NTT板子

不说别的。

这份NTT跑得比FFT快，不知道为什么。

以下代码针对\(10^5\)的数据范围。

#include<cstdio>
#include<vector>
#include<algorithm>
#include<cstring>
using namespace std;
inline int read() {
    int a = 0, c = getchar(), w = 1;
    for(; c < '0' || c > '9'; c = getchar()) if(c == '-') w = -1;
    for(; c >= '0' && c <= '9'; c = getchar()) a = a * 10 + c - '0';
    return a * w;
}

const int md = 998244353, gmd = 3;
inline int add(int x, int y) {
    x += y;
    return x >= md ? x - md : x;
}
inline void Add(int& x, int y) {
    x += y;
    if(x >= md) x -= md;
}
inline int sub(int x, int y) {
    x -= y;
    return x < 0 ? x + md : x;
}
inline int mul(int x, int y) {
    return (long long)x*y%md;
}
inline int qpow(int a, int x) {
    int ret = 1;
    while(x) {
        if(x&1) ret = mul(ret, a);
        a = mul(a, a);
        x >>= 1;
    }
    return ret;
}
inline int inv(int x) {
    return qpow(x, md-2);
}

const int maxn = 1<<17;
int w[2][1<<19], invn[1<<18];
void nttinit() {
    for(int i = 0; i <= 18; i++) {
        w[1][1<<i] = w[0][1<<i] = 1;
        int wn = qpow(gmd, (md-1)/(1<<i+1)), invwn = inv(wn);
        for(int j = (1<<i)+1; j < 1<<i+1; j++) {
            w[1][j] = mul(w[1][j-1], wn);
            w[0][j] = mul(w[0][j-1], invwn);
        }
    }
    for(int i = 1; i <= 1<<18; i <<= 1) invn[i] = inv(i);
}
void ntt(int a[], int n, bool typ) {
    for(int i = 1, j = n>>1; i < n; i++) {
        if(i < j) swap(a[i], a[j]);
        for(int k = n>>1; (j^=k) < k; k >>= 1);
    }
    for(int i = 1; i < n; i <<= 1) for(int j = 0; j < n; j += i<<1) for(int k = 0; k < i; k++) {
        int u = a[j+k], v = mul(w[typ][i+k], a[j+i+k]);
        a[j+k] = add(u, v);
        a[j+i+k] = sub(u, v);
    }
    if(!typ) for(int i = 0; i < n; i++) a[i] = mul(a[i], invn[n]);
}
int tmp[maxn<<1];
void Mul(int a[], int an, int b[], int bn) {
    if(an <= 48 || bn <= 48) {
        memset(tmp, 0, (an+bn-1)*sizeof(int));
        for(int i = 0; i < an; i++) for(int j = 0; j < bn; j++) Add(tmp[i+j], mul(a[i], b[j]));
        memcpy(a, tmp, (an+bn-1)*sizeof(int));
        return;
    }
    int n = 1;
    while(n < an+bn-1) n <<= 1;
    ntt(a, n, 1); ntt(b, n, 1);
    for(int i = 0; i < n; i++) a[i] = mul(a[i], b[i]);
    ntt(a, n, 0);
}

int n, m;
int a[maxn<<1], b[maxn<<1];

int main() {
    n = read(); m = read();
    nttinit();
    for(int i = 0; i < n+1; i++) a[i] = read();
    for(int i = 0; i < m+1; i++) b[i] = read();
    Mul(a, n+1, b, m+1);
    for(int i = 0; i < n+m+1; i++) printf("%d ", a[i]);
    printf("\n");
    return 0;
}

1640ms。

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
using namespace std;
inline int read() {
    int a = 0, c = getchar(), w = 1;
    for(; c < '0' || c > '9'; c = getchar()) if(c == '-') w = -1;
    for(; c >= '0' && c <= '9'; c = getchar()) a = a * 10 + c - '0';
    return a * w;
}

const double pi = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899;
struct complex {
    double r, v;
    complex() {}
    complex(double rr, double vv) {r = rr; v = vv;} 
};
inline complex operator + (complex a, complex b) {
    return complex(a.r+b.r, a.v+b.v);
}
inline complex operator - (complex a, complex b) {
    return complex(a.r-b.r, a.v-b.v);
}
inline complex operator - (complex x) {
    return complex(-x.r, -x.v);
}
inline complex operator * (complex a, complex b) {
    return complex(a.r*b.r-a.v*b.v, a.r*b.v+a.v*b.r);
}

const int maxn = 1<<17;
void fft(complex a[], int n, bool typ) {
    for(int i = 1, j = n>>1; i < n; i++) {
        if(i < j) swap(a[i], a[j]);
        for(int k = n>>1; (j^=k) < k; k >>= 1);
    }
    for(int i = 1; i < n; i <<= 1) for(int j = 0; j < n; j += i<<1) {
        complex w = complex(1, 0), wn = complex(cos(pi/(double)i), (typ?1:-1)*sin(pi/(double)i));
        for(int k = 0; k < i; k++) {
            complex u = a[j+k], v = w * a[j+i+k];
            a[j+k] = u + v;
            a[j+i+k] = u - v;
            w = w * wn;
        }
    }
    if(!typ) for(int i = 0; i < n; i++) a[i].r /= n;
}
complex tmp[maxn<<1];
void Mul(complex a[], int an, complex b[], int bn) {
    if(an <= 48 || bn <= 48) {
        for(int i = 0; i < an+bn-1; i++) tmp[i] = complex(0, 0);
        for(int i = 0; i < an; i++) for(int j = 0; j < bn; j++) tmp[i+j] = tmp[i+j] + a[i] * b[j];
        for(int i = 0; i < an+bn-1; i++) a[i] = tmp[i];
        return;
    }
    int n = 1;
    while(n < an+bn-1) n <<= 1;
    fft(a, n, 1); fft(b, n, 1);
    for(int i = 0; i < n; i++) a[i] = a[i] * b[i];
    fft(a, n, 0);
}

int n, m;
complex a[maxn<<1], b[maxn<<1];

int main() {
    n = read(); m = read();
    for(int i = 0; i < n+1; i++) a[i] = complex(read(), 0);
    for(int i = 0; i < m+1; i++) b[i] = complex(read(), 0);
    Mul(a, n+1, b, m+1);
    for(int i = 0; i < n+m+1; i++) printf("%d ", int(a[i].r+0.5));
    printf("\n");
    return 0;
}

1919ms。