Dinic算法模板

Posted 2020-08-24 Shadowdsp

详解：http://blog.csdn.net/wall_f/article/details/8207595

算法时间复杂度：O（E * V * V）

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <queue>
 4 #include <vector>
 5 using namespace std;
 6 #define N 105
 7 #define M 1010
 8 #define INF 0x3f3f3f3f
 9 
10 struct Edge {
11     int u, v, cap;
12     Edge () {}
13     Edge (int u, int v, int cap) : u (u), v (v), cap (cap) {}
14 }edge[N*N];
15 vector<int> G[N];
16 int S, T, cur[N], dis[N], tot;
17 
18 void Addedge(int u, int v, int cap) {
19     G[u].push_back(tot);
20     edge[tot++] = Edge(u, v, cap);
21     G[v].push_back(tot);
22     edge[tot++] = Edge(v, u, 0);
23 }
24 
25 int BFS() { // 找层次图
26     queue<int> que;
27     while(!que.empty()) que.pop();
28     memset(dis, INF, sizeof(dis));
29     que.push(S);
30     dis[S] = 0;
31     while(!que.empty()) {
32         int u = que.front(); que.pop();
33         for(int i = 0; i < G[u].size(); i++) {
34             Edge &e = edge[G[u][i]];
35             if(dis[e.v] == INF && e.cap > 0) {
36                 dis[e.v] = dis[u] + 1;
37                 que.push(e.v);
38             }
39         }
40     }
41     return dis[T] != INF;
42 }
43 
44 int DFS(int u, int maxflow) { // 找增广路
45     if(u == T) return maxflow; // 
46     for(int i = cur[u]; i < G[u].size(); i++) {
47         cur[u] = i;  // 当前弧优化
48         Edge &e = edge[G[u][i]];
49         if(dis[e.v] == dis[u] + 1 && e.cap > 0) {
50             int flow = DFS(e.v, min(e.cap, maxflow)); // 找到增广路上最小的流量增量
51             if(flow) {
52                 e.cap -= flow;
53                 edge[G[u][i]^1].cap += flow;
54                 return flow;
55             }
56         }
57     }
58     return 0; // 找不到增广路
59 }
60 
61 int Dinic() {
62     int ans = 0;
63     while(BFS()) {
64         int flow;
65         memset(cur, 0, sizeof(cur));
66         while(flow = DFS(S, INF)) ans += flow;
67     }
68     return ans;
69 }