POJ - 1679 The Unique MST （次小生成树）

2
3 3
1 2 1
2 3 2
3 1 3
4 4
1 2 2
2 3 2
3 4 2
4 1 2

3
Not Unique!

题意：求最小生成树是否唯一

思路：次小生成树的应用，先求出最小生成树，然后枚举删除的边，再求最小生成树，如果值一样，代表不唯一

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <queue>
#include <vector>
using namespace std;
const int maxn = 105;
const int inf = 0x3f3f3f3f;

struct Edge {
	int from, to, dist;
} edge[maxn*maxn];
int n, m;
int mst, fa[maxn];
int uni;

int cmp(Edge a, Edge b) {
	return a.dist < b.dist;
}

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

void init() {
	for (int i = 1; i <= n; i++)
		fa[i] = i;
}

void kruskal(){
	int num[maxn], cnt = 0;
	init();
	sort(edge, edge+m, cmp);
	mst = 0;
	for (int i = 0; i < m; i++) {
		int x = find(edge[i].from);
		int y = find(edge[i].to);
		if (x != y) {
			fa[y] = x;
			mst += edge[i].dist;
			num[cnt++] = i;  
		}
	}
	uni = 1;
	int ans, tmp;
	for (int k = 0; k < cnt; k++) {
		init();
		ans = 0;
		tmp = 0;
		for (int i = 0; i < m; i++) {
			if (i == num[k])
				continue; 
			int x = find(edge[i].from);
			int y = find(edge[i].to);
			if (x != y) {
				fa[y] = x;
				ans += edge[i].dist;
				tmp++;
			}
		}
		if (tmp != cnt) 
			continue;   
		if (ans == mst) {
			uni = 0;
			return;
		}
	}
}

int main() {
	int t, i, j;
	scanf("%d", &t);
	while(t --){
		scanf("%d%d", &n, &m);
		for(i = 0; i < m; i ++)
			scanf("%d%d%d", &edge[i].from, &edge[i].to, &edge[i].dist);
		kruskal();
		if(!uni)
			printf("Not Unique!\n");
		else printf("%d\n", mst);
	}
	return 0;
}

POJ - 1679 The Unique MST （次小生成树）,布布扣,bubuko.com

POJ - 1679 The Unique MST （次小生成树）

原文：http://blog.csdn.net/u011345136/article/details/38146065