【BZOJ-2179】FFT快速傅里叶 FFT

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
struct Complex{
	double r,i;
	Complex (double R=0.0,double I=0.0) {r=R,i=I;}
	Complex operator + (Complex & A) const {return Complex(r+A.r,i+A.i);}
	Complex operator - (Complex & A) const {return Complex(r-A.r,i-A.i);}
	Complex operator * (Complex & A) const {return Complex(r*A.r-i*A.i,r*A.i+i*A.r);} 
};
#define MAXN 600010
#define Pai acos(-1.0)
Complex A[MAXN],B[MAXN];
int len,N,ans[MAXN];
char s[MAXN];
inline void Prework()
{
	len=1;
	while (len < (N<<1)) len<<=1;  //扩展到2的幂次 
	for (int i=N; i<len; i++) A[i]=Complex(0,0),B[i]=Complex(0,0); //补零 
}
inline void Rader(Complex *x)
{
	for (int i=1,j=len>>1,k; i<len-1; i++)
		{
			if (i<j) swap(x[i],x[j]);
			k=len>>1;
			while (j>=k) j-=k,k>>=1;
			if (j<k) j+=k;
		}
}//位逆序置换 
inline void DFT(Complex *x,int opt)
{
	Rader(x);
	for (int h=2; h<=len; h<<=1) //操作的长度，h=1不用管 
		{
			Complex Wn( cos(opt*2*Pai/h) , sin(opt*2*Pai/h) );
			for (int i=0; i<len; i+=h)
				{
					Complex W(1,0);
					for (int j=i; j<i+h/2; j++)
						{
							Complex u=x[j],t=W*x[j+h/2];
							x[j]=u+t,x[j+h/2]=u-t; //蝴蝶操作 
							W=W*Wn;
						}
				}
		}
	if (opt==-1) //插值时要/len 
		for (int i=0; i<len; i++)
			x[i].r/=len;
}//opt=1 DFT opt=-1 IDFT 
inline void FFT(Complex *A,Complex *B)
{
	DFT(A,1); DFT(B,1);
	for (int i=0; i<len; i++)
		A[i]=A[i]*B[i]; //点值乘 
	DFT(A,-1);
}
int main()
{
	scanf("%d",&N);
	scanf("%s",s+1);
	for (int i=N,l=-1; i>=1; i--) A[++l].r=s[i]-‘0‘;
	scanf("%s",s+1);
	for (int i=N,l=-1; i>=1; i--) B[++l].r=s[i]-‘0‘;
	Prework();
	FFT(A,B);
	
	for (int i=0; i<len; i++) ans[i]=(int)(A[i].r+0.5);
	for (int i=0; i<len; i++) ans[i+1]+=ans[i]/10,ans[i]%=10;
	while (--len && !ans[len]);
	//高精乘的进位和去0
	 
	for (int i=len; i>=0; i--) putchar(ans[i]+‘0‘);
	puts(""); 
	return 0;
}