网络流专题之最大流 B - Dining POJ - 3281

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我是题目链接

我自己的建图方式,然后wa了,这样建图错误的原因是会有重边:
然后不死心,想着标记一下边,尝试后发现,标到反边我就糊涂了;
附上错误代码

#include <iostream>
#include <string>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cctype>
#include <vector>
#include <queue>
using namespace std;
const int N = 20100;
const int INF = 0x3f3f3f3f;
struct edge
{
    int to, cap, next;
} g[N*100];
int level[N], iter[N], head[N], que[N];
int n, m, cnt;
int a[N],b[N];
int vis[1000][1000];
int bis[1000][1000];
void add_edge(int v, int u, int cap)
{
    g[cnt].to = u, g[cnt].cap = cap, g[cnt].next = head[v], head[v] = cnt++;
    g[cnt].to = v, g[cnt].cap = 0, g[cnt].next = head[u], head[u] = cnt++;
}
bool bfs(int s, int t)
{
    memset(level, -1, sizeof level);
    level[s] = 0;
    int st = 0, en = 0;
    que[0] = s;
    while(st <= en)
    {
        int v = que[st++];
        for(int i = head[v]; i != -1; i = g[i].next)
        {
            int u = g[i].to;
            if(g[i].cap > 0 && level[u] < 0)
            {
                level[u] = level[v] + 1;
                que[++en] = u;
            }
        }
    }
    return level[t] == -1;
}
int dfs(int v, int t, int f)
{
    if(v == t) return f;
    int tm = f;
    for(int &i = iter[v]; i != -1; i = g[i].next)
    {
        int u = g[i].to;
        if(g[i].cap > 0 && level[v] < level[u])
        {
            int d = dfs(u, t, min(tm, g[i].cap));
            g[i].cap -= d, g[i^1].cap += d, tm -= d;
            if(tm == 0) break;
        }
    }
    if(tm == f) level[v] = -1;
    return f - tm;
}
int dinic(int s, int t)
{
    int flow = 0, f;
    while(true)
    {
        if(bfs(s, t)) return flow;
        memcpy(iter, head, sizeof head);
        flow += dfs(s, t, INF);
    }
}
int main()
{

    int f,d;
    while(~scanf("%d%d%d",&n,&f,&d))
    {
        cnt=0;
        memset(head, -1, sizeof head);
        memset(vis,0,sizeof(vis));
        memset(bis,-1,sizeof(bis));
        int s=0,t=n+f+d+1;
        for(int i=1; i<=n; i++)
        {
            add_edge(s,i,1);   //起点和牛
            int f1,d1;
            scanf("%d%d",&f1,&d1);
            for(int j=1; j<=f1; j++)
            {
                scanf("%d",&a[j]);
                add_edge(i,a[j]+n,1);//牛和饭
            }
            for(int j=1; j<=d1; j++)
            {
                scanf("%d",&b[j]);
                add_edge(b[j]+n+f,t,1);//菜和终点
            }
            for(int i=1; i<f1; i++)
            {
                for(int j=1; j<=d1; j++)
                {
                    if(vis[a[i]+n][b[j]+n+f]==0&&bis[b[j]+n+f][a[i]+n]==-1)
                    {
                        add_edge(a[i]+n,b[j]+n+f,1);
                        vis[a[i]+n][b[j]+n+f]=1; //饭和菜
                        bis[b[j]+n+f][a[i]+n]=0;
                    }

                }
            }
        }
        printf("%d\n", dinic(0, t));

    }
}

这里写图片描述

正确的建图方式:拆点,将牛拆出一个副本,让牛1和牛11的容量为1,其他的如图所示,这样避免了重边:

这里写图片描述

正确代码:

#include <iostream>
#include <string>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cctype>
#include <vector>
#include <queue>
using namespace std;
const int N = 20100;
const int INF = 0x3f3f3f3f;
struct edge
{
    int to, cap, next;
} g[N*100];
int level[N], iter[N], head[N], que[N];
int n, m, cnt;
int a[N],b[N];
void add_edge(int v, int u, int cap)
{
    g[cnt].to = u, g[cnt].cap = cap, g[cnt].next = head[v], head[v] = cnt++;
    g[cnt].to = v, g[cnt].cap = 0, g[cnt].next = head[u], head[u] = cnt++;
}
bool bfs(int s, int t)
{
    memset(level, -1, sizeof (level));
    level[s] = 0;
    int st = 0, en = 0;
    que[0] = s;
    while(st <= en)
    {
        int v = que[st++];
        for(int i = head[v]; i != -1; i = g[i].next)
        {
            int u = g[i].to;
            if(g[i].cap > 0 && level[u] < 0)
            {
                level[u] = level[v] + 1;
                que[++en] = u;
            }
        }
    }
    return level[t] == -1;
}
int dfs(int v, int t, int f)
{
    if(v == t) return f;
    int tm = f;
    for(int &i = iter[v]; i != -1; i = g[i].next)
    {
        int u = g[i].to;
        if(g[i].cap > 0 && level[v] < level[u])
        {
            int d = dfs(u, t, min(tm, g[i].cap));
            g[i].cap -= d, g[i^1].cap += d, tm -= d;
            if(tm == 0) break;
        }
    }
    if(tm == f) level[v] = -1;
    return f - tm;
}
int dinic(int s, int t)
{
    int flow = 0, f;
    while(true)
    {
        if(bfs(s, t)) return flow;
        memcpy(iter, head, sizeof head);
        flow += dfs(s, t, INF);
    }
}
int main()
{
    int f,d;
    while(~scanf("%d%d%d",&n,&f,&d))
    {
        cnt=0;
        memset(head, -1, sizeof head);
        int s=0,t=n+f+n+d+1;
        for(int i=1;i<=n;i++)
        {
              add_edge(i+f,i+f+n,1);//牛1和牛11;
        }
        for(int i=1; i<=f; i++)
        {
            add_edge(s,i,1);//起点和饭;
        }
        for(int i=1; i<=d; i++)
        {
            add_edge(i+f+n+n,t,1);//菜和终点;
        }
        for(int i=1; i<=n; i++)
        {
            int f1,d1;
            scanf("%d%d",&f1,&d1);
            for(int j=1; j<=f1; j++)//饭和牛1
            {
                scanf("%d",&a[j]);
                add_edge(a[j],i+f,1);
            }
            for(int j=1; j<=d1; j++)//牛11和菜
            {
                scanf("%d",&b[j]);
                add_edge(i+f+n,b[j]+f+n+n,1);
            }
        }
        printf("%d\n",dinic(s,t));
    }
}

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转载自blog.csdn.net/wuxiaowu547/article/details/82117518