【題解】AtCoder ABC160F – Distributing Integers

【題目敘述】https://atcoder.jp/contests/abc160/tasks/abc160_f
【解題想法】樹DP,換根,模逆元

#include <bits/stdc++.h>
using namespace std;

int n, sz[200005], mod = 1e9+7;
vector <int> g[200005];
long long ans[200005], inv[200005];

void build(int x){
    inv[1] = inv[0] = 1;
    for(int i = 2 ; i <= x; i++){
        inv[i] = (mod - mod / i * inv[mod % i] % mod) % mod;
    }
}
int dfs(int x, int pre){
    sz[x] = 1;
    for (int i:g[x]){
        if (i == pre) continue;
        sz[x] += dfs(i, x);
    }
    return sz[x];
}
void dfs2(int x, int pre){
    for (int i:g[x]){
        if (i == pre) continue;
        ans[i] = ans[x]*sz[i]%mod*inv[n-sz[i]]%mod;
        dfs2(i, x);
    }
}

int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cin >> n;
    int x, y;
    for (int i = 1; i < n; i++){
        cin >> x >> y;
        g[x].push_back(y);
        g[y].push_back(x);
    }
    dfs(1, 0);
    build(n);
    ans[1] = 1;
    for (int i = 1; i <= n; i++){
        ans[1] *= i;
        ans[1] %= mod;
        ans[1] *= inv[sz[i]];
        ans[1] %= mod;
    }
    dfs2(1, 0);
    for (int i = 1; i <= n; i++){
        cout << ans[i] << "\n";
    }
}
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