POJ 1679 The Unique MST 次小生成树

http://poj.org/problem?id=1679

问图的最小生成树是否唯一。

如果次小生成树结果=最小生成树，那么最小生成树就不唯一。

暴力删属于最小生成树的边，在跑kruskal即可。

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
struct Edge { int u, v, w; } e[10005];
bool operator<(const Edge &a, const Edge &b) { return a.w < b.w; }
int fa[105], mark[10005], re[10005];
int find(int i) { return fa[i] == i ? i : fa[i] = find(fa[i]); }
int kruskal(int n, int m, int d, int *f) {
int ans = 0, i, sets = n;
for (i = 1; i <= n; ++i) fa[i] = i;
for (i = 0; i < m; ++i)
if (i != d && find(e[i].u) != find(e[i].v)) {
fa[find(e[i].u)] = find(e[i].v);
ans += e[i].w; --sets; f[i] = 1;
if (sets == 1) break;
}
return sets == 1 ? ans : -1;
}
int main() {
int n, m, t, i;
scanf("%d", &t);
while (t--) {
scanf("%d%d", &n, &m);
for (i = 0; i < m; ++i) scanf("%d%d%d", &e[i].u, &e[i].v, &e[i].w);
sort(e, e + m); memset(mark, 0, sizeof mark);
int ans = kruskal(n, m, -1, mark);
for (i = 0; i < m; ++i) if (mark[i])
if (kruskal(n, m, i, re) == ans) {
puts("Not Unique!"); break;
}
if (i == m) printf("%d\n", ans);
}
return 0;
}

The Unique MST

Time Limit: 1000MS Memory Limit: 10000K

Total Submissions: 25747 Accepted: 9190

Description

Given a connected undirected graph, tell if its minimum spanning tree is unique.

Definition 1 (Spanning Tree): Consider a connected, undirected graph G = (V, E). A spanning tree of G is a subgraph of G, say T = (V’, E’), with the following properties:

1. V’ = V.

2. T is connected and acyclic.

Definition 2 (Minimum Spanning Tree): Consider an edge-weighted, connected, undirected graph G = (V, E). The minimum spanning tree T = (V, E’) of G is the spanning tree that has the smallest total cost. The total cost of T means the sum of the weights on all the edges in E’.

Input

The first line contains a single integer t (1 <= t <= 20), the number of test cases. Each case represents a graph. It begins with a line containing two integers n and m (1 <= n <= 100), the number of nodes and edges. Each of the following m lines contains a triple (xi, yi, wi), indicating that xi and yi are connected by an edge with weight = wi. For any two nodes, there is at most one edge connecting them.

Output

For each input, if the MST is unique, print the total cost of it, or otherwise print the string ‘Not Unique!’.

Sample Input

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

Sample Output

3
Not Unique!