346. 走廊泼水节

思路

看代码就能理解该题思路，核心思想就是按照边权顺序生成完全图，新增的边权设置决定唯一性，证明略。

AC code

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#include <iostream>
#include <cstring>
#include <algorithm>

using namespace std;

const int N = 6010;
int n;
struct Edge{
    int a, b, w;
    bool operator < (const Edge& e) const {
        return w < e.w;
    }
}e[N];
int p[N], s[N];

int find(int x){
    return p[x] == x ? p[x] : p[x] = find(p[x]);
}

int main(){
    int T;
    cin >> T;
    while(T--){
        cin >> n;
        for(int i = 0; i < n - 1; i++){
            int a, b, w;
            cin >> a >> b >> w;
            e[i] = {a, b, w};
        }
        sort(e, e + n - 1);
        for(int i = 1; i <= n; i++) p[i] = i, s[i] = 1;
        
        int res = 0;
        for(int i = 0; i < n - 1; i++){
            int a = find(e[i].a), b = find(e[i].b), w = e[i].w;
            if(a != b){
                res += (s[a] * s[b] - 1) * (w + 1);
                s[b] += s[a];
                p[a] = b;
            }
        }
        cout << res << endl;
    }
    return 0;    
}