hdu 3987 求割边最少的最小割

http://acm.hdu.edu.cn/showproblem.php?pid=3987

割边必然是满流的边

方法一：

重新建图，将满流的边改为容量为1，非满流的边改为容量为INF。再跑一边最大流就是割边的个数。

（要注意的是，改图的时候，应该对正向边进行判断，cap == 0则为满流）

方法二：

建图时，每条边的cap = cap*(E+1) + 1，则最后的最小割就是max_flow / (E+1) ,割边的个数就是max_flow%(E+1)

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
using namespace std;
const int M_node = 1090,M_edge = 500009,INF = 0x3f3f3f3f;
struct edge
{
int to,cap,next;
bool is_rev;
}edge[M_edge],edge2[M_node];
int head[M_node],level[M_node];
int pre[M_node];
int tot;
int n,m;
int s,t;
int ss,tt;
int vis[M_node];
void init()
{
memset(head,-1,sizeof(head));
tot = 0;
memset(vis,0,sizeof(vis));
}
void add_edge(int u,int v,int cap)
{
edge[tot].to = v;edge[tot].cap = cap;edge[tot].is_rev = false;edge[tot].next = head[u];head[u] = tot++;
edge[tot].to = u;edge[tot].cap = 0;edge[tot].is_rev = true;edge[tot].next = head[v];head[v] = tot++;
}
bool bfs(int s,int t)
{
memset(level,-1,sizeof(level));
level[s] = 0;
queue<int> q;
q.push(s);
while(!q.empty())
{
int v = q.front();
q.pop();
for(int i = head[v];i != -1;i = edge[i].next)
{
int u = edge[i].to;
if(level[u] < 0 && edge[i].cap > 0)
{
level[u] = level[v] + 1;
q.push(u);
}
}
}
return level[t] != -1;
}
int dfs(int v,int t,int f)
{
if(v == t) return f;
for(int &i = pre[v];i != -1;i = edge[i].next)
{
int u = edge[i].to;
if(level[u] > level[v] && edge[i].cap > 0)
{
int d = dfs(u,t,min(f,edge[i].cap));
if(d > 0)
{
edge[i].cap -= d;
edge[i^1].cap += d;
//pre[v] = i;
//printf("i = %d,v = %d,u = %d, d = %d\n",i,v,u,d);
//printf("edge[i].cap = %d\n",edge[i].cap);
return d;
}
}
}
level[v] = -1;
return 0;
}
int max_flow(int s,int t)
{
int flow = 0;
while(bfs(s,t))
{
for(int i = 0;i <= t;i++) pre[i] = head[i];
int f = 0;
while((f = dfs(s,t,INF)) > 0) flow += f;
}
return flow;
}
int main()
{
int T;
scanf("%d",&T);
int kas = 1;
while(T--)
{
scanf("%d%d",&n,&m);
init();
for(int i = 0;i < m;i++)
{
int u,v,cost,b;
scanf("%d%d%d%d",&u,&v,&cost,&b);
if(b)
{
add_edge(u,v,cost);
add_edge(v,u,cost);
}
else add_edge(u,v,cost);
}
s = n;
t = n + 1;
add_edge(s,0,INF);
add_edge(n-1,t,INF);
int ans = max_flow(s,t);
//printf("debug ---- ans = %d\n",ans);
for(int i = 0;i < n;i++)
{
for(int j = head[i];j != -1;j = edge[j].next)
{
if(edge[j].cap == 0 && edge[j].is_rev == false)
{
edge[j].cap = 1;
edge[j^1].cap = 0;
//add_edge(t+1+i,t+1+edge[j].to,1);
//printf("add_edge u = %d,v = %d\n",i,edge[j].to);
}
else if(edge[j].is_rev == false)
{
edge[j].cap = INF;
edge[j^1].cap = 0;
}
//add_edge(t+1+i,t+1+edge[j].to,INF);
}
}
ans = max_flow(s,t);
printf("Case %d: %d\n",kas++,ans);
}
return 0;
}