結果

問題 No.140 みんなで旅行
ユーザー shimomireshimomire
提出日時 2015-01-30 15:14:28
言語 C++11
(gcc 13.3.0)
結果
AC  
実行時間 107 ms / 5,000 ms
コード長 6,196 bytes
コンパイル時間 1,046 ms
コンパイル使用メモリ 122,584 KB
実行使用メモリ 21,308 KB
最終ジャッジ日時 2024-06-23 04:26:17
合計ジャッジ時間 2,454 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 19
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <cassert>// c
#include <iostream>// io
#include <iomanip>
#include <fstream>
#include <sstream>
#include <vector>// container
#include <map>
#include <set>
#include <queue>
#include <bitset>
#include <stack>
#include <algorithm>// other
#include <complex>
#include <numeric>
#include <functional>
#include <random>
#include <regex>
using namespace std;

using i32=int32_t;using i64=int64_t;using ll =i64;using uint=uint32_t;using ull=uint64_t;
template<typename T> using matrix=vector<vector<T> >;

#define ALL(c) (begin(c)),(end(c))
#define REP(i,n) FOR(i,0,n)
#define REPr(i,n) FORr(i,0,n)
#define FOR(i,l,r) for(int i=(int)(l);i<(int)(r);++i)
#define FORr(i,l,r) for(int i=(int)(r)-1;i>=(int)(l);--i)
#define EACH(it,o) for(auto it = (o).begin(); it != (o).end(); ++it)
#define IN(l,v,r) ((l)<=(v) && (v)<(r))
#define UNIQUE(v) v.erase(unique(ALL(v)),v.end())
//debug
#define DUMP(x)  cerr << #x << " = " << (x)
#define LINE()    cerr<< " (L" << __LINE__ << ")"

class range {
private:
	struct Iter{
		int v;
		int operator*(){return v;}
		bool operator!=(Iter& itr) {return v < itr.v;}
		void operator++() {++v;}
	};
	Iter i, n;
public:
	range(int n) : i({0}), n({n}) {}
	range(int i, int n) : i({i}), n({n}) {}
	Iter& begin() {return i;}
	Iter& end() {return n;}
};

//output
template<typename T> ostream& operator << (ostream& os, const vector<T>& as){REP(i,as.size()){if(i!=0)os<<" "; os<<as[i];}return os;}
template<typename T> ostream& operator << (ostream& os, const vector<vector<T>>& as){REP(i,as.size()){if(i!=0)os<<endl; os<<as[i];}return os;}
template<typename T> ostream& operator << (ostream& os, const set<T>& ss){for(auto a:ss){if(a!=ss.begin())os<<" "; os<<a;}return os;}
template<typename T1,typename T2> ostream& operator << (ostream& os, const pair<T1,T2>& p){os<<p.first<<" "<<p.second;return os;}
template<typename K,typename V> ostream& operator << (ostream& os, const map<K,V>& m){bool isF=true;for(auto& p:m){if(!isF)os<<endl;os<<p;isF=false;}return os;}
template<typename T1> ostream& operator << (ostream& os, const tuple<T1>& t){os << get<0>(t);return os;}
template<typename T1,typename T2> ostream& operator << (ostream& os, const tuple<T1,T2>& t){os << get<0>(t)<<" "<<get<1>(t);return os;}
template<typename T1,typename T2,typename T3> ostream& operator << (ostream& os, const tuple<T1,T2,T3>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4,typename T5> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4,T5>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t)<<" "<<get<4>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4,typename T5,typename T6> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4,T5,T6>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t)<<" "<<get<4>(t)<<" "<<get<5>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4,typename T5,typename T6,typename T7> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4,T5,T6,T7>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t)<<" "<<get<4>(t)<<" "<<get<5>(t)<<" "<<get<6>(t);return os;}

