1. 程式人生 > >洛谷 P3803 多項式乘法(FFT) —— FFT

洛谷 P3803 多項式乘法(FFT) —— FFT

題目:https://www.luogu.org/problemnew/show/P3803

終於學了FFT了!

參考部落格:https://www.cnblogs.com/zwfymqz/p/8244902.html

http://www.cnblogs.com/RabbitHu/p/FFT.html

程式碼如下:

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
typedef 
double db; int const xn=(1<<21);//*2 n+m db const Pi=acos(-1.0); int n,m,rev[xn],lim; struct com{db x,y;}a[xn],b[xn]; com operator + (com a,com b){return (com){a.x+b.x,a.y+b.y};} com operator - (com a,com b){return (com){a.x-b.x,a.y-b.y};} com operator * (com a,com b){return (com){a.x*b.x-a.y*b.y,a.x*b.y+b.x*a.y};}
int rd() { int ret=0,f=1; char ch=getchar(); while(ch<'0'||ch>'9'){if(ch=='-')f=0; ch=getchar();} while(ch>='0'&&ch<='9')ret=(ret<<3)+(ret<<1)+ch-'0',ch=getchar(); return f?ret:-ret; } void fft(com *a,int tp) { for(int i=0;i<lim;i++) if(i<rev[i])swap(a[i],a[rev[i]]);
for(int mid=1;mid<lim;mid<<=1)//mid<lim { com wn=(com){cos(Pi/mid),tp*sin(Pi/mid)}; for(int j=0,len=(mid<<1);j<lim;j+=len) { com w=(com){1,0}; for(int k=0;k<mid;k++,w=w*wn) { com x=a[j+k],y=w*a[j+mid+k]; a[j+k]=x+y; a[j+mid+k]=x-y; } } } } int main() { n=rd(); m=rd(); for(int i=0;i<=n;i++)a[i].x=rd(); for(int i=0;i<=m;i++)b[i].x=rd(); lim=1; int l=0; while(lim<=n+m)lim<<=1,l++; for(int i=0;i<lim;i++) rev[i]=(rev[i>>1]>>1)|((i&1)<<(l-1)); fft(a,1); fft(b,1); for(int i=0;i<lim;i++)a[i]=a[i]*b[i]; fft(a,-1); for(int i=0;i<=n+m;i++) printf("%d ",(int)(a[i].x/lim+0.5)); puts(""); return 0; }