Submission #31419

#	Time	Username	Problem	Language	Result	Execution time	Memory
31419		gs14004	카드 (kriii4_Z)	C++14	100 / 100	549 ms	3276 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> &a, bool inv){
		int n = a.size(), j = 0;
		for(int i=1; i<n; i++){
			int bit = (n >> 1);
			while(j >= bit){
				j -= bit;
				bit >>= 1;
			}
			j += bit;
			if(i < j) swap(a[i], a[j]);
		}
		for(int i=2; i<=n; i<<=1){
			double ang = 2 * acos(-1) / i * (inv ? -1 : 1);
			base x(cos(ang), sin(ang));
			for(int j=0; j<n; j+=i){
				base y(1);
				for(int k=0; k<i/2; k++){
					base u = a[j+k], v = a[j+k+i/2] * y;
					a[j+k] = u+v;
					a[j+k+i/2] = u-v;
					y *= x;
				}
			}
		}
		if(inv) for(int i=0; i<n; i++) a[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, lint mod){
		int n = 1;
		while(n < max(v.size(), w.size())) n <<= 1;
		n <<= 1;
		vector<base> v1(n), v2(n);
		vector<base> r1(n), r2(n);
		for(int i=0; i<v.size(); i++){
			v1[i] = base(v[i] >> 15, v[i] & 32767);
		}
		for(int i=0; i<w.size(); i++){
			v2[i] = base(w[i] >> 15, w[i] & 32767);
		}
		fft(v1, 0);
		fft(v2, 0);
		for(int i=0; i<n; i++){
			int j = (i ? (n - i) : i);
			base ans1 = (v1[i] + conj(v1[j])) * base(0.5, 0);
			base ans2 = (v1[i] - conj(v1[j])) * base(0, -0.5);
			base ans3 = (v2[i] + conj(v2[j])) * base(0.5, 0);
			base ans4 = (v2[i] - conj(v2[j])) * base(0, -0.5);
			r1[i] = (ans1 * ans3) + (ans1 * ans4) * base(0, 1);
			r2[i] = (ans2 * ans3) + (ans2 * ans4) * base(0, 1);
		}
		fft(r1, 1);
		fft(r2, 1);
		vector<lint> ret(n);
		for(int i=0; i<n; i++){
			lint av = (lint)round(r1[i].real());
			lint bv = (lint)round(r1[i].imag()) + (lint)round(r2[i].real());
			lint cv = (lint)round(r2[i].imag());
			av %= mod, bv %= mod, cv %= mod;
			ret[i] = (av << 30) + (bv << 15) + cv;
			ret[i] %= mod;
			ret[i] += mod;
			ret[i] %= 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, mod);
		ret.resize(l + 1);
		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, mod);
		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, mod);
		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:40:11: 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>&, lint)':
Z.cpp:54:11: 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:61:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i=0; i<w.size(); i++){
                 ^

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