bzoj 2194 快速傅里叶之二

 

而标准卷积是：

 

标准卷积是：下标之和为定值，而这里下标之差是定值，将b数组倒过来。

C[0] = C[n-1]

模板是绍兴一中NTT板子。

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

typedef long long LL;
const int maxn=210000;
const LL P=998244353;
const LL mod=998244353;
const LL g=3;
int N,na,nb;
LL a[maxn*2],b[maxn*2],W[2][maxn*2],rev[maxn*2],f[maxn*2],tmp[maxn*2];
LL inv[410000];
LL ff[410000];
LL pow_mod(LL a,int b)
{
    LL c=1;
    for (;b; b>>=1,a=a*a%P) if (b&1) c=c*a%P;
    return c;
}

void NTT(LL*a,int f,int N)
{
    for (int i=0;i<N;i++) if (i<rev[i]) swap(a[i],a[rev[i]]);
    for (int i=1;i<N;i<<=1)
        for (int j=0,t=N/(i<<1);j<N;j+=i<<1)
            for (int k=0,l=0,x,y;k<i;k++,l+=t) x=(LL)W[f][l]*a[j+k+i]%P,y=a[j+k],a[j+k]=(y+x)%P,a[j+k+i]=(y-x+P)%P;
    if (f) for (int i=0,x=pow_mod(N,P-2);i<N;i++) a[i]=(LL)a[i]*x%P;
}

void change(int N)
{
    for (int i=0;i<N;i++)
    {
        int x=i,y=0;
        for (int k=1; k<N; x>>=1,k<<=1) (y<<=1)|=x&1;
        rev[i]=y;
    }
}
void init(int N)
{
    W[0][0]=W[1][0]=1;
    for (int i=1,x=pow_mod(g,(P-1)/N),y=pow_mod(x,P-2); i<N; i++)
        W[0][i]=(LL)x*W[0][i-1]%P,W[1][i]=(LL)y*W[1][i-1]%P;
    change(N);
}



int main()
{
    //freopen("in.txt","r",stdin);
    int n;
    scanf("%d",&n);
    na = nb = n;

    N = 1;
    while(N<=na*2||N<=nb*2)
        N<<=1;

    init(N);

    for(int i=0;i<na;i++) {
        scanf("%I64d",&a[i]);
        scanf("%I64d",&b[nb-i-1]);
    }
    for(int i=na;i<N;i++)
        a[i] = 0;
    for(int i=nb;i<N;i++)
        b[i] = 0;

    NTT(a,0,N);
    NTT(b,0,N);

    for(int i=0;i<N;i++)
        a[i] = a[i]*b[i]%mod;

    NTT(a,1,N);


    for(int i=0;i<n;i++)
        printf("%I64d\n",a[i+n-1]);

    return 0;
}