poj 2914 全局最小割入门+Stoer_Wagner模板

最新推荐文章于 2024-08-01 16:22:04 发布

AC_Lee

最新推荐文章于 2024-08-01 16:22:04 发布

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本文介绍了一个经典的图论问题——寻找无向图中的最小割。通过详细的算法解释和代码实现，展示了如何利用Stoer-Wagner算法高效地找到连接图中两个部分所需的最少边数。

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题目：

Minimum Cut

Time Limit: 10000MS		Memory Limit: 65536K
Total Submissions: 9496		Accepted: 3981
Case Time Limit: 5000MS

Description

Given an undirected graph, in which two vertices can be connected by multiple edges, what is the size of the minimum cut of the graph? i.e. how many edges must be removed at least to disconnect the graph into two subgraphs?

Input

Input contains multiple test cases. Each test case starts with two integers N and M (2 ≤ N ≤ 500, 0 ≤ M ≤ N × (N − 1) ⁄ 2) in one line, where N is the number of vertices. Following are M lines, each line contains M integers A, B and C (0 ≤ A, B < N, A ≠ B, C > 0), meaning that there C edges connecting vertices A and B.

Output

There is only one line for each test case, which contains the size of the minimum cut of the graph. If the graph is disconnected, print 0.

Sample Input

Sample Output

2
1
2

全局最小割直接上模板...

板子用的时候注意顶点下标需要从1到n

代码：

#include <iostream>
#include <cstdio>
#include <string.h>
using namespace std;
const int maxn=510;
const int inf=0x3f3f3f3f;

int n,m,s,v[maxn],mat[maxn][maxn],dis[maxn];
bool vis[maxn];

int Stoer_Wagner(int n){
    int i, j;
    int res = inf;
    for (i = 0; i < n; i++)
        v[i] = i+1;//初始化第i个结点就是i
    while (n > 1)
    {
        int maxp = 1,prev = 0;
        for (i = 1; i < n; i++) //初始化到已圈集合的割大小,并找出最大距离的顶点
        {
            dis[v[i]] = mat[v[0]][v[i]];
            if (dis[v[i]] > dis[v[maxp]])
                maxp = i;
        }
        memset(vis, 0, sizeof(vis));
        vis[v[0]] = true;
        for (i = 1; i < n; i++)
        {
            if (i == n - 1)  //只剩最后一个没加入集合的点，更新最小割
            {
                res = min(res,dis[v[maxp]]);
                for (j = 0; j < n; j++)  //合并最后一个点以及推出它的集合中的点
                {
                    mat[v[prev]][v[j]] += mat[v[j]][v[maxp]];
                    mat[v[j]][v[prev]] = mat[v[prev]][v[j]];
                }
                v[maxp] = v[--n];//第maxp个节点去掉，第n个节点变成第maxp个
            }
            vis[v[maxp]] = true;
            prev = maxp;
            maxp = -1;
            for (j = 1; j < n; j++)
                if (!vis[v[j]])  //将上次求的maxp加入集合，合并与它相邻的边到割集
                {
                    dis[v[j]] += mat[v[prev]][v[j]];
                    if (maxp == -1 || dis[v[maxp]] < dis[v[j]])
                        maxp = j;
                }
        }
    }
    return res;
}

int main(){//904MS	1928K
    while (scanf("%d%d",&n,&m)==2){
        memset(mat,0,sizeof (mat));
        int x,y,z;
        while(m--){
            scanf("%d%d%d",&x,&y,&z);
            mat[x+1][y+1] += z;
            mat[y+1][x+1] += z;
        }
        printf("%d\n",Stoer_Wagner(n));
    }
}