最大流Dinic

不断用BFS构造分层网络，用DFS增广。中途用取指的cur优化DFS。

Dinic封装模板：

  1 #include <cstdio>
  2 #include <iostream>
  3 #include <algorithm>
  4 #include <cstring>
  5 #include <cmath>
  6 #include <queue>
  7 using namespace std;
  8 typedef long long L;
  9 const int maxn = 10000 + 10;
 10 const int maxm = 80000 + 10;
 11 const int INF = -1u >> 1;
 12 int fch[maxn], n, m;
 13 L ans = 0;
 14 bool vis[maxn];
 15 struct Tedge{
 16     int from, to, cap, flow, next;
 17 }adj[maxm];
 18 struct Dinic{
 19     int S, T, n, ms;
 20     int d[maxn], cur[maxn], fch[maxn];
 21     void init(int n){
 22         this -> n = n;
 23         memset(fch, -1, sizeof(fch));
 24         ms = 0;
 25         return ;
 26     }
 27     void AddEdge(int u, int v, int c){
 28         adj[ms] = (Tedge){u, v, c, 0, fch[u]};
 29         fch[u] = ms ++;
 30         adj[ms] = (Tedge){v, u, 0, 0, fch[v]};
 31         fch[v] = ms ++;
 32         return ;
 33     }
 34     bool BFS(){
 35         memset(vis, 0, sizeof(vis));
 36         queue<int> Q;
 37         Q.push(S); vis[S] = true; d[S] = 0;
 38         while(!Q.empty()){
 39             int x = Q.front(); Q.pop();
 40             for(int i = fch[x]; i != -1; i = adj[i].next){
 41                 Tedge& e = adj[i];
 42                 if(!vis[e.to] && e.cap > e.flow){
 43                     vis[e.to] = true;
 44                     d[e.to] = d[x] + 1;
 45                     Q.push(e.to);
 46                 }
 47             }
 48         }
 49         return vis[T];
 50     }
 51     int DFS(int x, int a){
 52         if(x == T || !a) return a;
 53         int flow = 0, f;
 54         for(int& i = cur[x]; i != -1; i = adj[i].next){
 55             Tedge& e = adj[i];
 56             if(d[e.to] == d[x] + 1 && (f = DFS(e.to, min(a, e.cap - e.flow))) > 0){
 57                 flow += f;
 58                 a -= f;
 59                 e.flow += f;
 60                 adj[i ^ 1].flow -= f;
 61                 if(!a) break;
 62             }
 63         }
 64         return flow;
 65     }
 66     L Max_Flow(int S, int T){
 67         this -> S = S;
 68         this -> T = T;
 69         L flow = 0;
 70         while(BFS()){
 71             for(int i = 0; i < n; i ++) cur[i] = fch[i];
 72             flow += DFS(S, INF);
 73         }
 74         return flow;
 75     }
 76 }sol;
 77 void read(int &x){
 78     x = 0; int sig = 1; char ch = getchar();
 79     while(!isdigit(ch)) { if(ch == ‘-‘) sig = -1; ch = getchar(); }
 80     while(isdigit(ch)) x = 10 * x + ch - ‘0‘, ch = getchar();
 81     x *= sig; return ;
 82 }
 83 void init(){
 84     read(n); read(m);
 85     sol.init(n);
 86     int u, v, w;
 87     for(int i = 0; i < m; i++){
 88         read(u); read(v); read(w);
 89         sol.AddEdge(u, v, w);
 90     }
 91     return ;
 92 }
 93 void work(){
 94     ans = sol.Max_Flow(1, n);
 95     return ;
 96 }
 97 void print(){
 98     printf("%lld\n", ans);
 99     return ;
100 }
101 int main(){
102     init();
103     work();
104     print();
105     return 0;
106 }