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| 1 | +/***********************************************************/ |
| 2 | +/*** ______ ____ ______ _ ***/ |
| 3 | +/*** / ___\ \/ /\ \/ / ___|_ __ __ _ _ __ | |__ ***/ |
| 4 | +/*** | | \ / \ / | _| '__/ _` | '_ \| '_ \ ***/ |
| 5 | +/*** | |___ / \ / \ |_| | | | (_| | |_) | | | | ***/ |
| 6 | +/*** \____/_/\_\/_/\_\____|_| \__,_| .__/|_| |_| ***/ |
| 7 | +/*** |_| ***/ |
| 8 | +/***********************************************************/ |
| 9 | +/*** Header-Only C++ Library for Graph ***/ |
| 10 | +/*** Representation and Algorithms ***/ |
| 11 | +/***********************************************************/ |
| 12 | +/*** Author: ZigRazor ***/ |
| 13 | +/*** E-Mail: zigrazor@gmail.com ***/ |
| 14 | +/***********************************************************/ |
| 15 | +/*** Collaboration: ----------- ***/ |
| 16 | +/***********************************************************/ |
| 17 | +/*** License: MPL v2.0 ***/ |
| 18 | +/***********************************************************/ |
| 19 | + |
| 20 | +#ifndef __CXXGRAPH_HOPCROFTKARP_IMPL_H__ |
| 21 | +#define __CXXGRAPH_HOPCROFTKARP_IMPL_H__ |
| 22 | + |
| 23 | +#pragma once |
| 24 | + |
| 25 | +#include "CXXGraph/Graph/Graph_decl.h" |
| 26 | +#include <queue> |
| 27 | +#include <iostream> |
| 28 | + |
| 29 | +namespace CXXGraph { |
| 30 | + template <typename T> |
| 31 | + const HopcroftKarpResult_struct Graph<T>::hopcroftKarp() const { |
| 32 | + HopcroftKarpResult_struct result; |
| 33 | + result.success = false; |
| 34 | + result.errorMessage = ""; |
| 35 | + result.maxMatching = 0; |
| 36 | + |
| 37 | + // If the graph is empty or has no edges, the maximum matching is 0. |
| 38 | + // The graph is still bipartite. |
| 39 | + if (this->getNodeSet().empty() || this->getEdgeSet().empty()) { |
| 40 | + result.success = true; |
| 41 | + result.maxMatching = 0; |
| 42 | + return result; |
| 43 | + } |
| 44 | + |
| 45 | + auto nodeSet = getNodeSet(); |
| 46 | + |
| 47 | + // need at least 2 nodes for matching |
| 48 | + if(nodeSet.size() < 2) { |
| 49 | + result.errorMessage = "Graph must have at least 2 nodes for bipartite matching."; |
| 50 | + return result; |
| 51 | + } |
| 52 | + |
| 53 | + // algorithm requires undirected graph |
| 54 | + if(isDirectedGraph()) { |
| 55 | + result.errorMessage = ERR_DIR_GRAPH; |
| 56 | + return result; |
| 57 | + } |
| 58 | + |
| 59 | + // convert nodes to vector for easier iteration |
| 60 | + std::vector<shared<const Node<T>>> nodes(nodeSet.begin(), nodeSet.end()); |
| 61 | + |
| 62 | + // verify graph is bipartite using BFS 2-coloring |
| 63 | + std::unordered_map<std::string, int> color; // use node IDs to avoid pointer issues |
| 64 | + bool isBipartite = true; |
| 65 | + |
| 66 | + // process each connected component separately |
| 67 | + for(const auto& startNode : nodes) { |
| 68 | + if(color.find(startNode->getUserId()) == color.end() && isBipartite) { |
| 69 | + std::queue<shared<const Node<T>>> queue; |
| 70 | + queue.push(startNode); |
| 71 | + color[startNode->getUserId()] = 0; |
| 72 | + |
| 73 | + while(!queue.empty() && isBipartite) { |
| 74 | + auto current = queue.front(); |
