POJ1679

題目鏈接：http://poj.org/problem?id=1679

問給出的圖中的最小生成樹是否唯一。

我們求次小生成樹，如果兩個生成樹的權值和相等，說明最小生成樹不唯一。

這裏我使用了kruskal，遍歷最小生成樹中的邊，刪除後重新求最小生成樹，來確定次小生成樹。

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
using namespace std;
const int INF = 1e9+10;

struct Edge{
    int from, to, len;
}e[10005];

int used[205], n, m;
int cnt, father[205];

int fnd(int x){
    if (father[x] != x) father[x] = fnd(father[x]);
    return father[x];
}

bool uni(int x, int y){
    int fx = fnd(x), fy = fnd(y);
    if (fx == fy) return false;
    father[fx] = fy;
    return true;
}


bool cmp(Edge a, Edge b){
    return a.len < b.len;
}

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

int kruskal(int use){
    int ans = 0, num = 0;
    for (int i = 1; i <= m; i++){
        if (i == use) continue;
        int from = e[i].from, to = e[i].to, len = e[i].len;
        if (uni(from, to)){
            ans += len; num++;
            if (use == 0) used[++cnt] = i;
        }
    }
    if (num < n-1) return -1;
    return ans;
}

int main(){
    std::ios::sync_with_stdio(false);
    int T;
    cin >> T;
    while(T--){
        cin >> n >> m; cnt = 0;
        for (int i = 1; i <= m; i++){
            int from, to, len;
            cin >> from >> to >> len;
            e[i] = Edge{from, to, len};
        }
        init();
        sort(e+1, e+m+1, cmp);
        int ans = kruskal(0);
        int ans2 = INF;
        for (int i = 1; i <= cnt; i++) init(), ans2 = min(ans2, kruskal(used[i]));

        if (ans2 == ans) cout << "Not Unique!" << endl;
        else cout << ans << endl;
    }
    return 0;
}