分治FFT/NTT

Posted 2022-04-01 liguanlin1124

粘板子：

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
typedef long long ll;
const int MOD = 998244353;
const int N = 100050;
const int M = N*3;
template<typename T>
inline void read(T&x)

    T f = 1,c = 0;char ch=getchar();
    while(ch<‘0‘||ch>‘9‘)if(ch==‘-‘)f=-1;ch=getchar();
    while(ch>=‘0‘&&ch<=‘9‘)c=c*10+ch-‘0‘;ch=getchar();
    x = f*c;

template<typename T>inline void Mod(T&x)if(x>=MOD)x-=MOD;
int fastpow(int x,int y)

    int ret = 1;
    while(y)
    
        if(y&1)ret=1ll*ret*x%MOD;
        x=1ll*x*x%MOD;y>>=1;
    
    return ret;

int inv(int x)return fastpow(x,MOD-2);
int to[M],lim,L,LL[M];
void init(int len)

    lim=LL[2]=1;
    while(lim<len)lim<<=1,LL[lim<<1]=LL[lim]+1;

void get_lim(int len)

    lim = len,L = LL[len];
    for(int i=1;i<=lim;i++)to[i]=((to[i>>1]>>1)|((i&1)<<(L-1)));

void ntt(int*a,int len,int k)

    for(int i=0;i<len;i++)
        if(i<to[i])swap(a[i],a[to[i]]);
    for(int i=1;i<len;i<<=1)
    
        int w0 = fastpow(3,(MOD-1)/(i<<1));
        for(int j=0;j<len;j+=(i<<1))
        
            int w = 1;
            for(int o=0;o<i;o++,w=1ll*w*w0%MOD)
            
                int w1 = a[j+o],w2 = 1ll*a[j+o+i]*w%MOD;
                Mod(a[j+o] = w1+w2);
                Mod(a[j+o+i] = w1+MOD-w2);
            
        
    
    if(k==-1)
    
        for(int i=1;i<len>>1;i++)swap(a[i],a[len-i]);
        int Inv = inv(len);
        for(int i=0;i<len;i++)a[i]=1ll*a[i]*Inv%MOD;
    

int a[M],b[M],c[M];
int f[M],g[M],n;
void cdq(int l,int r)

    if(l==r)return ;
    int mid = (l+r)>>1;
    cdq(l,mid);
    get_lim(2*(r-l+1));
    for(int i=0;i<lim;i++)a[i]=b[i]=0;
    for(int i=0;i<=mid-l;i++)a[i]=f[l+i];
    for(int i=1;i<=r-l+1;i++)b[i]=g[i];
    ntt(a,lim,1),ntt(b,lim,1);
    for(int i=0;i<=lim;i++)c[i]=1ll*a[i]*b[i]%MOD;
    ntt(c,lim,-1);
    for(int i=mid+1-l;i<=r-l;i++)Mod(f[i+l]+=c[i]);
    cdq(mid+1,r);

int main()

//    freopen("tt.in","r",stdin);
    read(n);init(n<<1);f[0]=1;
    for(int i=1;i<n;i++)read(g[i]);
    cdq(0,lim-1);
    for(int i=0;i<n;i++)printf("%d ",f[i]);
    puts("");
    return 0;

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