FFT模板

桃扇骨 2022-07-16 00:41 174阅读 0赞

HDU 1402 A\*B 高精度

#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;
    }