#414538 (C++14) No.827 総神童数

提出ソース
結果

問題	No.827 総神童数
コンテスト
ユーザー	ningenMe
提出日時	2020-01-06 03:45:21
言語	C++14 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	148 ms / 2,000 ms
コード長	13,462 bytes
コンパイル時間	2,042 ms
コンパイル使用メモリ	182,976 KB
実行使用メモリ	33,344 KB
最終ジャッジ日時	2024-11-22 23:47:10
合計ジャッジ時間	7,729 ms
ジャッジサーバーID （参考情報）	judge5 / judge4
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ファイルパターン	結果
sample	AC * 3
other	AC * 36
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;

#define REP(i,n) for(long long i = 0; i < (n); i++)
#define FOR(i, m, n) for(long long i = (m);i < (n); ++i)
#define ALL(obj) (obj).begin(),(obj).end()
#define SPEED cin.tie(0);ios::sync_with_stdio(false);

template<class T> using V = vector<T>;
template<class T, class U> using P = pair<T, U>;
template<class T> using PQ = priority_queue<T>;
template<class T> using PQR = priority_queue<T,vector<T>,greater<T>>;

constexpr long long MOD = (long long)1e9 + 7;
constexpr long long MOD2 = 998244353;
constexpr long long HIGHINF = (long long)1e18;
constexpr long long LOWINF = (long long)1e15;
constexpr long double PI = 3.1415926535897932384626433;

template <class T> vector<T> make_v(size_t N,T init){return vector<T>(N,init);}
template <class... T> auto make_v(size_t N,T... t){return vector<decltype(make_v(t...))>(N,make_v(t...));}
template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}}
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;}
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;}
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;}
template <template <class tmp>  class T, class U> ostream &operator<<(ostream &o, const T<U> &obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr)o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
void print(void) {cout << endl;}
template <class Head> void print(Head&& head) {cout << head;print();}
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);}
template <class T> void chmax(T& a, const T b){a=max(a,b);}
template <class T> void chmin(T& a, const T b){a=min(a,b);}
void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;}
void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;}
void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;}


template<class T = int> class Tree {
public:
	int nodeNum;
	int isWeighted;
	int maxBit;
	int idx;
	vector<vector<int>> edge;
	vector<vector<T>> weight;
	vector<int> depth;
	vector<int> order;
	vector<T> dist;
	
	vector<int> parent;
	vector<T> parentDist;
	
	vector<vector<int>> child;
	vector<vector<T>> childDist;
 
	vector<vector<int>> ancestor;
	vector<vector<int>> descendant;
	
	vector<int> eulerTour;
    vector<T> eulerTourDist;
	vector<int> eulerTourIdxL;
	vector<int> eulerTourIdxR;
    vector<int> eulerTourDive,eulerTourFloat;
    vector<T> eulerTourDiveDist,eulerTourFloatDist;
	vector<int> eulerTourDiveIdxL,eulerTourFloatIdxL;
	vector<int> eulerTourDiveIdxR,eulerTourFloatIdxR;
 
	Tree(const int nodeNum, const int isWeighted = 0, const int maxBit = 20) : 
	nodeNum(nodeNum),
	isWeighted(isWeighted),
	maxBit(maxBit),
	edge(nodeNum),
	depth(nodeNum),
	order(nodeNum)
	{
		if(isWeighted) weight.resize(nodeNum);
		if(isWeighted) dist.resize(nodeNum);
	}
 
	//O(1) anytime
	void makeEdge(const int& from, const int& to, const T& w = 0) {
		edge[from].push_back(to);
		if(isWeighted)	weight[from].push_back(w);
	}
 
	//O(N) anytime
	void makeDepth(const int root) {
		depth[root] = 0;
		if(isWeighted) dist[root] = 0;
		idx = 0;
		dfs1(root);
		order[idx++] = root;
	}
 
