BZOJ2179【FFT】【NTT】

FFT【快速傅里叶变换】：

/* I will wait for you */

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<ctime>
#include<algorithm>
#include<iostream>
#include<fstream>
#include<vector>
#include<queue>
#include<deque>
#include<set>
#include<map>
#include<string>
#define make make_pair
#define fi first
#define se second

using namespace std;

typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;

const int maxn=200010;
const int maxm=1010;
const int maxs=26;
const int INF=1<<29;
const int P=1000000007;
const double error=1e-9;
const double Pi=3.14159265358979323846;

struct complex
{
	double re,im;
	complex(double x=0.0,double y=0.0) { re=x;im=y; }
	complex operator + (complex a) { return complex(re+a.re,im+a.im); }
	complex operator - (complex a) { return complex(re-a.re,im-a.im); }
	complex operator * (complex a) { return complex(re*a.re-im*a.im,re*a.im+im*a.re); }
}a[maxn],b[maxn],w[2][maxn];

int n,m,rev[maxn];char ca[maxn],cb[maxn];

void fft(complex* a,int f)
{
	for(int i=0;i<n;i++) if(rev[i]>i) swap(a[i],a[rev[i]]);
	
	complex x,y;
	for(int i=1;i<n;i<<=1) for(int j=0,l=n/(i<<1);j<n;j+=(i<<1)) for(int k=0,t=0;k<i;k++,t+=l)
		x=a[j+k],y=w[f][t]*a[i+j+k],a[j+k]=x+y,a[i+j+k]=x-y;
	
	if(f) for(int i=0;i<n;i++) a[i].re/=n;
}

void work()
{
	memset(rev,0,sizeof(rev));
	for(int i=0;i<n;i++) for(int j=1,x=i;j<n;j<<=1,x>>=1) (rev[i]<<=1)|=(x&1);
	for(int i=0;i<n;i++) w[0][i]=w[1][i]=complex(cos(2*Pi*i/n),sin(2*Pi*i/n)),w[1][i].im=-w[1][i].im;
}

void read()
{
	scanf("%d",&m);scanf("%s%s",ca,cb);
	for(int i=0;i<m;i++) a[i].re=ca[i]-'0';
	for(int i=0;i<m;i++) b[i].re=cb[i]-'0';
	for(n=1;n<(m<<1);n<<=1);
}

void write()
{
	for(int i=m*2-2,c=0,t;i>=0;i--) t=a[i].re+c+0.1,a[i].re=i?t%10:t,c=t/10;
	for(int i=0;i<2*m-1;i++) printf("%g",a[i].re);putchar(10);
}

int main()
{
	read();work();fft(a,0);fft(b,0);
	for(int i=0;i<n;i++) a[i]=a[i]*b[i];
	fft(a,1);write();
	return 0;
}

NTT【数论变换】：

/* I will wait for you */

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<ctime>
#include<algorithm>
#include<iostream>
#include<fstream>
#include<vector>
#include<queue>
#include<deque>
#include<set>
#include<map>
#include<string>
#define make make_pair
#define fi first
#define se second

using namespace std;

typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;

const int maxn=200010;
const int maxm=1010;
const int maxs=26;
const int INF=1<<29;
const int P=479<<21^1;
const int G=3;
const double error=1e-9;

LL a[maxn],b[maxn],w[2][maxn],tem[maxn];
int n,m,s[2],rev[maxn];char ca[maxn],cb[maxn];

LL qpow(LL a,LL b)
{
	LL ans=1;
	for(;b;a=a*a%P,b>>=1) if(b&1) ans=ans*a%P;
	return ans;
}

void ntt(LL *a,int f)
{
	for(int i=0;i<n;i++) if(rev[i]>i) swap(a[i],a[rev[i]]);
	
	LL x,y,c=qpow(n,P-2);
	for(int i=1;i<n;i<<=1) for(int j=0,l=n/(i<<1);j<n;j+=(i<<1)) for(int k=0,t=0;k<i;k++,t+=l)
		x=a[j+k],y=w[f][t]*a[i+j+k]%P,a[j+k]=(x+y)%P,a[i+j+k]=(x-y+P)%P;
		
	if(f) for(int i=0;i<n;i++) (a[i]*=c)%=P;
}

void work()
{
	memset(rev,0,sizeof(rev));
	s[0]=qpow(G,(P-1)/n);s[1]=qpow(s[0],P-2);
	for(int i=0;i<n;i++) for(int j=1,x=i;j<n;j<<=1,x>>=1) (rev[i]<<=1)|=(x&1);
	for(int i=0;i<n;i++) for(int j=0;j<2;j++) w[j][i]=i?w[j][i-1]*s[j]%P:1;
}

void read()
{
	scanf("%d",&m);scanf("%s%s",ca,cb);
	for(int i=0;i<m;i++) a[i]=ca[i]-'0';
	for(int i=0;i<m;i++) b[i]=cb[i]-'0';
	for(n=1;n<(m<<1);n<<=1);
}

void write()
{
	for(int i=m*2-2,c=0,t;i>=0;i--) t=a[i]+c,a[i]=i?t%10:t,c=t/10;
	for(int i=0;i<2*m-1;i++) printf("%d",a[i]);putchar(10);
}	

int main()
{
	read();work();ntt(a,0);ntt(b,0);
	for(int i=0;i<n;i++) (a[i]*=b[i])%=P;
	ntt(a,1);write();
	return 0;
}

理论上NTT的速度要比FFT快.但是我写的反而要慢不少.不明觉厉.