>->push_back(predecessor_[j]);</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  j = predecessor_[j];</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  }</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> }</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  </div>
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<div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_bellman_ford.html#a48b9f284876a7bfaa4d6841cac33554e"> 100</a></span> <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_bellman_ford.html#a48b9f284876a7bfaa4d6841cac33554e">BellmanFord::ShortestPath</a>(<span class="keywordtype">int</span> end_node, std::vector<int>* <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>) {</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  Initialize();</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  Update();</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">if</span> (distance_[end_node] == <a class="code" href="classoperations__research_1_1_bellman_ford.html#ad437d1ef7c1ace92a552ef6de9cae7f1">kInfinity</a>) {</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  }</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">if</span> (!Check()) {</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  }</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  FindPath(end_node, <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>);</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> }</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  </div>
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<div class="line"><a name="l00113"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#ad7c912405ec283963f6a4f6dda80c674"> 113</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#ad7c912405ec283963f6a4f6dda80c674">BellmanFordShortestPath</a>(<span class="keywordtype">int</span> node_count, <span class="keywordtype">int</span> start_node, <span class="keywordtype">int</span> end_node,</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  std::function<int64_t(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph,</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  int64_t disconnected_distance,</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  std::vector<int>* <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>) {</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <a class="code" href="classoperations__research_1_1_bellman_ford.html">BellmanFord</a> bf(node_count, start_node, std::move(graph),</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  disconnected_distance);</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keywordflow">return</span> bf.<a class="code" href="classoperations__research_1_1_bellman_ford.html#a48b9f284876a7bfaa4d6841cac33554e">ShortestPath</a>(end_node, <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>);</div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> }</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="ttc" id="aclassoperations__research_1_1_bellman_ford_html"><div class="ttname"><a href="classoperations__research_1_1_bellman_ford.html">operations_research::BellmanFord</a></div><div class="ttdef"><b>Definition:</b> <a href="bellman__ford_8cc_source.html#l00023">bellman_ford.cc:23</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_bellman_ford_html_a48b9f284876a7bfaa4d6841cac33554e"><div class="ttname"><a href="classoperations__research_1_1_bellman_ford.html#a48b9f284876a7bfaa4d6841cac33554e">operations_research::BellmanFord::ShortestPath</a></div><div class="ttdeci">bool ShortestPath(int end_node, std::vector< int > *nodes)</div><div class="ttdef"><b>Definition:</b> <a href="bellman__ford_8cc_source.html#l00100">bellman_ford.cc:100</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_bellman_ford_html_a56ced16ea2e109c940af9336b0ad99d7"><div class="ttname"><a href="classoperations__research_1_1_bellman_ford.html#a56ced16ea2e109c940af9336b0ad99d7">operations_research::BellmanFord::BellmanFord</a></div><div class="ttdeci">BellmanFord(int node_count, int start_node, std::function< int64_t(int, int)> graph, int64_t disconnected_distance)</div><div class="ttdef"><b>Definition:</b> <a href="bellman__ford_8cc_source.html#l00027">bellman_ford.cc:27</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_bellman_ford_html_ad437d1ef7c1ace92a552ef6de9cae7f1"><div class="ttname"><a href="classoperations__research_1_1_bellman_ford.html#ad437d1ef7c1ace92a552ef6de9cae7f1">operations_research::BellmanFord::kInfinity</a></div><div class="ttdeci">static constexpr int64_t kInfinity</div><div class="ttdef"><b>Definition:</b> <a href="bellman__ford_8cc_source.html#l00025">bellman_ford.cc:25</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html"><div class="ttname"><a href="integral__types_8h.html">integral_types.h</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html_a808bd435380aa1e2bbd6f13ac7759897"><div class="ttname"><a href="integral__types_8h.html#a808bd435380aa1e2bbd6f13ac7759897">kint64max</a></div><div class="ttdeci">static const int64_t kint64max</div><div class="ttdef"><b>Definition:</b> <a href="integral__types_8h_source.html#l00032">integral_types.h:32</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ad7c912405ec283963f6a4f6dda80c674"><div class="ttname"><a href="namespaceoperations__research.html#ad7c912405ec283963f6a4f6dda80c674">operations_research::BellmanFordShortestPath</a></div><div class="ttdeci">bool BellmanFordShortestPath(int node_count, int start_node, int end_node, std::function< int64_t(int, int)> graph, int64_t disconnected_distance, std::vector< int > *nodes)</div><div class="ttdef"><b>Definition:</b> <a href="bellman__ford_8cc_source.html#l00113">bellman_ford.cc:113</a></div></div>
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<div class="ttc" id="arouting__search_8cc_html_a6b7983ccd32c86cbbc3d4d9cda4cac17"><div class="ttname"><a href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a></div><div class="ttdeci">int nodes</div><div class="ttdef"><b>Definition:</b> <a href="routing__search_8cc_source.html#l03686">routing_search.cc:3686</a></div></div>
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<div class="ttc" id="ashortestpaths_8h_html"><div class="ttname"><a href="shortestpaths_8h.html">shortestpaths.h</a></div></div>
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