【模板】网络流

来源：互联网发布：js search汉字编辑：程序博客网时间：2024/05/17 04:36

1.边从2标号算起，j和j^1互为反边。

2.棋盘一般都是二分图模型，连边注意方向！

3.分配限制用最大流卡流，取舍限制用最小割决策。

常见模型：最大匹配模型、最小割模型、最小路径覆盖模型

有时候需要配合二分。

Code:

#include<cstdio>#include<algorithm>using namespace std;const int Sn = 10010, Sm = 1000010 *2, oo = (int)1e9;int n,m,s,t,la[Sn],to[Sm],nx[Sm],rs[Sm],fy[Sm],dn,bn=1;int ln[Sn],l,r,vis[Sn],V,hei[Sn],top;int next[Sn],hd,tl,tmp,dis[Sn],il[Sn],pp[Sn],pre[Sn];int maxflow,totfy;void link(int u, int v, int w){     bn++, to[bn] = v, rs[bn] = w, nx[bn] = la[u], la[u] = bn;     bn++, to[bn] = u, rs[bn] = 0, nx[bn] = la[v], la[v] = bn;}bool bfs(){     vis[t] = ++V, hei[t] = 1;     for(ln[l=r=1] = t; l <= r; l++)  for(int j = la[ln[l]]; j; j = nx[j])       if(rs[j^1] && vis[to[j]] != V)       {    hei[to[j]] = hei[ln[l]] + 1, vis[to[j]] = V;    ln[++r] = to[j]; if(to[j] == s) return true;       }     return false;}int dfs(int d, int p){     int flow = 0, f;     if(d == t || p == 0) return p;     for(int j = la[d]; j; j = nx[j])  if(vis[to[j]] == V && hei[to[j]] == hei[d] - 1)       if(rs[j] && ( f = dfs(to[j], min(p,rs[j])) ) > 0)       {    rs[j] -= f, rs[j^1] += f;    flow += f, p -= f;    if(!p) return flow;       }     hei[d] = oo;     return flow;}bool spfa(){     for(int i = 1; i <= dn; i ++) dis[i] = oo;     dis[s] = 0, pp[s] = oo; // WA     for(il[hd=tl=s] = true; hd; tmp=hd, hd=next[hd], next[tmp]=il[tmp]=0)  for(int j = la[hd], o; j; j = nx[j])       if(rs[j] && (o = dis[hd] + fy[j]) < dis[to[j]] && o <= dis[t])       {    dis[to[j]] = dis[hd] + fy[j], pp[to[j]] = min(pp[hd], rs[j]);    pre[to[j]] = j ^ 1;    if(!il[to[j]]) { if(hd != tl && dis[to[j]] < dis[next[hd]]) next[to[j]] = next[hd], next[hd] = to[j]; else next[tl] = to[j], tl = to[j];  il[to[j]] = true; }       }     if(dis[t] == oo) return false;     for(int j = t; j != s; j = to[pre[j]])  rs[pre[j]^1] -= pp[t], rs[pre[j]] += pp[t];     totfy += dis[t] * pp[t], maxflow += pp[t];     return true;}