FFT

#include<iostream>
#include<cstdlib>
#include<cmath>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<string>
#include<map>
#include<queue>
#include<vector>
#include<set>
#define inf 1000000000
#define maxn 200000+5
#define maxm 10000+5
#define eps 1e-10
#define ll long long
#define for0(i,n) for(int i=0;i<=(n);i++)
#define for1(i,n) for(int i=1;i<=(n);i++)
#define for2(i,x,y) for(int i=(x);i<=(y);i++)
#define for3(i,x,y) for(int i=(x);i>=(y);i--)
#define for4(i,x) for(int i=head[x],y=e[i].go;i;i=e[i].next,y=e[i].go)
using namespace std;
int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=10*x+ch-'0';ch=getchar();}
    return x*f;
}
struct cp{
    double x,y;
    inline cp operator +(cp b){return (cp){x+b.x,y+b.y};}
    inline cp operator -(cp b){return (cp){x-b.x,y-b.y};}
    inline cp operator *(cp b){return (cp){x*b.x-y*b.y,x*b.y+y*b.x};}
};
const double PI=acos(-1.0);
cp a[maxn],b[maxn],c[maxn],y[maxn];
int n,m,len,rev[maxn],ans[maxn];
char s[maxn];
void fft(cp *x,int n,int flag){
    for0(i,n-1)y[rev[i]]=x[i];
    for0(i,n-1)x[i]=y[i];
    for(int m=2;m<=n;m<<=1){
        cp wn=(cp){cos(2.0*PI/m*flag),sin(2.0*PI/m*flag)};//w£¨m£¬1£©
        for(int i=0;i<n;i+=m){
            cp w=(cp){1.0,0};int mid=m>>1;
            for0(j,mid-1){
                cp u=x[i+j],v=x[i+j+mid]*w;
                x[i+j]=u+v;x[i+j+mid]=u-v;
                w=w*wn;
            }
        }
    }
    if(flag==-1)for0(i,n-1)x[i].x/=n;
}

int main(){
    //freopen("input.txt","r",stdin);
    //freopen("output.txt","w",stdout);
    n=read();
    scanf("%s",s);
    for0(i,n-1)a[i].x=s[n-1-i]-'0';
    scanf("%s",s);
    for0(i,n-1)b[i].x=s[n-1-i]-'0';
    m=1;n=2*n-1;
    while(m<=n)m<<=1,len++;n=m;
    for0(i,n-1){
        int t=i,ret=0;
        for1(j,len)ret<<=1,ret|=t&1,t>>=1;
        rev[i]=ret;
    }    
    fft(a,n,1);fft(b,n,1);
    for0(i,n-1)c[i]=a[i]*b[i];
    fft(c,n,-1);
    for0(i,n-1)ans[i]=c[i].x+0.5;
    for0(i,n-1)ans[i+1]+=ans[i]/10,ans[i]%=10;
    n++;
    while(!ans[n]&&n)n--;
    for3(i,n,0)putchar('0'+ans[i]);
    return 0;
}

 

posted @ 2016-06-13 20:35  HTWX  阅读(197)  评论(0编辑  收藏  举报