    //for makeDepth
	void dfs1(int from, int prev = -1){
		for(int i = 0; i < edge[from].size(); ++i){
			int to = edge[from][i];
			if(to==prev) continue;
			depth[to] = depth[from] + 1;
			if(isWeighted) dist[to] = dist[from] + weight[from][i];
			dfs1(to,from);
			order[idx++] = to;
		}
	}
 
    //O(N) anytime
	int diameter(void){
		makeDepth(0);
		int tmp = max_element(depth.begin(), depth.end()) - depth.begin();
		makeDepth(tmp);
		return *max_element(depth.begin(), depth.end());
	}
 
	//O(N) after makeDepth
	void makeParent(void) {
		parent.resize(nodeNum);
		iota(parent.begin(),parent.end(),0);
		for (int i = 0; i < nodeNum; ++i) for (auto j : edge[i]) if (depth[i] > depth[j]) parent[i] = j;
 
		if(isWeighted) {
			parentDist.resize(nodeNum);
			for (int i = 0; i < nodeNum; ++i) for (int j = 0; j < edge[i].size(); ++j) if (depth[i] > depth[edge[i][j]]) parentDist[i] = weight[i][j];
		}
	}
 
	//O(N) after makeDepth
	void makeChild(void) {
		child.resize(nodeNum);
		for (int i = 0; i < nodeNum; ++i) for (auto j : edge[i]) if (depth[i] < depth[j]) child[i].push_back(j);
 
		if(isWeighted) {
			childDist.resize(nodeNum);
			for (int i = 0; i < nodeNum; ++i) for (int j = 0; j < edge[i].size(); ++j) if (depth[i] < depth[edge[i][j]]) childDist[i].push_back(weight[i][j]);
		}
	}
 
	//O(NlogN) after makeDepth
	void makeAncestor(void) {
		ancestor.resize(nodeNum,vector<int>(maxBit));
		for (int i = 0; i < nodeNum; ++i) ancestor[i][0] = i;
		for (int i = 0; i < nodeNum; ++i) for (auto j : edge[i]) if (depth[i] > depth[j]) ancestor[i][0] = j;
		for (int bit = 1; bit < maxBit; ++bit) for (int i = 0; i < nodeNum; ++i) ancestor[i][bit] = ancestor[ancestor[i][bit - 1]][bit - 1];
	}
 
	//O(N^2) after makeDepth
	void makeDescendant(void) {
		descendant.resize(nodeNum);
		for (int i = 0; i < nodeNum; ++i) descendant[i].push_back(i);
		for (int i = 0; i < nodeNum; ++i) for (auto j : edge[order[i]]) if (depth[order[i]] < depth[j]) for(auto k: descendant[j]) descendant[order[i]].push_back(k);
	}
 
	//O(logN) after makeAncestor
	int lca(int l, int r) {
		if (depth[l] < depth[r]) swap(l, r);
		int diff = depth[l] - depth[r];
		for (int bit = 0; bit < maxBit; ++bit) if (diff & (1 << bit)) l = ancestor[l][bit];
		if(l==r) return l;
		for (int bit = maxBit - 1; 0 <= bit; --bit) if(ancestor[l][bit]!=ancestor[r][bit]) l = ancestor[l][bit], r = ancestor[r][bit];
		return ancestor[l][0];
	}
 
	//O(N) after makeChild and makeParent
	void makeEulerTour(void){
        dfs2(order[nodeNum-1]);
		eulerTourIdxL.resize(nodeNum);
		eulerTourIdxR.resize(nodeNum);
		for(int i = 0; i < eulerTour.size(); ++i) eulerTourIdxR[eulerTour[i]] = i;
		for(int i = eulerTour.size()-1; 0 <= i; --i) eulerTourIdxL[eulerTour[i]] = i;
		return;
	}
 
    //for makeEulerTour
	void dfs2(int from, int prev = -1){
		eulerTour.push_back(from);
        if(isWeighted) eulerTourDist.push_back(parentDist[from]);
 
        for(int i = 0; i < child[from].size(); ++i){
            int to = child[from][i];            
            dfs2(to,from);            
    		eulerTour.push_back(from);
            if(isWeighted) eulerTourDist.push_back(-childDist[from][i]);
        }
	}

