二分图最大匹配——匈牙利算法

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DFS实现，适用于稠密图：(复杂度O(VE))

#include<bits/stdc++.h>using namespace std;const int mx = 105;vector<int> G[mx];int match[mx]; ///match表示匹配的对象编号bool vis[mx];bool dfs(int i){vis[i] = true;for (int j = 0; j < G[i].size(); ++j){int v = G[i][j], mv = match[v];if (mv < 0 || !vis[mv] && dfs(mv)){match[v] = mv;match[mv] = v;return true;}}return false;}///返回匹配的对数int maxmatch(int n){int ans = 0;memset(match, -1, sizeof(match));for (int i = 0; i < n; ++i)if (match[i] < 0){memset(vis, 0, sizeof(vis));if (dfs(i)) ++ans;}return ans;}

BFS实现，适用于稀疏图：(复杂度O(V^3))

#include<bits/stdc++.h>using namespace std;const int mx = 105;int G[mx][mx];int cx[mx], cy[mx]; ///匹配的对象编号int pred[mx]; /// 记录交错轨和标记Y集合中访问过的点int q[mx]; ///queueint maxmatch(int nx, int ny){int ans = 0, y, sta, fin, i, j;memset(cx, -1, sizeof(cx));memset(cy, -1, sizeof(cy));for (i = 0; i < nx; ++i){if (cx[i] != -1) continue;///对x中的每个未盖点i执行一次bfs找交错轨fill(pred, pred + ny, -2); ///初始值sta = fin = 0;for (j = 0; j < ny; ++j) ///把i的邻接点加入队列if (G[i][j]){pred[j] = -1; ///-1表示遍历到，是邻接点q[fin++] = j;}while (sta < fin) ///BFS{y = q[sta];if (cy[y] == -1) break; ///找到了一个未匹配点，即找到了一条交错轨///若没break说明y已经被匹配给了cy[y]了++sta;for (j = 0; j < ny; ++j)if (pred[j] == -2 && G[cy[y]][j]) ///从cy[y]出发，将它的邻接顶点加入队列{pred[j] = y;q[fin++] = j;}}if (sta == fin) continue; ///未找到交错轨while (pred[y] >= 0) ///更改交错轨上的匹配状态{cx[cy[pred[y]]] = y;cy[y] = cy[pred[y]];y = pred[y];}cx[i] = y, cy[y] = i;++ans;}return ans;}

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