atcoder 160 F

題目：https://atcoder.jp/contests/abc160/tasks/abc160_f

逆元 ：https://blog.csdn.net/qq_35416331/article/details/81059747

換根dp：https://www.cnblogs.com/Kanoon/p/12644109.html 

#include<iostream>
#include<algorithm>
#include<queue>
#include<cmath>
#include<math.h>
#include<string>
#include<string.h>
#include<map>
#include<unordered_map>
#include<unordered_set>
#include<set>
#include<stack>
#include<sstream>
//#include <Eigen/Dense>
//#include <Eigen/Geometry>
//using namespace Eigen;
using namespace std;
 
int n;
const int maxn = 2e5 + 100;
int mod = 1e9 + 7;
vector<int> g[maxn];
int vis[maxn], sz[maxn];
long long ans[maxn], inv[maxn];
 
void inv_n(int n)
{
	inv[1] = 1;
	for (long long i = 2; i <= n; i++)
	{
		inv[i] = inv[mod%i] * (mod - mod / i) % mod;
	}
}
 
 
int dfs1(int cur,int p)
{
	sz[cur] = 1;
	for (int i : g[cur])
	{
		if (i != p)	
			sz[cur] += dfs1(i, cur);
	}
	return sz[cur];
}
 
void dfs2(int cur, int p)
{
	ans[cur] = ans[p] * sz[cur] % mod * inv[(n - sz[cur])] % mod;//ans[p] * sz[cur] * inv[(n - sz[cur])] % mod溢出報錯
	for (int i : g[cur])
	{
		if (i != p)
			dfs2(i,cur);
	}
}
int main()
{
	int u, v;
	cin >> n;
	inv_n(n);
	for (int i = 0; i < n - 1; i++)
	{
		cin >> u >> v;
		g[u].push_back(v);
		g[v].push_back(u);
	}
	ans[1] = 1;
	for (int i = 1; i <= n; i++)
		ans[1] = ans[1] * i%mod;
	dfs1(1, 0);
	for (int i = 1; i <= n; i++)
		ans[1] = ans[1] * inv[sz[i]] % mod;
	
	for (int i : g[1])
		dfs2(i, 1);
	for (int i = 1; i <= n; i++)
		cout << ans[i] << endl;
 
	return 0;
}

 

#include<iostream>
#include <algorithm>
#include<queue>
#include<cmath>
#include<math.h>
#include<string>
#include<string.h>
#include<map>
#include<set>
using LL = long long;
using namespace std;

const int M = 2e5 + 100;
const int mod = 1e9 + 7;

vector<int> e[M];
int n, sz[M], ans[M];
int fac[M], inv[M], inv2[M];

LL mul(LL a, LL b) {
	return a * b % mod;
}

void init() 
{
	fac[0] = 1;
	for (int i = 1; i <= n; i++) 
		fac[i] = mul(fac[i - 1], i);
	inv[1] = 1;
	for (int i = 2; i <= n; i++) 
		//常規公式爲inv[i] = mul((- mod / i), inv[mod % i])，爲使得逆元爲正數，分子加上mod仍有i*inv[i] = 1(mod p)
		inv[i] = mul((mod - mod / i), inv[mod % i]);

}

void dfs(int u, int fa) 
{
	sz[u] = 1;
	for (int v : e[u]) 
	{
		if (v != fa) 
		{
			dfs(v, u);
			sz[u] += sz[v];
		}
	}
}

void reroot(int u, int fa) 
{
	ans[u] = mul(mul(ans[fa], sz[u]), inv[n - sz[u]]);
	for (int v : e[u]) 
	{
		if (v != fa) 
		{
			reroot(v, u);
		}
	}
}

int main() {
	cin >> n;
 	init();
	for (int i = 0; i < n - 1; i++) 
	{
		int u, v; 
		cin >> u >> v;
		e[u].push_back(v);
		e[v].push_back(u);
	}
	dfs(1, 0);
	ans[1] = fac[n];
	for (int i = 1; i <= n; i++) 
		ans[1] = mul(ans[1], inv[sz[i]]);
	for (int v : e[1]) 
		reroot(v, 1);
	for (int i = 1; i <= n; i++) 
		cout << ans[i] << "\n";
}