HDU 1402

http://acm.hdu.edu.cn/showproblem.php?pid=1402

fft做O(nlog(n))大数乘法，kuangbin的模板

#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <math.h>
using namespace std;
const double PI = acos(-1.0);
//复数结构体
struct Complex
{
    double x,y;//实部和虚部 x+yi
    Complex(double _x = 0.0,double _y = 0.0)
    {
        x = _x;
        y = _y;
    }
    Complex operator -(const Complex &b)const
    {
        return Complex(x-b.x,y-b.y);
    }
    Complex operator +(const Complex &b)const
    {
        return Complex(x+b.x,y+b.y);
    }
    Complex operator *(const Complex &b)const
    {
        return Complex(x*b.x-y*b.y,x*b.y+y*b.x);
    }
};
/*
* 进行FFT和IFFT前的反转变换。
* 位置i和 （i二进制反转后位置）互换
* len必须去2的幂
*/
void change(Complex y[],int len)
{
    int i,j,k;
    for(i = , j = len/;i <len-;i++)
    {
        if(i < j)swap(y[i],y[j]);
        //交换互为小标反转的元素，i<j保证交换一次
        //i做正常的+1，j左反转类型的+1,始终保持i和j是反转的
        k = len/;
        while(j >= k)
        {
            j -= k;
            k /= ;
        }
        if(j < k)j += k;
    }
}
/*
* 做FFT
* len必须为2^k形式，
* on==1时是DFT，on==-1时是IDFT
*/
void fft(Complex y[],int len,int on)
{
    change(y,len);
    for(int h = ; h <= len; h <<= )
    {
        Complex wn(cos(-on**PI/h),sin(-on**PI/h));
        for(int j = ;j < len;j+=h)
        {
            Complex w(,);
            for(int k = j;k < j+h/;k++)
            {
                Complex u = y[k];
                Complex t = w*y[k+h/];
                y[k] = u+t;
                y[k+h/] = u-t;
                w = w*wn;
            }
        }
    }
    if(on == -)
        for(int i = ;i < len;i++)
            y[i].x /= len;
}
const int MAXN = ;
Complex x1[MAXN],x2[MAXN];
char str1[MAXN/],str2[MAXN/];
int sum[MAXN];
int main()
{
    while(~scanf("%s%s",str1,str2))
    {
        int len1 = strlen(str1);
        int len2 = strlen(str2);
        int len = ;
        while(len < len1* || len < len2*)len<<=;
        for(int i = ;i < len1;i++)
            x1[i] = Complex(str1[len1--i]-'',);
        for(int i = len1;i < len;i++)
            x1[i] = Complex(,);
        for(int i = ;i < len2;i++)
            x2[i] = Complex(str2[len2--i]-'',);
        for(int i = len2;i < len;i++)
            x2[i] = Complex(,);
        //求DFT
        fft(x1,len,);
        fft(x2,len,);
        for(int i = ;i < len;i++)
            x1[i] = x1[i]*x2[i];
        fft(x1,len,-);
        for(int i = ;i < len;i++)
            sum[i] = (int)(x1[i].x+0.5);
        for(int i = ;i < len;i++)
        {
            sum[i+]+=sum[i]/;
            sum[i]%=;
        }
        len = len1+len2-;
        while(sum[len] <=  && len > )len--;
        for(int i = len;i >= ;i--)
            printf("%d",sum[i]);
        printf("\n");
    }
    return ;
}