fft模板
手写类:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 | #include<cstdio> #include<cmath> const int LEN=300000; const double pi= acos (-1); inline int read(){ int x=0; char ch= getchar (); while (ch< '0' ||ch> '9' )ch= getchar (); while (ch>= '0' &&ch<= '9' )x=(x<<1)+(x<<3)+ch- '0' ,ch= getchar (); return x; } struct complex{ double r,v; complex( double a=0, double b=0):r(a),v(b){} inline complex operator+( const complex& b){ return complex(r+b.r,v+b.v);} inline complex operator-( const complex& b){ return complex(r-b.r,v-b.v);} inline complex operator*( const complex& b){ return complex(r*b.r-v*b.v,v*b.r+r*b.v);} }; inline void swap(complex& a,complex& b){complex t(a);a=b;b=t;} int n,m,L,H,R[LEN]; complex a[LEN],b[LEN]; complex w[LEN]; int ans[LEN]; void FFT(complex* a, int f){ for ( int i=0;i<L;i++) if (i<R[i])swap(a[i],a[R[i]]); for ( int len=2;len<=L;len<<=1){ int l=len>>1; complex wn( cos (pi/l),f* sin (pi/l)); for ( int i=1;i<l;i++) w[i]=w[i-1]*wn; for ( int st=0;st<L;st+=len) for ( int k=0;k<l;k++){ complex x=a[st+k],y=w[k]*a[st+k+(len>>1)]; a[st+k]=x+y,a[st+k+(len>>1)]=x-y; } } } int main(){ w[0].r=1; n=read()+1,m=read()+1; for ( int i=0;i<n;i++) a[i]=read(); for ( int i=0;i<m;i++) b[i]=read(); for (H=0,L=1;L<(n+m-1);H++)L<<=1; for ( int i=0;i<L;i++) R[i]=(R[i>>1]>>1)|((i&1)<<(H-1)); FFT(a,1),FFT(b,1); for ( int i=0;i<L;i++) a[i]=a[i]*b[i]; FFT(a,-1); for ( int i=0;i<n+m-1;i++) printf ( "%d " , int (a[i].r/L+0.5)); return 0; } |
内置:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | #include<bits/stdc++.h> #define pi acos(-1) using namespace std; typedef complex< double > E; int n,m; E a[262145],b[262145]; void fft(E *x, int n, int type) { if (n==1) return ; E l[n>>1],r[n>>1]; for ( int i=0;i<n;i+=2) l[i>>1]=x[i],r[i>>1]=x[i+1]; fft(l,n>>1,type);fft(r,n>>1,type); E wn( cos (2*pi/n), sin (type*2*pi/n)),w(1,0),t; for ( int i=0;i<n>>1;i++,w*=wn) t=w*r[i],x[i]=l[i]+t,x[i+(n>>1)]=l[i]-t; } int main() { scanf ( "%d%d" ,&n,&m); for ( int i=0,x;i<=n;i++) scanf ( "%d" ,&x),a[i]=x; for ( int i=0,x;i<=m;i++) scanf ( "%d" ,&x),b[i]=x; m=n+m; for (n=1;n<=m;n<<=1); fft(a,n,1);fft(b,n,1); for ( int i=0;i<=n;i++)a[i]=a[i]*b[i]; fft(a,n,-1); for ( int i=0;i<=m;i++) printf ( "%d " ,( int )(a[i].real()/n+0.5)); return 0; } |
递推:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | #include<bits/stdc++.h> #define N 262145 #define pi acos(-1) using namespace std; typedef complex< double > E; int n,m,L; int R[N]; E a[N],b[N]; void fft(E *a, int f) { for ( int i=0;i<n;i++) if (i<R[i])swap(a[i],a[R[i]]); for ( int i=1;i<n;i<<=1) { E wn( cos (pi/i),f* sin (pi/i)); for ( int p=i<<1,j=0;j<n;j+=p) { E w(1,0); for ( int k=0;k<i;k++,w*=wn) { E x=a[j+k],y=w*a[j+k+i]; a[j+k]=x+y;a[j+k+i]=x-y; } } } } int main() { scanf ( "%d%d" ,&n,&m); for ( int i=0,x;i<=n;i++) scanf ( "%d" ,&x),a[i]=x; for ( int i=0,x;i<=m;i++) scanf ( "%d" ,&x),b[i]=x; m=n+m; for (n=1;n<=m;n<<=1)L++; for ( int i=0;i<n;i++)R[i]=(R[i>>1]>>1)|((i&1)<<(L-1)); fft(a,1);fft(b,1); for ( int i=0;i<=n;i++)a[i]=a[i]*b[i]; fft(a,-1); for ( int i=0;i<=m;i++) printf ( "%d " ,( int )(a[i].real()/n+0.5)); return 0; } |
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