結果

問題 No.931 Multiplicative Convolution
ユーザー oteraotera
提出日時 2020-08-19 08:34:36
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,342 ms / 2,000 ms
コード長 7,554 bytes
コンパイル時間 2,249 ms
コンパイル使用メモリ 136,444 KB
最終ジャッジ日時 2025-01-13 03:40:37
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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 * 14
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 # 

/**
 *    author:  otera    
**/
#include<iostream>
#include<string> 
#include<cstdio>
#include<cstring>
#include<vector>
#include<cmath>
#include<algorithm> 
#include<functional>
#include<iomanip>
#include<queue>
#include<deque>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
using namespace std;

#define int long long
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
typedef long double ld;
const int inf=1e9+7;
const ll INF=1LL<<60 ;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef complex<ld> Point;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<int, int> P;
typedef pair<ld, ld> LDP;
typedef pair<ll, ll> LP;
#define fr first
#define sc second
#define all(c) c.begin(),c.end()
#define pb push_back
#define debug(x)  cerr << #x << " = " << (x) << endl;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

long long modpow(long long a, long long n, long long mod) {
    long long res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}

long long modinv(long long a, long long mod) {
    long long b = mod, u = 1, v = 0;
    while (b) {
        long long t = a/b;
        a -= t*b; swap(a, b);
        u -= t*v; swap(u, v);
    }
    u %= mod;
    if (u < 0) u += mod;
    return u;
}

const int MOD = 998244353;

namespace NTT {
    // const int MOD = 998244353;  // to be set appropriately
    const long long PR = 3;     // to be set appropriately
    
    void trans(vector<long long> &v, bool inv = false) {
        int n = (int)v.size();
        for (int i = 0, j = 1; j < n-1; j++) {
            for (int k = n>>1; k > (i ^= k); k >>= 1);
            if (i > j) swap(v[i], v[j]);
        }
        for (int t = 2; t <= n; t <<= 1) {
            long long bw = modpow(PR, (MOD-1)/t, MOD);
            if (inv) bw = modinv(bw, MOD);
            for (int i = 0; i < n; i += t) {
                long long w = 1;
                for (int j = 0; j < t/2; ++j) {
                    int j1 = i + j, j2 = i + j + t/2;
                    long long c1 = v[j1], c2 = v[j2] * w % MOD;
                    v[j1] = c1 + c2;
                    v[j2] = c1 - c2 + MOD;
                    while (v[j1] >= MOD) v[j1] -= MOD;
                    while (v[j2] >= MOD) v[j2] -= MOD;
                    w = w * bw % MOD;
                }
            }
        }
        if (inv) {
            long long inv_n = modinv(n, MOD);
            for (int i = 0; i < n; ++i) v[i] = v[i] * inv_n % MOD;
        }
    }
    
    // C is A*B
    vector<long long> mult(vector<long long> A, vector<long long> B) {
        int size_a = 1; while (size_a < A.size()) size_a <<= 1;
        int size_b = 1; while (size_b < B.size()) size_b <<= 1;
        int size_fft = max(size_a, size_b) << 1;
        
        vector<long long> cA(size_fft, 0), cB(size_fft, 0), cC(size_fft, 0);
        for (int i = 0; i < A.size(); ++i) cA[i] = A[i];
        for (int i = 0; i < B.size(); ++i) cB[i] = B[i];
        
        trans(cA); trans(cB);
        for (int i = 0; i < size_fft; ++i) cC[i] = cA[i] * cB[i] % MOD;
        trans(cC, true);
        
        vector<long long> res((int)A.size() + (int)B.size() - 1);
        for (int i = 0; i < res.size(); ++i) res[i] = cC[i];
        return res;
    }
};

ll get_root(ll p) {
    for(int r = 2; r < p; ++ r) {
        int x = 1;
        set<int> se;
        while(true) {
            if(se.size() == p - 1) return r;
            if(se.count(x)) break;
            se.insert(x);
            x = x * r % p;
        }
    }
    assert(false);
}

