FFT快速傅里叶变化

纪念人生第一次FFT

前排感谢iamzky，讲解非常详细

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;

const int MAXN=200010;
class BigNum
{
public:
    double r,i;
    BigNum(double _r=0.0,double _i=0.0){r=_r;i=_i;}
    BigNum operator+(const BigNum T){return BigNum(r+T.r,i+T.i);}
    BigNum operator-(const BigNum T){return BigNum(r-T.r,i-T.i);};
    BigNum operator*(const BigNum T){return BigNum(r*T.r-i*T.i,r*T.i+i*T.r);};
};

void Brc(BigNum *T,int N)
{
    int i,j,k;
    for(i=1,j=N/2;i<N-1;i++)
    {
        if(i<j) swap(T[i],T[j]);
        k=N/2;
        while(j>=k)
        {
            j-=k;
            k>>=1;
        }
        if(j<k) j+=k;
    }
}

void FFT(BigNum *T,int N,int flag)
{
    Brc(T,N);
    for(int i=2;i<=N;i<<=1)
    {
        BigNum wn(cos(2*M_PI/i),flag*sin(2*M_PI/i));
        for(int j=0;j<N;j+=i)
        {
            BigNum w(1,0);
            for(int k=j;k<j+i/2;k++)
            {
                BigNum u=T[k];
                BigNum t=w*T[k+i/2];
                T[k]=u+t;
                T[k+i/2]=u-t;
                w=w*wn;
            }
        }
    } 
    if(flag==-1)
        for(int i=0;i<N;i++)
            T[i].r/=N;
}

string s1,s2;
BigNum A[MAXN],B[MAXN],C[MAXN];
int a[MAXN],b[MAXN],sum[MAXN];
int N;

int main()
{
    cin>>s1>>s2;
    int L1=s1.size();
    int L2=s2.size();
    for(N=1;N<max(L1,L2);N<<=1);N<<=1;
    for(int i=0;i<L1;i++) a[L1-i-1]=s1[i]-'0';
    for(int i=0;i<L2;i++) b[L2-i-1]=s2[i]-'0';
    for(int i=0;i<N;i++) A[i]=BigNum(a[i]);
    for(int i=0;i<N;i++) B[i]=BigNum(b[i]);
    FFT(A,N,1);FFT(B,N,1);  
    for(int i=0;i<N;i++)C[i]=A[i]*B[i];
    FFT(C,N,-1);
    for(int i=0;i<N;i++)sum[i]=C[i].r+0.5;  
    for(int i=0;i<N;i++)
    {  
        sum[i+1]+=sum[i]/10;  
        sum[i]%=10;  
    }  
    int l=L1+L2-1;  
    while(sum[l]==0&&l>0)l--;  
    for(int i=l;i>=0;i--)  
    cout<<sum[i];
    return 0;
}