yukicoder No.206

yukicoder206.cpp

#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <numeric>
#include <functional>
#include <cmath>
#include <queue>
#include <stack>
#include <complex>

#define repd(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) repd(i,0,n)

using namespace std;
typedef long long ll;
typedef complex<double> cmpd;


int inputValue(){
    int a;
    cin >> a;
    return a;
};

void inputArray(int * p, int a){
    rep(i, a){
        cin >> p[i];
    }
};

void inputVector(vector<int> * p, int a){
    rep(i, a){
        int input;
        cin >> input;
        p -> push_back(input);
    }
}

template <typename T>
void output(T a, int precision) {
    if(precision > 0){
        cout << setprecision(precision)  << a << "\n";
    }
    else{
        cout << a << "\n";
    }
}

// 高速フーリエ変換
vector<cmpd> dft(vector<cmpd> & f, int deg, bool dir){
    // 終了条件
    if (deg == 1) {
        return f;
    }
    
    // 半分の長さのf0, f1をつくる
    vector<cmpd> f0(deg >> 1), f1(deg >> 1);
    
    // f0: 奇数番目, f1: 偶数番目
    rep(i, deg >> 1){
        f0[i] = f[i << 1];
        f1[i] = f[i << 1 | 1];
    }
    
    // それぞれについてdft
    f0 = dft(f0 , deg >> 1, dir);
    f1 = dft(f1 , deg >> 1, dir);
    
    // dir: 順変換ならtrue, 逆変換ならfalse
    cmpd zeta = (dir == true) ? polar<double>(1, 2 * M_PI / deg) : polar<double>(1, -2 * M_PI / deg);
    
    cmpd pow_zeta(1);
    
    rep(i, deg){
        f[i] = f0[i % (deg >> 1)] + pow_zeta * f1[i % (deg >> 1)];
        pow_zeta *= zeta;
    }
    return f;
}

vector<cmpd> idft(vector<cmpd> & f, int deg){
    // fのサイズは整形されている
    vector<cmpd> ret = dft(f, deg, false);
    rep(i, deg){
        ret[i] /= deg;
    }
    return ret;
}

// 多項式乗算
vector<cmpd> multipoly (vector<cmpd> & a, vector<cmpd> & b){
    
    // 多項式を2^n次に整形．係数が0のところは0詰め
    int nmax = (int)a.size() + (int)b.size() - 1;
    int n = 1;
    while(n < nmax) n <<= 1;
    a.resize(n);
    b.resize(n);
    
    vector<cmpd> fc(n);
    vector<cmpd> fa = dft(a, n, true);
    vector<cmpd> fb = dft(b, n, true);
    rep(i, n){
        fc[i] = fa[i] * fb[i];
    }
    return idft(fc, n);
}

int main(int argc, const char * argv[]) {
    
    // source code
    int L = inputValue();
    int M = inputValue();
    int N = inputValue();
    N++;
    vector<cmpd> A(N);
    rep(i, L){
        A[inputValue()] = 1;
    }
    vector<cmpd> B(N);
    rep(i, M){
        B[N - inputValue()] = 1;
    }
    int Q = inputValue();
    
    auto C = multipoly(A, B);
    
    repd(i, N, N + Q){
        output((int)(C[i].real() + 0.5), 0);
    }
    
    
    
    return 0;
}