	//O(NlogN) after makeEulerTour
	void makeEulerTourEdge(void) {
		eulerTourDive.push_back(order[nodeNum-1]);
		if(isWeighted) eulerTourDiveDist.push_back(0);
		for(int i = 1; i < eulerTour.size(); ++i) {
			int l = eulerTour[i-1];
			int r = eulerTour[i];
			if(depth[l] < depth[r]) {
				eulerTourDive.push_back(i);
				if(isWeighted) eulerTourDiveDist.push_back(eulerTourDist[i]);
			}
			else {
				eulerTourFloat.push_back(i);
				if(isWeighted) eulerTourFloatDist.push_back(eulerTourDist[i]);
			}
		}
		eulerTourDiveIdxL.resize(nodeNum);
		eulerTourDiveIdxR.resize(nodeNum);
		eulerTourFloatIdxL.resize(nodeNum);
		eulerTourFloatIdxR.resize(nodeNum);
		for(int i = 0; i < nodeNum; ++i) {
			int l = eulerTourIdxL[i];
			int r = eulerTourIdxR[i];
			eulerTourDiveIdxL[i]  =  upper_bound(eulerTourDive.begin() ,eulerTourDive.end() ,l) - eulerTourDive.begin()     ;
			eulerTourDiveIdxR[i]  = (upper_bound(eulerTourDive.begin() ,eulerTourDive.end() ,r) - eulerTourDive.begin())  -1;
			eulerTourFloatIdxL[i] =  upper_bound(eulerTourFloat.begin(),eulerTourFloat.end(),l) - eulerTourFloat.begin()    ;
			eulerTourFloatIdxR[i] = (upper_bound(eulerTourFloat.begin(),eulerTourFloat.end(),r) - eulerTourFloat.begin()) -1;
			eulerTourDiveIdxR[i]  = max(eulerTourDiveIdxL[i]-1 ,eulerTourDiveIdxR[i]);
			eulerTourFloatIdxR[i] = max(eulerTourFloatIdxL[i]-1,eulerTourFloatIdxR[i]);
		}
	}
		// iの部分木の頂点に加算するとき
		// [ eulerTourIdxL[i]  ,eulerTourIdxR[i]  ]に　+val
		// [i]の頂点クエリ
		// [eulerTourIdxL[i],eulerTourIdxL[i]]

		// iの部分木の辺に加算するとき
		// [ eulerTourDiveIdxL[i]  ,eulerTourDiveIdxR[i]  ]に　+val
		// [ eulerTourFloatIdxL[i] ,eulerTourFloatIdxR[i] ]に　-val
		// [0,i]のパスクエリ
		// [ 0, eulerTourDiveIdxL[i] ) + [0, eulerTourFloatIdxL[i])
 
};
 
//depth,dist
//https://atcoder.jp/contests/abc126/tasks/abc126_d
 
//lca
//https://atcoder.jp/contests/abc014/tasks/abc014_4
 
//child
//https://atcoder.jp/contests/abc133/tasks/abc133_e

//diameter
//https://atcoder.jp/contests/agc033/tasks/agc033_c

//eulerTour
//https://yukicoder.me/problems/no/900


//Combination Mod
class CombinationMod {
public:
	vector<long long> fac,finv,inv;
	long long mod;

	CombinationMod(int N,long long mod) : fac(N + 1), finv(N + 1), inv(N + 1), mod(mod) {
		fac[0] = fac[1] = finv[0] = finv[1] = inv[1] = 1;
		for (int i = 2; i <= N; ++i) {
			fac[i] = fac[i - 1] * i % mod;
			inv[i] = mod - inv[mod%i] * (mod / i) % mod;
			finv[i] = finv[i - 1] * inv[i] % mod;
		}
	}
	
	long long num(int n, int k) {
		return ((n < 0 || k < 0 || n < k) ? 0 : fac[n] * (finv[k] * finv[n - k] % mod) % mod);
	}
};

