再写FFT模板

　　没什么好说的，今天又考了FFT（虽然不用FFT也能过）但是确实有忘了怎么写FFT了，于是乎只有重新写一遍FFT模板练一下手了。第一部分普通FFT，第二部分数论FFT，记一下模数2^23*7*17+1

　　

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
typedef double real;
namespace task1
{
        const int maxn = ;
        const real pi = 3.1415926535897932;
        struct Complex
        {
                real x,y;
                Complex(){}
                Complex(real x,real y=):x(x),y(y){}
        };
        Complex operator + (Complex c1,Complex c2)
        {
                return Complex(c1.x+c2.x,c1.y+c2.y);
        }
        Complex operator - (Complex c1,Complex c2)
        {
                return Complex(c1.x-c2.x,c1.y-c2.y);
        }
        Complex operator * (Complex c1,Complex c2)
        {
                return Complex(c1.x*c2.x-c1.y*c2.y,c1.y*c2.x+c1.x*c2.y);
        }
        Complex operator / (Complex c1,real k)
        {
                return Complex(c1.x/k,c1.y/k);
        }
        char s1[maxn],s2[maxn];
        Complex g1[maxn],g2[maxn],rr[maxn];
        int lst[maxn];
        void FFT(Complex g[],int l,int p)
        {
                int x;
                for (int i=;i<l;i++)
                {
                        x=;
                        for (int j=,k=(l>>);j<l;j<<=,k>>=)
                                if (i&j)x+=k;
                        if (x<i)
                                swap(g[x],g[i]);
                }
                Complex wt,w,tmp;
                for (int i=;i<l;i<<=)
                {
                        wt=Complex(cos(pi/i*p),sin(pi/i*p));
                        for (int j=;j<l;j+=(i<<))
                        {
                                Complex w=Complex(,);
                                for (int k=;k<i;k++)
                                {
                                        tmp=g[j+k];
                                        g[j+k]=g[j+k]+g[i+j+k]*w;
                                        g[i+j+k]=tmp-g[i+j+k]*w;
                                        w=w*wt;
                                }
                        }
                }
        }
        void main()
        {
                int l1,l2;
                scanf("%s",s1);
                scanf("%s",s2);
                l1=(int)strlen(s1);
                l2=(int)strlen(s2);
                for (int i=;i<l1;i++)
                        g1[(l1-i-)/]=g1[(l1-i-)/].x*+s1[i]-'';
                for (int i=;i<l2;i++)
                        g2[(l2-i-)/]=g2[(l2-i-)/].x*+s2[i]-'';
                int l=max(l1,l2)/+;
                while (l!=(l&(-l)))l-=l&(-l);
                l<<=;
                FFT(g1,l,);
                FFT(g2,l,);
                for (int i=;i<l;i++)rr[i]=g1[i]*g2[i];
                FFT(rr,l,-);
                for (int i=;i<l;i++)
                {
                        rr[i]=rr[i]/l;
                        lst[i]=(int)(rr[i].x+0.5);
                }
                for (int i=;i<l;i++)
                {
                        lst[i+]+=lst[i]/;
                        lst[i]%=;
                }
                while (l> && !lst[l-])l--;
                printf("%d",lst[l-]);
                for (int i=l-;i>=;i--)
                        printf("%04d",lst[i]);
                printf("\n");
        }
}
namespace task2
{
        typedef long long qword;
        const int maxn = ;
        const qword p = ;
        char s1[maxn],s2[maxn];
        qword g1[maxn],g2[maxn];;
        qword rr[maxn];
        qword pow_mod(qword x,qword y)
        {
                qword ret=;
                while (y)
                {
                        if (y&)ret=ret*x%p;
                        x=x*x%p;
                        y>>=;
                }
                return ret;
        }
        void FFT(qword g[],int l,int f)
        {
                int x=;
                for (int i=;i<l;i++)
                {
                        x=;
                        for (int j=,k=(l>>);j<l;j<<=,k>>=)
                                if (i&j)x+=k;
                        if (i<x)
                                swap(g[i],g[x]);
                }
                qword w,wt,tmp;
                for (int i=,t=;i<l;i<<=,t++)
                {
                        wt=pow_mod(,**(<<(-t)))%p;
                        if (f==-)
                                //wt=-wt;
                                wt=pow_mod(wt,p-);
                        for (int j=;j<l;j+=(i<<))
                        {
                                w=;
                                for (int k=;k<i;k++)
                                {
                                        tmp=g[j+k];
                                        g[j+k]=(g[j+k]+g[i+j+k]*w)%p;
                                        g[i+j+k]=(tmp-g[i+j+k]*w)%p;
                                        w=w*wt%p;
                                }
                        }
                }
        }
        void main()
        {
                int l1,l2;
            //    for (int i=0;i<5;i++)
            //            printf("[1/%d*pi]:%d\n",(1<<i),7*17*(1<<(23-i)));
                scanf("%s",s1);
                scanf("%s",s2);
                l1=(int)strlen(s1);
                l2=(int)strlen(s2);
                for (int i=;i<l1;i++)
                        g1[i]=s1[l1-i-]-'';
                for (int i=;i<l2;i++)
                        g2[i]=s2[l2-i-]-'';
                int l=max(l1,l2);
                while (l!=(l&(-l)))l-=l&(-l);
                l<<=;
                FFT(g1,l,);
                FFT(g2,l,);
                for (int i=;i<l;i++)rr[i]=g1[i]*g2[i]%p;
                FFT(rr,l,-);
                qword invl=pow_mod(l,p-);
                for (int i=;i<l;i++)rr[i]=(rr[i]*invl%p+p)%p;
                for (int i=;i<l;i++)
                {
                        rr[i+]+=rr[i]/;
                        rr[i]%=;
                }
                while (l> && ! rr[l-])l--;
                for (int i=l-;i>=;i--)
                        printf("%d",(int)rr[i]);
        }
}

int main()
{
        freopen("input.txt","r",stdin);
        task1::main();
        task2::main();
}