結果

問題 No.435 占い(Extra)
ユーザー koyumeishikoyumeishi
提出日時 2016-04-19 05:04:02
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 6,253 bytes
コンパイル時間 1,665 ms
コンパイル使用メモリ 122,200 KB
実行使用メモリ 42,880 KB
最終ジャッジ日時 2024-04-17 02:11:20
合計ジャッジ時間 4,929 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 WA -
testcase_01 WA -
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ソースコード

diff # 

#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
using namespace std;

namespace {
	using Integer = long long; //__int128;
	template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
	template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
	template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(int i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
	template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

	template<class H> void print(const H& head){ cout << head; }
	template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
	template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

	template<class H> void eprint(const H& head){ cerr << head; }
	template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; print(tail...); }
	template<class ... T> void eprintln(const T& ... values){ print(values...); cerr << endl; }

	string operator "" _s (const char* str, size_t size){ return move(string(str)); }
	constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
	constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
	constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

	inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

	mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

	template<class T> string join(const vector<T>& v, const string& sep){
		stringstream ss; for(int i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str();
	}
}

constexpr long long mod = 9_ten + 7;

#include <complex>
template<typename T = double>
class Fast_Fourier_Transform{
	// return the vector of F[t] or f[x] where
	// F[t] = sum of { f[x] * exp(-j * theta * t * x) } in x = 0 .. N-1 (FFT)
	// f(x) = 1/N * sum of { F[t] * exp(j * theta * t * x) } in t = 0 .. N-1 (inverse FFT)
	// where theta = 2*PI / N
	// N == 2^k
	static vector< complex<T> > do_fft(vector< complex<T> > A, bool inverse){
		const T PI = atan2(1, 0) * 2.0;
		const complex<T> j = complex<T>(0,1); // 0 + j*1.0 (j is the imaginary unit)

		int N = A.size();
		int k = 0;	// N = 2^k
		while(N>>k > 0) k++;
		
		for(int bit=0; bit<N; bit++){
			int rbit = 0;
			for(int i=0, tmp_bit = bit; i<k-1; i++, rbit <<= 1, tmp_bit >>=  1){
				rbit |= tmp_bit & 1;
			}
			rbit >>= 1;
			if(bit < rbit){
				swap(A[bit], A[rbit]);
			}
		}

		int dist = 1;
		T theta = -PI;
		if(inverse) theta = -theta;

		for(int level = 1; level<k; level++){
			complex<T> W_n = exp(j * theta);
			complex<T> W(1,0);
			for(int x=0; x < (1<<level-1); x++){
				for(int y=x; y+dist < N; y += (dist<<1)){
					complex<T> tmp = A[ y+dist ] * W;
					A[ y+dist ] = A[ y ] - tmp;
					A[ y ] += tmp;
				}
				W *= W_n;
			}
			dist <<= 1;
			theta *= 0.5;
		}

		if(inverse){
			T k = 1.0/N;
			for(int i=0; i<N; i++){
				A[i] *= k;
			}
		}
		return A;
	}


	template<typename U=T>
	static void vec_resize(vector<U> &A, const U val){
		int n = A.size();
		int k = 1;
		while(n > k) k<<=1;
		A.resize(k, val);
	}

public:
	Fast_Fourier_Transform(){};

	static vector< complex<T> > FFT(vector< complex<T> > A){
		vec_resize<complex<T>>(A, complex<T>(0,0));
		return do_fft(A, false);
	}

	static vector< complex<T> > IFFT(vector< complex<T> > A){
		//vec_resize<complex<T>>(A, complex<T>(0,0));
		return do_fft(A, true);
	}

	static vector< complex<T> > FFT(vector<T> A){
		vec_resize<T>(A, 0);
		vector<complex<T>> B(A.size());
		for(int i=0; i<B.size(); i++){
			B[i] = complex<T>(A[i], 0);
		}

		return do_fft(B, false);
	}

	static vector< complex<T> > FFT(vector<int> A){
		vec_resize<int>(A, T(0));
		vector<complex<T>> B(A.size());
		for(int i=0; i<B.size(); i++){
			B[i] = complex<T>(A[i], 0);
		}
		return do_fft(B, false);
	}

	static vector<long long> round(vector<complex<T>> &&A){
		vector<long long> ret(A.size());
		for(int i=0; i<A.size(); i++){
			ret[i] = A[i].real() + (A[i].real()<0?-0.5:0.5);
		}
		return ret;
	}

	// vector<double> C | C[i] = ΣA[i]B[j]
	static vector<complex<T>> convolution(vector<T> &A, vector<T> &B){
		//reverse(B.begin(), B.end());

		int n = max(A.size(), B.size());
		//A.resize(n, 0);
		//B.resize(n, 0);

		auto A_FFT = FFT(A);
		auto B_FFT = FFT(B);
		for(int i=0; i<n; i++){
			A_FFT[i] *= B_FFT[i];
		}
		return IFFT(A_FFT);
	}
};



int main(){
	int t;
	cin >> t;

	const int sz = 3000;
	vector<vector<int>> nCk(sz, vector<int>(sz, 0));
	nCk[0][0] = 1;
	for(int i=1; i<sz; i++){
		for(int j=0; j<=i; j++){
			nCk[i][j] = (nCk[i-1][j] + (j>0?nCk[i-1][j-1]:0)) % 9;
		}
	}

	vector<double> B(nCk[sz-1].begin(), nCk[sz-1].end());
	B.resize(1<<18);
	//reverse(B.begin(), B.end());

	vector<double> A(1<<18, 0);

	while(t--){
		string s;
		cin >> s;

		bool zero = true;
		for(int i=0; i<s.size(); i++){
			if(s[i] != '0'){
				zero = false;
				break;
			}
		}
		if(zero){
			println(0);
			continue;
		}

		while(s.size() > sz){
			fill(A.begin(), A.end(), 0.0);
			for(int i=0; i<s.size(); i++){
				A[i] = (s[i] - '0') * 10;
			}

			auto res = Fast_Fourier_Transform<>::round( Fast_Fourier_Transform<>::convolution(A,B) );

			string t;

			for(int i=0; i<s.size()-sz+1; i++){
				int val = res[i+sz-1] / 10;
				val %= 9;
				t += val + '0';
			}
			//cerr << t << endl;
			swap(s,t);
		}

		vector<int> v(s.size());
		for(int i=0; i<s.size(); i++){
			v[i] = s[i] - '0';
			if(v[i] == 0) v[i] = 9;
		}

		long long ans = 0;
		int n = s.size();
		for(int i=0; i<n; i++){
			long long k = nCk[n-1][i];
			ans += (k * v[i]);
			ans %= 9;
		}

		if(ans == 0) ans = 9;

		println(ans);
	}
	return 0;
}
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