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!’.

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!

代码如下

#include <cstdio>
#include <algorithm>
#include <cstring>
#define N 100005
using namespace std;
struct node{
int a, b, c, n;
bool operator < (const node & A) const{
return c < A.c;
}
}e[N], d[N];
int g[105][105], f[105], h[105], vis[N], v[N], cnt, n, m;
void cr(int a, int b, int c){
d[++cnt].a = a; d[cnt].b = b; d[cnt].c = c; d[cnt].n = h[a]; h[a] = cnt;
}
int find(int x){
return x == f[x]? x: f[x] = find(f[x]);
}
void dfs(int a){
int i, b, j, c;
v[a] = 1;
for(i = h[a]; i; i = d[i].n){
b = d[i].b; c = d[i].c;
if(!v[b]){
v[b] = 1;
for(j = 1; j <= n; j++) if(v[j]) g[b][j] = g[j][b] = max(g[a][j], c);
dfs(b);
}
}
}
int main(){
int i, j, T, ans, a, b, c, flag;
scanf("%d", &T);
while(T--){
memset(v, 0, sizeof(v));
memset(vis, 0, sizeof(vis));
memset(h, 0, sizeof(h));
memset(g, 0, sizeof(g));
ans = cnt = flag = 0;
scanf("%d%d", &n, &m);
for(i = 1; i <= n; i++) f[i] = i;
for(i = 1; i <= m; i++) scanf("%d%d%d", &e[i].a, &e[i].b, &e[i].c);
sort(e + 1, e + i);
for(i = 1; i <= m; i++){
a = find(e[i].a); b = find(e[i].b); c = e[i].c;
if(a != b){
f[a] = b;
cr(a, b, c);
cr(b, a, c);
ans += c;
vis[i] = 1;
}
}
dfs(1);
for(i = 1; i <= m; i++){
if(!vis[i]){
a = e[i].a; b = e[i].b; c = e[i].c;
if(c == g[a][b]) flag = 1;
}
}
if(flag) printf("Not Unique!\n");
else printf("%d\n", ans);
}
return 0;
}