struct ComplexNumber {
    double real, imag;
    inline ComplexNumber& operator = (const ComplexNumber &c) {real = c.real; imag = c.imag; return *this;}
    friend inline ostream& operator << (ostream &s, const ComplexNumber &c) {return s<<'<'<<c.real<<','<<c.imag<<'>';}
};
inline ComplexNumber operator + (const ComplexNumber &x, const ComplexNumber &y) {
    return {x.real + y.real, x.imag + y.imag};
}
inline ComplexNumber operator - (const ComplexNumber &x, const ComplexNumber &y) {
    return {x.real - y.real, x.imag - y.imag};
}
inline ComplexNumber operator * (const ComplexNumber &x, const ComplexNumber &y) {
    return {x.real * y.real - x.imag * y.imag, x.real * y.imag + x.imag * y.real};
}
inline ComplexNumber operator * (const ComplexNumber &x, double a) {
    return {x.real * a, x.imag * a};
}
inline ComplexNumber operator / (const ComplexNumber &x, double a) {
    return {x.real / a, x.imag / a};
}

const int MAX = 1<<19;               // must be 2^n

struct FFT {
    vector<ComplexNumber> AT, BT, CT;

    void DTM(vector<ComplexNumber> &F, bool inv) {
        int N = MAX;
        for (int t = N; t >= 2; t >>= 1) {
            double ang = acos(-1.0)*2/t;
            for (int i = 0; i < t/2; i++) {
                ComplexNumber w = {cos(ang*i), sin(ang*i)};
                if (inv) w.imag = -w.imag;
                for (int j = i; j < N; j += t) {
                    ComplexNumber f1 = F[j] + F[j+t/2];
                    ComplexNumber f2 = (F[j] - F[j+t/2]) * w;
                    F[j] = f1;
                    F[j+t/2] = f2;
                }
            }
        }
        for (int i = 1, j = 0; i < N; i++) {
            for (int k = N >> 1; k > (j ^= k); k >>= 1);
            if (i < j) swap(F[i], F[j]);
        }
    }
    
    // C is A*B
    void mult(vector<long long> &A, vector<long long> &B, vector<long long> &C) {
        AT.assign(MAX, {0.0, 0.0});
        BT.assign(MAX, {0.0, 0.0});
        CT.assign(MAX, {0.0, 0.0});
        for (int i = 0; i < MAX; ++i) AT[i] = {(double)A[i], 0.0};
        for (int i = 0; i < MAX; ++i) BT[i] = {(double)B[i], 0.0};
        
        DTM(AT, false);
        DTM(BT, false);
        
        for (int i = 0; i < MAX; ++i) CT[i] = AT[i] * BT[i];
        
        DTM(CT, true);
        
        for (int i = 0; i < MAX; ++i) {
            CT[i] = CT[i] / MAX;
            C[i] = (long long)(CT[i].real + 0.5);
        }
    }
};

void solve() {
	int p; cin >> p;
    // vector<int> a(MAX, 0), b(MAX, 0);
    vector<int> a(p, 0), b(p, 0);
    rep(i, p - 1) {
        cin >> a[i + 1];
    }
    rep(i, p - 1) {
        cin >> b[i + 1];
    }
    if(p == 2) {
        cout << a[1] * b[1] % MOD << endl;
        return;
    }
    int r = get_root(p);
    vector<int> x(1<<17), y(1<<17);
    int v = 1;
    rep(i, p - 1) {
        x[i] = a[v], y[i] = b[v]; // v = r ^ i
        // cerr << v << " ";
        v = v * r % p;
    }
    // cerr << endl;
    auto z = NTT::mult(x, y);
    // vector<int> c(MAX);
    // FFT fft;
    // fft.mult(a, b, c);
    vector<int> ans(p, 0);
    v = 1;
    rep(i, (int)z.size()) {
        ans[v] += z[i]; // v = r ^ i
        // ans[v] += c[i];
        ans[v] %= MOD;
        v = v * r % p;
    }
    for(int i = 1; i <= p - 1; ++ i) {
        cout << ans[i] << " ";
    }
    cout << endl;
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//int t; cin >> t; rep(i, t)solve();
	solve();
    return 0;
}
0