加权重心(换根DP)

题目

换根DP，手推一下即可。

代码如下：

#include <bits/stdc++.h>
#define int long long
#define MAXN 100010
using namespace std;

int N, A, B, L, C, minn = 0x3f3f3f3f3f3f3f3f, size[MAXN], dp[MAXN];
vector<pair<int, int>> tree[MAXN];

void dfs1(int u, int pa) {
    size[u] = tree[u][0].first;
    for (int i = 1; i < (int) tree[u].size(); i++) {
        int v = tree[u][i].first, w = tree[u][i].second;
        if (v == pa)
            continue;
        dfs1(v, u);
        size[u] += size[v];
        dp[u] += dp[v] + size[v] * w;
    }
}

void dfs(int u, int pa) {
    for (int i = 1; i < (int) tree[u].size(); i++) {
        int v = tree[u][i].first, w = tree[u][i].second;
        if (v == pa)
            continue;
        dp[v] = dp[u] - size[v] * w + (size[1] - size[v]) * w;
        dfs(v, u);
    }
}

signed main () {
    scanf("%lld", &N);
    for (int i = 1; i <= N; i++) {
        scanf("%lld", &C);
        tree[i].push_back({C, 0});
    }
    for (int i = 1; i < N; i ++) {
        scanf("%lld%lld%lld", &A, &B, &L);
        tree[A].push_back({B, L});
        tree[B].push_back({A, L});
    }
    dfs1(1, 0);
    dfs(1, 0);
    for (int i = 1; i <= N; i++) {
        minn = min(minn, dp[i]);
    }
    printf("%lld", minn);
}