POJ2914 Minimum Cut 【全域最小割】（Stoer_Wagner）

標籤：poj2914

Minimum Cut

Time Limit: 10000MS		Memory Limit: 65536K
Total Submissions: 7610		Accepted: 3203
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 integersA, 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

3 30 1 11 2 12 0 14 30 1 11 2 12 3 18 140 1 10 2 10 3 11 2 11 3 12 3 14 5 14 6 14 7 15 6 15 7 16 7 14 0 17 3 1

Sample Output

212

Source

Baidu Star 2006 Semifinal 
Wang, Ying (Originator) 
Chen, Shixi (Test cases)題意：求裸的最小割。題解：過程有點像求“最大產生樹”，每次找到將最後的點（即割點值最小的點）隔離出去的最小割大小nowcut，然後用nowcut更新結果mincut，然後將最後兩個點合并，方式是將最後一個點合并到倒數第二個點，邊也都合并過去，就這樣迴圈下去直到只剩下一個頂點，此時mincut即為所求。

#include <stdio.h>#include <string.h>#define inf 0x7fffffff#define maxn 502int map[maxn][maxn], W[maxn], hash[maxn];bool vis[maxn];void getMap(int n, int m){    int i, u, v, c;    memset(map, 0, sizeof(map));    for(i = 0; i < m; ++i){        scanf("%d%d%d", &u, &v, &c);        map[u][v] += c; map[v][u] += c;    }}int Stoer_Wagner(int n){    int minCut = inf, nowCut, now, pre, i, j;    for(i = 0; i < n; ++i) hash[i] = i;    while(n > 1){        nowCut = -1; now = 1; vis[hash[0]] = 1; pre = 0;        for(i = 1; i < n; ++i){            W[hash[i]] = map[hash[0]][hash[i]];            vis[hash[i]] = 0;            if(W[hash[i]] > nowCut){                nowCut = W[hash[i]]; now = i;            }        }        for(j = 1; j < n; ++j){            vis[hash[now]] = 1;            if(j == n - 1){                if(nowCut < minCut) minCut = nowCut;                for(i = 0; i < n; ++i){                    map[hash[pre]][hash[i]] += map[hash[now]][hash[i]];                    map[hash[i]][hash[pre]] += map[hash[now]][hash[i]];                }                hash[now] = hash[--n];                break;            }            pre = now; nowCut = -1;            for(i = 1; i < n; ++i){                if(!vis[hash[i]]){                    W[hash[i]] += map[hash[pre]][hash[i]];                    if(W[hash[i]] > nowCut){                        nowCut = W[hash[i]]; now = i;                    }                }            }        }    }    return minCut;}void solve(int n){    printf("%d\n", Stoer_Wagner(n));}int main(){    freopen("stdin.txt", "r", stdin);    int n, m;    while(scanf("%d%d", &n, &m) == 2){        getMap(n, m);        solve(n);    }    return 0;}

POJ2914 Minimum Cut 【全域最小割】（Stoer_Wagner）