BZOJ 3527 [Zjoi2014]力

本文介绍了一种利用快速傅立叶变换(FFT)实现高效卷积运算的方法,并提供了详细的C++实现代码。通过FFT将时域上的卷积转换为空域上的乘法,大大提升了计算效率。

摘要生成于 C知道 ,由 DeepSeek-R1 满血版支持, 前往体验 >

乘进去之后是裸的卷积,FFT解决,卷积题熟练度++

//By Richard
#include <cstdio>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <ctime>
#define rep(x,y,z) for (int x=(y);(x)<=(z);(x)++)
#define per(x,y,z) for (int x=(y);(x)>=(z);(x)--)
#define log2(x) (31-__builtin_clz(x))
#define mod (int)(1e9+7)
#define inf 0x3f3f3f3f
#define cls(x) memset(x,0,sizeof(x))
#ifdef DEBUG
#define debugdo(X) X
#define debugndo(X)
#define debugout(X) cout<<(#X)<<"="<<(X)<<endl
#else
#define debugdo(X)
#define debugndo(X) X
#define debugout(X)
#endif // debug
#ifdef ONLINE_JUDGE
#define debugdo(X)
#define debugndo(X)
#define debugout(X)
#endif
#define sqr(x) ((x)*(x))
#define putarray(x,n) rep(iiii,1,n) printf("%d ",x[iiii])
#define mp make_pair
using namespace std;
typedef pair<int,int> pairs;
typedef long long LL;
/read3.0
template <typename T>
inline void read(T &x){char ch;x=0;bool flag=false;ch=getchar();while (ch>'9'||ch<'0') {ch=getchar();if (ch=='-') flag=true;}while ((ch<='9'&&ch>='0')){x=x*10+ch-'0';ch=getchar();}if (flag) x*=-1;}
template <typename T>
inline void read(T &x,T &y){read(x);read(y);}
/variables&functions

const int maxn=1048576;
const double pi=3.1415926535897932384626433832795028841971693993751058209749446;
int r[maxn],n,m,l,nn;
struct cp
{
	double x,y;
	cp(double a=0,double b=0):x(a),y(b){}
	cp operator+(cp a){return cp(x+a.x,y+a.y);}
	cp operator-(cp a){return cp(x-a.x,y-a.y);}
	cp operator*(cp a){return cp(x*a.x-y*a.y,x*a.y+y*a.x);}
	cp operator/(int a){return cp(x/a,y/a);}
}A[maxn],B[maxn],AA[maxn];
inline void swap(cp &a,cp &b){cp t=a;a=b;b=t;}
void FFT(cp *a,int n,int op)
{
	rep(i,0,n-1) if (i<r[i]) swap(a[i],a[r[i]]);
	for (int i=1;i<n;i<<=1)
	{
		cp wn(cos(pi/i),sin(pi/i)*op);
		for (int j=0;j<n;j+=i<<1)
		{
			cp w(1,0);
			for (int k=0;k<i;k++,w=w*wn)
			{
				cp x=a[j+k],y=a[i+j+k]*w;
				a[j+k]=x+y;
				a[i+j+k]=x-y;
			}
		}
	}
}
int main()
{
	read(n);
	m=n;
	nn=n;
	rep(i,0,n-1) scanf("%lf",&A[i].x);
	rep(i,0,n-1) AA[n-i-1].x=A[i].x;
	rep(i,1,n-1) B[i].x=(double)1/(i)/(i);

	m+=n-2;
	for (l=0,n=1;n<=m;n<<=1,++l);
	rep(i,0,n-1) r[i]=(r[i>>1]>>1)|((i&1)<<(l-1));
	FFT(A,n,1);FFT(B,n,1);
	rep(i,0,n-1) A[i]=B[i]*A[i];
	FFT(A,n,-1);
	rep(i,0,n-1) A[i].x=A[i].x/n;
	
	FFT(AA,n,1);
	rep(i,0,n-1) AA[i]=B[i]*AA[i];
	FFT(AA,n,-1);
	rep(i,0,n-1) AA[i].x=AA[i].x/n;

	rep(i,0,nn-1) printf("%lf\n",-AA[nn-i-1].x+A[i].x);
	return 0;
}


评论
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值