//input
char tmp[1000];
#define nextInt(n) scanf("%d",&n)
#define nextLong(n) scanf("%lld",&n) //I64d
#define nextDouble(n) scanf("%lf",&n) 
#define nextChar(n) scanf("%c",&n)
#define nextString(n) scanf("%s",tmp);n=tmp

// values
template<typename T> T INF(){assert(false);};
template<> int INF<int>(){return 1<<28;};
template<> ll INF<ll>(){return 1LL<<58;};
template<> double INF<double>(){return 1e16;};

template<class T> T EPS(){assert(false);};
template<> int EPS<int>(){return 1;};
template<> ll EPS<ll>(){return 1LL;};
template<> double EPS<double>(){return 1e-8;};
template<> long double EPS<long double>(){return 1e-8;};

template<typename T,typename U> T pmod(T v,U M){return (v%M+M)%M;}

ll gcd_positive(ll a,ll b) { return b == 0 ? a : gcd_positive(b,a%b); }
ll gcd(ll a,ll b) { return gcd_positive(abs(a), abs(b)); }
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}

ll MOD=1e9+7;

template <ll M=(ll)1e9+7> class modU{
public:
	ll pmod(ll v){return (v%M+M)%M;}
	ll ainv(ll a){return pmod(-a);}
	ll add(ll a,ll b){return pmod(a+b);}
	ll mul(ll a,ll b){return pmod(a*b);}
	ll pow(ll x, ll N){
		ll res=1;
		while(N>0){
			if(N%2)res=mul(res,x);
			x=mul(x,x);
			N/=2;
		}
		return res;
	}

	//O(logM)
	ll minv(ll a){return pow(a,M-2);}

	// O(M)
	vector<ll> minvs(){
		vector<ll> inv(M + 1);inv[1] = 1;
		for (int i = 2; i <= M; ++i)inv[i] = mul(inv[M % i],M - M / i);
		return inv;
	}

	//O(N) 条件 N>=0 
	vector<ll> factmemo=vector<ll>(2000050,-1);
	inline ll fact(const int N){
		if(factmemo[N]!=-1)return factmemo[N];
		return factmemo[N]=N==0?1:mul(N,fact(N-1));
	}
	//条件 N>=0
	inline ll nPr(const int N,const int r){		
		if(r>N)return 0;
		return mul(fact(N),minv(fact(N-r)));
	}
	inline ll nCr(const int N,const int r){
		if(N<0){
			if(0 <= r) return (r%2?-1:+1)*nCr(-N +r-1,r);
			else if(r<=N) return ((N-r)%2?-1:+1)*nCr(-r-1,N-r);
			else return 0;	
		}
		if(0<= r && r<=N) return mul(mul(fact(N),minv(fact(r))),minv(fact(N-r)));
		return 0;
	}
};

class Main{
	public:
	modU<> mu;
	
	// |A| -> |B| の全射の個数
	vector<vector<ll>> surjective_count(int A,int B){
		vector<vector<ll>> dp(A,vector<ll>(B));
		dp[0][0]=1;

		REP(a,A)REP(b,B){
			if(a-1>=0 && b-1>=0){ // create a new point
				dp[a][b] += dp[a-1][b-1]; dp[a][b] %= MOD;
			}
			if(a-1>=0){// add to an already exist point
				dp[a][b] += b * dp[a-1][b]; dp[a][b] %= MOD;
			}
		}
		return dp;
	}

	void run(){
		int N;cin >> N;
		vector<vector<ll>> dp=surjective_count(N+1,N+1);	

		ll res = 0;
		FOR(i,1,N+1){//create i groups
			FOR(j,i,N+1){//夫婦 j pairs
				ll val = mu.mul(mu.nCr(N,j),dp[j][i]);
				val=mu.mul(val,mu.pow(i*(i-1),N-j));
				res=mu.add(res, val);
			}
		}
		cout << res <<endl;
	}
};

int main(){
	cout <<fixed<<setprecision(20);
	cin.tie(0);
	ios::sync_with_stdio(false);
	Main().run();
	return 0;
}
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