hdu Pseudoforest

Pseudoforest

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)

Total Submission(s): 157    Accepted Submission(s): 69

Problem Description

In graph theory, a pseudoforest is an undirected graph in which every connected component has at most one cycle. The maximal pseudoforests of G are the pseudoforest subgraphs of G that are not contained within any larger pseudoforest of G. A pesudoforest is larger than another if and only if the total value of the edges is greater than another one’s.

 

Input

The input consists of multiple test cases. The first line of each test case contains two integers, n(0 < n <= 10000), m(0 <= m <= 100000), which are the number of the vertexes and the number of the edges. The next m lines, each line consists of three integers, u, v, c, which means there is an edge with value c (0 < c <= 10000) between u and v. You can assume that there are no loop and no multiple edges. The last test case is followed by a line containing two zeros, which means the end of the input.

 

Output

Output the sum of the value of the edges of the maximum pesudoforest.

 

Sample Input

3 3
0 1 1
1 2 1
2 0 1
4 5
0 1 1
1 2 1
2 3 1
3 0 1
0 2 2
0 0

 

Sample Output

3
5

 

Source

“光庭杯”第五届华中北区程序设计邀请赛 暨 WHU第八届程序设计竞赛

 

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lcy

 

分析：变形的最小生成树（Kruska算法），找到一个森林，使得每棵树都最多有一个环。在每棵树的根上再记录是否有环，以方便合并是判断。

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
int fa[10010], ok[10010];

int find(int x) {
    if (x != fa[x])
        fa[x] = find(fa[x]);
    return fa[x];
}

typedef struct S {
    int u, v, w;
} EDGE;
EDGE edge[100010];

bool cmp(EDGE a, EDGE b) {
    return a.w > b.w;
}

int main() {
    int n, m, a, b, i, j, f1, f2, cnt, ans, k, t, T;
    while (scanf("%d%d", &n, &m) != EOF && n) {
        memset(ok, 0, sizeof (ok));
        for (i = 0; i < n; ++i)
            fa[i] = i;
        cnt = 0;
        ans = 0;
        for (i = 0; i < m; ++i) {
            scanf("%d%d%d", &edge[i].u, &edge[i].v, &edge[i].w);
        }

        sort(edge, edge + m, cmp);

        for (i = 0; i < m; ++i) {
            f1 = find(edge[i].u);
            f2 = find(edge[i].v);
            if (f1 == f2) {
                if (!ok[f1]) {
                    ans += edge[i].w;
                    ok[f1] = 1;
                }
            } else if (f1 != f2) {
                if (ok[f1] && ok[f2])
                    continue;
                else if (ok[f1] && !ok[f2]) {
                    fa[f2] = f1;
                    ans += edge[i].w;
                } else {
                    fa[f1] = f2;
                    ans += edge[i].w;
                }
            }
        }
        printf("%d\n", ans);
    }
    return 0;
}