FFT快速傅里叶变化

Posted 2020-08-13 InWILL

纪念人生第一次FFT

 1 #include<iostream>
 2 #include<cmath>
 3 using namespace std;
 4 
 5 const int MAXN=200010;
 6 class BigNum
 7 {
 8 public:
 9     double r,i;
10     BigNum(double _r=0.0,double _i=0.0){r=_r;i=_i;}
11     BigNum operator+(const BigNum T){return BigNum(r+T.r,i+T.i);}
12     BigNum operator-(const BigNum T){return BigNum(r-T.r,i-T.i);};
13     BigNum operator*(const BigNum T){return BigNum(r*T.r-i*T.i,r*T.i+i*T.r);};
14 };
15 
16 void Brc(BigNum *T,int N)
17 {
18     int i,j,k;
19     for(i=1,j=N/2;i<N-1;i++)
20     {
21         if(i<j) swap(T[i],T[j]);
22         k=N/2;
23         while(j>=k)
24         {
25             j-=k;
26             k>>=1;
27         }
28         if(j<k) j+=k;
29     }
30 }
31 
32 void FFT(BigNum *T,int N,int flag)
33 {
34     Brc(T,N);
35     for(int i=2;i<=N;i<<=1)
36     {
37         BigNum wn(cos(2*M_PI/i),sin(2*M_PI/i));
38         for(int j=0;j<N;j+=i)
39         {
40             BigNum w(1,0);
41             for(int k=j;k<j+i/2;k++)
42             {
43                 BigNum u=T[k];
44                 BigNum t=w*T[k+i/2];
45                 T[k]=u+t;
46                 T[k+i/2]=u-t;
47                 w=w*wn;
48             }
49         }
50     } 
51     if(flag==-1)
52         for(int i=0;i<N;i++)
53             T[i].r/=N;
54 }