【学习笔记】FFT

1、内容

由于noble_太懒 不想写了

非常好的博客：

https://www.cnblogs.com/rvalue/p/7351400.html

http://www.cnblogs.com/candy99/p/6641972.html

http://www.gatevin.moe/acm/fft%E7%AE%97%E6%B3%95%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0/

http://hzwer.com/6896.html 黄学长模板

https://oi.men.ci/fft-notes/

https://blog.csdn.net/ggn_2015/article/details/68922404

http://www.cnblogs.com/zwfymqz/p/8244902.html

http://www.cnblogs.com/19992147orz/p/8041323.html

2、模板

洛谷A了，maxn要开大一点

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 typedef complex<double> com;
 4 const int maxn=3e7;
 5 const double PI=acos(-1);
 6 com a[maxn], b[maxn];
 7 int rev[maxn];
 8 
 9 void FFT(com* a,int n,int type){
10     for(int i=0;i<n;i++){
11         if(rev[i]>i) swap(a[i],a[rev[i]]); 
12     }
13     
14     for(int step=1;step<n;step<<=1){ //待合并区域中点 
15         com wn(cos(PI/step),type*sin(PI/step));
16         for(int j=0;j<n;j+=(step<<1)){ //step<<1是区间右端点 
17             com w(1,0); //幂 
18             for(int k=j;k<j+step;k++,w*=wn){//枚举左半部分 
19                 com x=a[k], y=w*a[k+step];
20                 a[k]=x+y; a[k+step]=x-y;
21             }
22         }
23     }
24 //    if(type==-1) for(int i=0;i<n;i++) a[i]/=n;
25 }
26 int main()
27 {
28     int n1,n2,n,x,L=0;
29     scanf("%d%d",&n1,&n2);
30     for(int i=0;i<=n1;i++){
31         scanf("%d",&x); a[i]=x;
32     }
33     for(int i=0;i<=n2;i++){
34         scanf("%d",&x); b[i]=x;
35     }
36     for(n=1;n<=n1+n2;n*=2) L++;
37     for(int i=0;i<n;i++){
38         rev[i]=(rev[i>>1]>>1)|((i&1)<<(L-1));
39     }
40     FFT(a,n,1); FFT(b,n,1);
41     for(int i=0;i<=n;i++) a[i]*=b[i];
42     FFT(a,n,-1);
43     for(int i=0;i<=n1+n2;i++){
44         printf("%d ",(int)(a[i].real()/n+0.5));
45     }
46     return 0;
47 }