//verify https://atcoder.jp/contests/abc021/tasks/abc021_d

//Factorial Mod
vector<long long> FactorialMod(long long N, long long mod) {
    vector<long long> res(N + 1, 1);
    for (long long i = 1; i <= N; ++i) res[i] = (res[i - 1] * i) % mod;
    return res;
}


template<long long mod> class ModInt {
public:
	long long x;
	ModInt():x(0) {
		// do nothing
	}
	ModInt(long long y) : x(y>=0?(y%mod): (mod - (-y)%mod)%mod) {
		// do nothing
	}
	ModInt &operator+=(const ModInt &p) {
		if((x += p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator+=(const long long y) {
        ModInt p(y);
		if((x += p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator+=(const int y) {
        ModInt p(y);
		if((x += p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator-=(const ModInt &p) {
		if((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator-=(const long long y) {
        ModInt p(y);
		if((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator-=(const int y) {
        ModInt p(y);
		if((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator*=(const ModInt &p) {
		x = (x * p.x % mod);
		return *this;
	}
	ModInt &operator*=(const long long y) {
        ModInt p(y);
		x = (x * p.x % mod);
		return *this;
	}
	ModInt &operator*=(const int y) {
        ModInt p(y);
		x = (x * p.x % mod);
		return *this;
	}
	ModInt &operator/=(const ModInt &p) {
		*this *= p.inv();
		return *this;
	}
	ModInt &operator/=(const long long y) {
        ModInt p(y);
		*this *= p.inv();
		return *this;
	}
	ModInt &operator/=(const int y) {
        ModInt p(y);
		*this *= p.inv();
		return *this;
	}
	ModInt operator=(const int y) {
        ModInt p(y);
        *this = p;
        return *this;
    }
    ModInt operator=(const long long y) {
        ModInt p(y);
		*this = p;
        return *this;
    }
	ModInt operator-() const { return ModInt(-x); }
	ModInt operator++() { 
        x++;
        if(x>=mod) x-=mod;
        return *this; 
    }
	ModInt operator--() { 
        x--;
        if(x<0) x+=mod;
        return *this; 
    }
	ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
	ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
	ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
	ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
	bool operator==(const ModInt &p) const { return x == p.x; }
	bool operator!=(const ModInt &p) const { return x != p.x; }
	ModInt inv() const {
		int a = x, b = mod, u = 1, v = 0, t;
		while(b > 0) {
			t = a / b;
			swap(a -= t * b, b);
			swap(u -= t * v, v);
		}
		return ModInt(u);
	}
	ModInt pow(long long n) const {
		ModInt ret(1), mul(x);
		while(n > 0) {
			if(n & 1) ret *= mul;
			mul *= mul;
			n >>= 1;
		}
		return ret;
	}
	friend ostream &operator<<(ostream &os, const ModInt &p) {
		return os << p.x;
	}
	friend istream &operator>>(istream &is, ModInt &a) {
		long long t;
		is >> t;
		a = ModInt<mod>(t);
		return (is);
	}
};
using modint = ModInt<MOD>;


int main() {
    SPEED
    int N; cin >> N;
    Tree<> tree(N);
    for(int i = 0; i < N-1; ++i){
        int u,v; cin >> u >> v;
        u--,v--;
        tree.makeEdge(u,v);
        tree.makeEdge(v,u);
    }
    tree.makeDepth(0);
    CombinationMod CM(N,MOD);
    auto F = FactorialMod(N,MOD);
    vector<modint> cor(N,1);
    for(ll i = 0; i < N; ++i){
        cor[i] *= F[i];
        cor[i] *= F[N-1-i];
        cor[i] *= CM.num(N,i+1);
    }
    modint ans = 0;
    for(int i = 0; i < N; ++i){
        ans += cor[tree.depth[i]];
    }
    cout << ans << endl;

    return 0;
}