Submission #31414

#	Time	Username	Problem	Language	Result	Execution time	Memory
31414		gs14004	카드 (kriii4_Z)	C++14	0 / 100	469 ms	4868 KiB

Z

#include <bits/stdc++.h>
using namespace std;
typedef long long lint;
typedef pair<int, int> pi;
const int MAXN = 3005;
const int mod = 1e9 + 7;

namespace fft{
	typedef complex<double> base;
	void fft(vector<base> &v, bool inv){
		int n = v.size();
		vector<base> w(n/2), aux(n);
		for(int i=0; i<n/2; i++){
			int k = i&-i;
			if(i == k){
				double ang = 2 * M_PI * i / n;
				if(inv) ang *= -1;
				w[i] = base(cos(ang), sin(ang));
			}
			else w[i] = w[i-k] * w[k];
		}
		for(int i=n/2; i; i>>=1){
			aux = v;
			for(int k=0; 2*k<n; k+=i){
				for(int j=0; j<i; j++){
					base a = aux[2*k + j], b = aux[2*k + j + i] * w[k];
					v[k + j] = a + b;
					v[k + j + n/2] = a - b;
				}
			}
		}
		if(inv){
			for(int i=0; i<n; i++){
				v[i] /= n;
			}
		}
	}
	vector<lint> multiply(vector<lint> &v, vector<lint> &w){
		vector<base> fv(v.begin(), v.end()), fw(w.begin(), w.end());
		int n = 1;
		while(n < max(v.size(), w.size())) n <<= 1;
		n <<= 1;
		fv.resize(n);
		fw.resize(n);
		fft(fv, 0);
		fft(fw, 0);
		for(int i=0; i<n; i++) fv[i] *= fw[i];
		fft(fv, 1);
		vector<lint> ret(n);
		for(int i=0; i<n; i++) ret[i] = round(fv[i].real());
		return ret;
	}
	vector<lint> multiply(vector<lint> &v, vector<lint> &w, int b){
		int n = 1;
		while(n < max(v.size(), w.size())) n <<= 1;
		n <<= 1;
		vector<base> v1(n), v2(n), v3(n), v4(n), r1(n), r2(n), r3(n);
		for(int i=0; i<v.size(); i++){
			v1[i] = base(v[i] / b, 0);
			v2[i] = base(v[i] % b, 0);
		}
		for(int i=0; i<w.size(); i++){
			v3[i] = base(w[i] / b, 0);
			v4[i] = base(w[i] % b, 0);
		}
		fft(v1, 0);
		fft(v2, 0);
		fft(v3, 0);
		fft(v4, 0);
		for(int i=0; i<n; i++){
			r1[i] = v1[i] * v3[i];
			r2[i] = v1[i] * v4[i] + v2[i] * v3[i];
			r3[i] = v2[i] * v4[i];
		}
		fft(r1, 1);
		fft(r2, 1);
		fft(r3, 1);
		vector<lint> ret(n);
		for(int i=0; i<n; i++){
			ret[i] = ((lint)round(r1[i].real()) % mod) * b * b + 
				((lint)round(r2[i].real()) % mod) * b + (lint)round(r3[i].real()) % mod;
		}
		return ret;
	}
}

lint ipow(lint x, lint p){
	lint ret = 1, piv = x % mod;
	while(p){
		if(p&1) ret *= piv;
		piv *= piv;
		ret %= mod;
		piv %= mod;
		p >>= 1;
	}
	return ret % mod;
}

lint fact[MAXN], invf[MAXN];

lint bino(int x, int y){
	return fact[x] * (invf[x-y] * invf[y] % mod) % mod;
}

int n, l;
int cnt[MAXN];
lint dp[12][MAXN], func[MAXN];

vector<lint> solve(int x, int c){
	if(c == 0){
		vector<lint> ret(l + 1);
		ret[0] = 1;
		return ret;
	}
	if(c % 2 == 1){
		vector<lint> a = solve(x, c-1);
		vector<lint> b;
		for(int i=0; i<=l; i++){
			a[i] = (a[i] * invf[i]) % mod;
			b.push_back(i < x ? 0 : invf[i]);
		}
		auto ret = fft::multiply(a, b, 1<<15);
		for(int i=0; i<=l; i++){
			ret[i] %= mod;
			ret[i] *= fact[i];
			ret[i] %= mod;
		}
		return ret;
	}
	else{
		auto tmp = solve(x, c / 2);
		for(int i=0; i<=l; i++) tmp[i] = (tmp[i] * invf[i]) % mod;
		auto ret = fft::multiply(tmp, tmp, 1<<15);
		ret.resize(l + 1);
		for(int i=0; i<=l; i++){
			ret[i] %= mod;
			ret[i] *= fact[i];
			ret[i] %= mod;
		}
		return ret;
	}
}

int main(){
	fact[0] = invf[0] = 1;
	for(int i=1; i<MAXN; i++){
		fact[i] = fact[i-1] * i % mod;
		invf[i] = ipow(fact[i], mod - 2);
	}
	cin >> n >> l;
	for(int i=0; i<n; i++){
		int x;
		cin >> x;
		cnt[x]++;
	}
	dp[0][0] = 1;
	for(int i=0; i<=10; i++){
		vector<lint> func = solve(i, cnt[i]);
		vector<lint> a, b;
		for(int j=0; j<=l; j++){
			a.push_back(func[j] * invf[j] % mod);
			b.push_back(dp[i][j] * invf[j] % mod);
		}
		auto ret = fft::multiply(a, b, 1<<15);
		for(int j=0; j<=l; j++) dp[i+1][j] = ((ret[j] % mod) * fact[j] % mod);
	}
	dp[11][l] *= ipow(ipow(n, l), mod - 2);
	dp[11][l] %= mod;
	cout << dp[11][l];
}

Compilation message (stderr)

Z.cpp: In function 'std::vector<long long int> fft::multiply(std::vector<long long int>&, std::vector<long long int>&)':
Z.cpp:41:11: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(n < max(v.size(), w.size())) n <<= 1;
           ^
Z.cpp: In function 'std::vector<long long int> fft::multiply(std::vector<long long int>&, std::vector<long long int>&, int)':
Z.cpp:55:11: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(n < max(v.size(), w.size())) n <<= 1;
           ^
Z.cpp:58:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i=0; i<v.size(); i++){
                 ^
Z.cpp:62:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i=0; i<w.size(); i++){
                 ^

• Subtask 1: 0 / 13
• Subtask 2: 0 / 87