多项式半家桶

基于 NTT 实现（不是任意模数）。

有卷积，求逆，exp，ln，除法。

使用指南明天写。

code

#include<bits/stdc++.h>
namespace PolyBasedNTT{
using std::memset;using std::memcpy;using std::swap;using std::reverse;using std::fill;using std::copy;
#define N LENconst int Mod = 998244353,G = 3,Gi = 332748118;const int LEN = 4e6 + 10;int lastnnn = 0,lastlim = 0,initinvn = 0,_to[N],_inv[N];int qpow(int a,int b,int Mod = Mod){int res = 1;for(;b;b >>= 1,a = 1ll*a*a%Mod)if(b&1) res = 1ll*res*a%Mod;return res;}int invi(int a){return qpow(a,Mod-2,Mod);}template<class T>T FMod(const T x){return x >= Mod?x - Mod:x;}void bfconvolution(int *a,int *b,int lena,int lenb){static int w[N];for(int i = 0;i < lena; ++i) for(int j = 0;j < lenb; ++j)w[i+j] = FMod(w[i+j]+1ll*a[i]*b[j]%Mod);copy(w,w+lena+lenb,a);fill(w,w+lena+lenb,0);}int _prepare(int n){if(lastnnn == n) return lastlim;lastnnn = n;uint lim = 1,ct = -1;while(lim <= n) lim <<= 1,ct++;for(int i = 0;i < lim; ++i) _to[i] = (_to[i>>1]>>1)|((i&1)<<ct);return (lastlim = lim);}void mult(int *f,int *g,int len){for(int i = 0;i < len; ++i) f[i] = 1ll*f[i]*g[i]%Mod;}void clear(int *f,int len,int val = 0){memset(f,val,4*len);}void cpy(int *f,int *g,int len){memcpy(f,g,4*len);}void NTT(int *a,int n,bool type = true){n = _prepare(n);for(int i = 0;i < n; ++i) if(i < _to[i]) swap(a[i],a[_to[i]]);for(int mid = 1;mid < n;mid <<= 1){int W = qpow(type?G:Gi,(Mod-1)/(mid<<1));for(int Res = mid<<1,j = 0;j < n;j += Res){int w = 1;for(int k = 0;k < mid; ++k,w = 1ll*w*W%Mod){int x = a[j+k],y = 1ll*w*a[j+k+mid]%Mod;a[j+k] = FMod(x+y);a[j+k+mid] = FMod(x-y+Mod);}}}}void convolution(int *a,int *b,int n,int m){int len = n + m,llen = invi(_prepare(len)),Len = _prepare(len);static int sav[N];clear(sav,len);cpy(sav,b,len);NTT(a,len);if(a != b) NTT(b,len);for(int i = 0;i < Len; ++i) a[i] = 1ll*a[i]*b[i]%Mod;NTT(a,len,false);for(int i = 0;i < len; ++i) a[i] = 1ll*a[i]*llen%Mod;fill(a+len,a+Len,0);cpy(b,sav,len);}void invp(int *b,int *a,int n){if(n == 1) return b[0] = invi(a[0]),void();invp(b,a,(n+1)>>1);static int c[N];int emm = 2*n-1,len = _prepare(emm);cpy(c,a,n);clear(c+n,len-n+1);NTT(c,emm);NTT(b,emm);for(int i = 0;i < len; ++i) b[i] = FMod(2ll-1ll*b[i]*c[i]%Mod+Mod)*b[i]%Mod;NTT(b,emm,0);int invn = invi(len);for(int i = 0;i < n; ++i) b[i] = 1ll*b[i]*invn%Mod;clear(b+n,len-n+1);}void invp(int *a,int n){static int b[N];invp(b,a,n);cpy(a,b,n+1);clear(b,lastlim);}void sqrtp(int *a,int n){static int b1[N],b2[N],b3[N];int m = n + 1;n = 1;while(n <= m) n <<= 1;b1[0] = 1;for(int len = 2;len <= n;len <<= 1){for(int i = 0;i < (len>>1); ++i) b2[i] = b1[i];for(int i = 0;i < len; ++i) b3[i] = a[i];invp(b2,len);convolution(b3,b2,len,len);for(int i = 0;i < len; ++i) b1[i] = FMod(b1[i]+b3[i])*499122177ll%Mod;clear(b2,lastlim);clear(b3,lastlim);clear(b1+len,lastlim-len);}cpy(a,b1,m);clear(b1,n+n);clear(b2,n+n);clear(b3,n+n);}void rev(int *f,int len){reverse(f,f+len);}void modp(int *f,int *g,int n,int m){static int q[N],t[N];int L = n-m+1;rev(g,m);cpy(q,g,L);rev(g,m);rev(f,n);cpy(t,f,L);rev(f,n);invp(q,L);convolution(q,t,L,L);rev(q,L);fill(q+L,q+lastlim,0);convolution(g,q,n,n);for(int i = 0;i < m-1; ++i) g[i] = FMod(f[i]-g[i]+Mod);cpy(f,q,L);clear(f+L,n-L);clear(q,lastlim);clear(t,lastlim);}void Diff(int *f,int n){for(int i = 0;i < n - 1; ++i) f[i] = 1ll*(i+1)*f[i+1]%Mod;f[n-1] = 0;}void Init(int *inv,int n){if(initinvn >= n) return;if(initinvn == 0){inv[0] = inv[1] = 1;for(int i = 2;i <= n; ++i) inv[i] = 1ll*inv[Mod%i]*(Mod-Mod/i)%Mod;initinvn = n;}else{for(int i = initinvn + 1;i <= n; ++i) inv[i] = 1ll*inv[Mod%i]*(Mod-Mod/i)%Mod;initinvn = n;}}void integral(int *f,int n){Init(_inv,n);for(int i = n; i; --i) f[i] = 1ll*f[i-1]*_inv[i]%Mod;f[0] = 0;}void ln(int *f,int n){static int g[N];cpy(g,f,n);invp(g,n);int LL = lastlim;Diff(f,n);convolution(f,g,n,n);integral(f,n-1);clear(g,LL);}void exp(int *f,int m){static int s[N],s2[N];int n = 1;while(n < m) n <<= 1;n <<= 1;s2[0] = 1;for(int len = 2;len <= n;len <<= 1){cpy(s,s2,len>>1);ln(s,len);for(int i = 0;i < len; ++i) s[i] = FMod(f[i]-s[i]+Mod);s[0] = FMod(s[0] + 1);convolution(s2,s,len,len);}cpy(f,s2,m);clear(s,n);clear(s2,n+n);}
#undef N
}using namespace PolyBasedNTT;