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
1 #include<iostream> 2 #include<cstdio> 3 #include<cmath> 4 using namespace std; 5 6 const int MAXN=200010; 7 class BigNum 8 { 9 public: 10 double r,i; 11 BigNum(double _r=0.0,double _i=0.0){r=_r;i=_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);}; 14 BigNum operator*(const BigNum T){return BigNum(r*T.r-i*T.i,r*T.i+i*T.r);}; 15 }; 16 17 void Brc(BigNum *T,int N) 18 { 19 int i,j,k; 20 for(i=1,j=N/2;i<N-1;i++) 21 { 22 if(i<j) swap(T[i],T[j]); 23 k=N/2; 24 while(j>=k) 25 { 26 j-=k; 27 k>>=1; 28 } 29 if(j<k) j+=k; 30 } 31 } 32 33 void FFT(BigNum *T,int N,int flag) 34 { 35 Brc(T,N); 36 for(int i=2;i<=N;i<<=1) 37 { 38 BigNum wn(cos(2*M_PI/i),flag*sin(2*M_PI/i)); 39 for(int j=0;j<N;j+=i) 40 { 41 BigNum w(1,0); 42 for(int k=j;k<j+i/2;k++) 43 { 44 BigNum u=T[k]; 45 BigNum t=w*T[k+i/2]; 46 T[k]=u+t; 47 T[k+i/2]=u-t; 48 w=w*wn; 49 } 50 } 51 } 52 if(flag==-1) 53 for(int i=0;i<N;i++) 54 T[i].r/=N; 55 } 56 57 string s1,s2; 58 BigNum A[MAXN],B[MAXN],C[MAXN]; 59 int a[MAXN],b[MAXN],sum[MAXN]; 60 int N; 61 62 int main() 63 { 64 cin>>s1>>s2; 65 int L1=s1.size(); 66 int L2=s2.size(); 67 for(N=1;N<max(L1,L2);N<<=1);N<<=1; 68 for(int i=0;i<L1;i++) a[L1-i-1]=s1[i]-'0'; 69 for(int i=0;i<L2;i++) b[L2-i-1]=s2[i]-'0'; 70 for(int i=0;i<N;i++) A[i]=BigNum(a[i]); 71 for(int i=0;i<N;i++) B[i]=BigNum(b[i]); 72 FFT(A,N,1);FFT(B,N,1); 73 for(int i=0;i<N;i++)C[i]=A[i]*B[i]; 74 FFT(C,N,-1); 75 for(int i=0;i<N;i++)sum[i]=C[i].r+0.5; 76 for(int i=0;i<N;i++) 77 { 78 sum[i+1]+=sum[i]/10; 79 sum[i]%=10; 80 } 81 int l=L1+L2-1; 82 while(sum[l]==0&&l>0)l--; 83 for(int i=l;i>=0;i--) 84 cout<<sum[i]; 85 return 0; 86 }