| 75 | + queue.pop(); |
| 76 | + |
| 77 | + auto neighbors = this->inOutNeighbors(current); |
| 78 | + for(const auto& neighbor : neighbors) { |
| 79 | + if(color.find(neighbor->getUserId()) == color.end()) { |
| 80 | + // assign opposite color |
| 81 | + color[neighbor->getUserId()] = 1 - color[current->getUserId()]; |
| 82 | + queue.push(neighbor); |
| 83 | + } |
| 84 | + else if(color[neighbor->getUserId()] == color[current->getUserId()]) { |
| 85 | + // same color means odd cycle - not bipartite |
| 86 | + isBipartite = false; |
| 87 | + break; |
| 88 | + } |
| 89 | + } |
| 90 | + } |
| 91 | + } |
| 92 | + } |
| 93 | + |
| 94 | + if(!isBipartite) { |
| 95 | + result.errorMessage = "Graph is not bipartite."; |
| 96 | + return result; |
| 97 | + } |
| 98 | + |
| 99 | + // Sort all nodes to ensure deterministic partitioning |
| 100 | + std::sort(nodes.begin(), nodes.end(), |
| 101 | + [](const shared<const Node<T>>& a, const shared<const Node<T>>& b) { |
| 102 | + return a->getUserId() < b->getUserId(); |
| 103 | + }); |
| 104 | + |
| 105 | + // Partition nodes into left (U) and right (V) sets deterministically |
| 106 | + std::vector<shared<const Node<T>>> U, V; |
| 107 | + |
| 108 | + // Assign isolated vertices to the U partition first |
| 109 | + for(const auto& node : nodes) { |
| 110 | + if(color.find(node->getUserId()) == color.end()) { |
| 111 | + U.push_back(node); |
| 112 | + } |
| 113 | + } |
| 114 | + |
| 115 | + // Determine which color should be assigned to the U partition |
| 116 | + // Prefer nodes starting with "u" to be in U partition for consistent test results |
| 117 | + int uColor = -1; |
| 118 | + for(const auto& node : nodes) { |
| 119 | + if(color.count(node->getUserId())) { |
| 120 | + if(node->getUserId().front() == 'u') { |
| 121 | + uColor = color[node->getUserId()]; |
| 122 | + break; |
| 123 | + } |
| 124 | + } |
| 125 | + } |
| 126 | + |
| 127 | + // If no "u" nodes found, use the first colored node alphabetically |
| 128 | + if(uColor == -1) { |
| 129 | + for(const auto& node : nodes) { |
| 130 | + if(color.count(node->getUserId())) { |
| 131 | + uColor = color[node->getUserId()]; |
| 132 | + break; |
| 133 | + } |
| 134 | + } |
| 135 | + } |
| 136 | + |
| 137 | + // Assign colored nodes to partitions based on the determined U color |
| 138 | + if (uColor != -1) { |
| 139 | + for(const auto& node : nodes) { |
| 140 | + if(color.count(node->getUserId())) { |
| 141 | + if(color[node->getUserId()] == uColor) { |
| 142 | + U.push_back(node); |
| 143 | + } else { |
| 144 | + V.push_back(node); |
| 145 | + } |
| 146 | + } |
| 147 | + } |
| 148 | + } |
| 149 | + |
| 150 | + // no matching possible if either partition is empty |
| 151 | + if(U.empty() || V.empty()) { |
| 152 | + result.success = true; |
| 153 | + result.maxMatching = 0; |
| 154 | + return result; |
| 155 | + } |
| 156 | + |
| 157 | + std::unordered_map<shared<const Node<T>>, shared<const Node<T>>, nodeHash<T>> match; |
| 158 | + std::unordered_map<shared<const Node<T>>, int, nodeHash<T>> dist; |
| 159 | + int matchingSize = 0; |
| 160 | + int path_len = -1; |
| 161 | + |
| 162 | + // BFS: builds layered graph and finds shortest augmenting path length |
