Fast number theory Transformation Template (NTT)

The principle of rapid number theory change (NTT) is actually the same principle as the fast Fourier transform. For the Fermat prime of a shape such as m= c*2^n+1, it is assumed that its original root is G. So deceive g^ (m-1) ==1 and just (m-1) can divide 2^n. So the NTT transform can be performed in the modulo p field. The rotation factor is g^ ((m-1)/n). The other principles are the same as the FFT principle. This solves the floating-point error of the FFT in special cases.

/* * Author:islands * Created time:2015/7/30 9:25:47 * File Name:test.cpp */#include <iostream> #include <cst dio> #include <cstdlib> #include <cstring> #include <cmath> #include <algorithm> #include <string> #include <vector> #include <stack> #include <queue> #include <set> #include <   time.h>using namespace std; #define MP (x, y) make_pair (x, y) const int inf = 0x3fffffff;typedef long long ll;const int Mmax  = 1<<18;const int mod = (479<<21) +1;const int g = 3;    Original Root ll quick_mod (ll A,ll b) {ll ans=1;        for (; b;b/=2) {if (b&1) Ans=ans*a%mod;    A=a*a%mod; } return ans;    int rev (int x,int R)//butterfly operation {int ans=0;        for (int i=0; i<r; i++) {if (x& (1<<i)) {ans+=1<< (r-i-1); }} return ans;    void NTT (int n,ll a[],int on)//length n (2 times) {int r=0;    for (;; r++) {if ((1<<r) ==n) break; } for (int i=0; i<n;        i++) {int Tmp=rev (I,R);    if (i<tmp) swap (a[i],a[tmp]);        } for (int s=1; s<=r; s++) {int m=1<<s;        LL Wn=quick_mod (g, (mod-1)/m);            for (int k=0; k<n; k+=m) {LL w=1;                for (int j=0; j<m/2; J + +) {LL t,u;                t=w* (a[k+j+m/2]%mod)%mod;                U=a[k+j]%mod;                a[k+j]= (u+t)%mod;                A[k+j+m/2]= ((u-t)%mod+mod)%mod;            W=w*wn%mod;        }}} if (On==-1) {for (int i=1;i<n/2;i++) swap (a[i],a[n-i]);        LL Inv=quick_mod (n,mod-2);    for (int i=0;i<n;i++) A[i]=a[i]%mod*inv%mod; }}ll a[mmax+10],b[mmax+10];    LL Ans[mmax+10];int Main () {//freopen ("In.txt", "R", stdin);    int n,m;    string S1;    String S2;        while (CIN&GT;&GT;S1&GT;&GT;S2) {n=s1.size ();        M=s2.size ();        memset (a,0,sizeof A); memset (b,0,sizeof B);       for (int i=n-1; i>=0; i--) a[i]=s1[n-i-1]-' 0 ';        for (int i=m-1; i>=0; i--) b[i]=s2[m-i-1]-' 0 ';        int tmp=1;        while (Tmp<max (n,m)) tmp*=2;        n=tmp;        NTT (2*n,a,1);        NTT (2*n,b,1);        for (int i=0; i<2*n; i++) A[i]=a[i]*b[i]%mod;        NTT (2*n,a,-1);        Memset (ans,0,sizeof ans);            for (int i=0;i<2*n;i++) {ans[i]+=a[i];                if (ans[i]>=10) {ANS[I+1]+=ANS[I]/10;            ans[i]%=10;        }} int e=0;                for (int i=2*n-1;i>=0;i--) {if (Ans[i]) {e=i;            Break        }} for (int i=e;i>=0;i--) {printf ("%lld", Ans[i]);    } printf ("\ n"); }}

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Fast number theory Transformation Template (NTT)