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裸最大流，求最大流一般步骤如下：
（1）所有正向边权初始化为容量，反向边权初始化为0
（2）找增广路
（3）找到则进入（4），否则得到最大流并退出
（4） 增广路上所有边减去最小边权，相应的方向边加上最小边权，然后返回（2）
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 | #include <iostream>#include <cstdio>#include <cmath>#include <cstdlib>#include <cstring>#include <vector>#include <ctime>#include <deque>#include <queue>using namespace std;struct MaxFlow {private: const static int maxn = 2e2 + 7; struct Edge { int u, v, w; Edge(int u = 0, int v = 0, int w = 0): u(u), v(v), w(w) {} }; vector<vector<int> > G; vector<Edge> E; int S, T, maxflow; bool vis[maxn]; int Q[maxn], fa[maxn], Y[maxn], head, tail, flow[maxn];public: void init(int s, int t, int n) { G.clear(); G.resize(n + 2); E.clear(); S = s; T = t; maxflow = 0; } void add(int u, int v, int w) { E.push_back(Edge(u, v, w)); E.push_back(Edge(v, u, 0)); int sz = E.size(); G[u].push_back(sz - 2); G[v].push_back(sz - 1); } bool bfs(int src) { head = tail = 0; memset(vis, 0, sizeof(vis)); Q[tail ++] = src; flow[0] = 0x7fffffff; vis[src] = true; while (head < tail) { int node = Q[head ++]; if (node == T) { maxflow += flow[head - 1]; int p = head - 1; while (p) { E[Y[p]].w -= flow[head - 1]; E[Y[p] ^ 1].w += flow[head - 1]; p = fa[p]; } return true; } for (int i = 0; i < G[node].size(); i ++) { int e = G[node][i]; if (!vis[E[e].v] && E[e].w) { vis[E[e].v] = true; fa[tail] = head - 1; Y[tail] = e; flow[tail] = min(flow[head - 1], E[e].w); Q[tail ++] = E[e].v; } } } return false; } int solve() { while (bfs(S)); return maxflow; }} ;MaxFlow solver;int main() {#ifndef ONLINE_JUDGE freopen("in.txt", "r", stdin);#endif // ONLINE_JUDGE int n, m; while (cin >> m >> n) { solver.init(1, n, n); for (int i = 0; i < m; i ++) { int u, v, w; scanf("%d%d%d", &u, &v, &w); solver.add(u, v, w); } cout << solver.solve() << endl; } return 0;} |
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原文地址：http://www.cnblogs.com/jklongint/p/4675178.html