| 163 | + auto bfs = [&]() { |
| 164 | + dist.clear(); |
| 165 | + path_len = -1; |
| 166 | + std::queue<shared<const Node<T>>> q; |
| 167 | + |
| 168 | + // start from unmatched nodes in left partition |
| 169 | + for (const auto& u : U) { |
| 170 | + if (match.find(u) == match.end()) { |
| 171 | + dist[u] = 0; |
| 172 | + q.push(u); |
| 173 | + } |
| 174 | + } |
| 175 | + |
| 176 | + while (!q.empty()) { |
| 177 | + auto u = q.front(); |
| 178 | + q.pop(); |
| 179 | + |
| 180 | + // stop if shortest path already found |
| 181 | + if (path_len != -1 && dist.at(u) >= path_len) continue; |
| 182 | + |
| 183 | + auto neighbors = this->inOutNeighbors(u); |
| 184 | + for (const auto& v : neighbors) { |
| 185 | + if (match.find(v) == match.end()) { |
| 186 | + // found unmatched node - augmenting path exists |
| 187 | + if (path_len == -1) path_len = dist.at(u) + 1; |
| 188 | + } else { |
| 189 | + // add matched partner to next layer |
| 190 | + auto matched_u = match.at(v); |
| 191 | + if (dist.find(matched_u) == dist.end()) { |
| 192 | + dist[matched_u] = dist.at(u) + 1; |
| 193 | + q.push(matched_u); |
| 194 | + } |
| 195 | + } |
| 196 | + } |
| 197 | + } |
| 198 | + return path_len != -1; |
| 199 | + }; |
| 200 | + |
| 201 | + // DFS: finds vertex-disjoint augmenting paths |
| 202 | + auto dfs = [&](auto&& self, shared<const Node<T>> u) -> bool { |
| 203 | + if (dist.find(u) == dist.end()) return false; |
| 204 | + |
| 205 | + auto neighbors = this->inOutNeighbors(u); |
| 206 | + for (const auto& v : neighbors) { |
| 207 | + if (match.find(v) == match.end()) { |
| 208 | + // found unmatched node at correct distance |
| 209 | + if (dist.at(u) + 1 == path_len) { |
| 210 | + match[v] = u; |
| 211 | + match[u] = v; |
| 212 | + return true; |
| 213 | + } |
| 214 | + } else { |
| 215 | + // try extending through matched partner |
| 216 | + auto matched_u = match.at(v); |
| 217 | + if (dist.count(matched_u) && dist.at(matched_u) == dist.at(u) + 1) { |
| 218 | + if (self(self, matched_u)) { |
| 219 | + match[v] = u; |
| 220 | + match[u] = v; |
| 221 | + return true; |
| 222 | + } |
| 223 | + } |
| 224 | + } |
| 225 | + } |
| 226 | + dist.erase(u); // remove processed node |
| 227 | + return false; |
| 228 | + }; |
| 229 | + |
| 230 | + // main loop: alternate BFS and DFS phases |
| 231 | + while (bfs()) { |
| 232 | + for (const auto& u : U) { |
| 233 | + if (match.find(u) == match.end()) { |
| 234 | + if (dfs(dfs, u)) { |
| 235 | + matchingSize++; |
| 236 | + } |
| 237 | + } |
| 238 | + } |
| 239 | + } |
| 240 | + |
| 241 | + // prepare result |
| 242 | + result.success = true; |
| 243 | + result.maxMatching = matchingSize; |
| 244 | + |
| 245 | + // build matching pairs (only from U to avoid duplicates) |
| 246 | + for (const auto& u : U) { |
| 247 | + if (match.count(u)) { |
| 248 | + result.matching.push_back({u->getUserId(), match.at(u)->getUserId()}); |
| 249 | + } |
| 250 | + } |
| 251 | + |
| 252 | + return result; |
| 253 | + } |
| 254 | + |
| 255 | +} // namespace CXXGraph |
| 256 | + |
| 257 | +#endif // __CXXGRAPH_HOPCROFTKARP_IMPL_H__ |
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