大数相乘模板

#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 r,i;
complex(double _r = 0.0,double _i = 0.0)
{
r = _r; i = _i;
}
complex operator +(const complex &b)
{
return complex(r+b.r,i+b.i);
}
complex operator -(const complex &b)
{
return complex(r-b.r,i-b.i);
}
complex operator *(const complex &b)
{
return complex(r*b.r-i*b.i,r*b.i+i*b.r);
}
};
/*
* 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 = 1, j = len/2;i < len-1; 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/2;
while( j >= k)
{
j -= k;
k /= 2;
}
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 = 2; h <= len; h <<= 1)
{
complex wn(cos(-on*2*PI/h),sin(-on*2*PI/h));
for(int j = 0;j < len;j+=h)
{
complex w(1,0);
for(int k = j;k < j+h/2;k++)
{
complex u = y[k];
complex t = w*y[k+h/2];
y[k] = u+t;
y[k+h/2] = u-t;
w = w*wn;
}
}
}
if(on == -1)
for(int i = 0;i < len;i++)
y[i].r /= len;
}
const int MAXN = 200010;
complex x1[MAXN],x2[MAXN];
char str1[MAXN/2],str2[MAXN/2];
int sum[MAXN];
int main()
{
while(scanf("%s%s",str1,str2)==2)
{
int len1 = strlen(str1);
int len2 = strlen(str2);
int len = 1;
while(len < len1*2 || len < len2*2)len<<=1;
for(int i = 0;i < len1;i++)
x1[i] = complex(str1[len1-1-i]-'0',0);
for(int i = len1;i < len;i++)
x1[i] = complex(0,0);
for(int i = 0;i < len2;i++)
x2[i] = complex(str2[len2-1-i]-'0',0);
for(int i = len2;i < len;i++)
x2[i] = complex(0,0);
//求DFT
fft(x1,len,1);
fft(x2,len,1);
for(int i = 0;i < len;i++)
x1[i] = x1[i]*x2[i];
fft(x1,len,-1);
for(int i = 0;i < len;i++)
sum[i] = (int)(x1[i].r+0.5);
for(int i = 0;i < len;i++)
{
sum[i+1]+=sum[i]/10;
sum[i]%=10;
}
len = len1+len2-1;
while(sum[len] <= 0 && len > 0)len--;
for(int i = len;i >= 0;i--)
printf("%c",sum[i]+'0');
printf("\n");
}
return 0;
}