[Codeforces954H][DP]Path Counting

翻译

题解

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<queue>
#include<vector>
#include<ctime>
#include<map>
#define LL long long
#define mp(x,y) make_pair(x,y)
using namespace std;
const LL mod=1e9+7;
inline LL read()
{
	LL f=1,x=0;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
inline void write(int x)
{
	if(x<0)putchar('-'),x=-x;
	if(x>9)write(x/10);
	putchar(x%10+'0');
}
inline void print(int x){write(x);printf(" ");}
LL pow_mod(LL a,LL b)
{
	LL ret=1;
	while(b)
	{
		if(b&1)ret=ret*a%mod;
		a=a*a%mod;b>>=1;
	}
	return ret;
}
int n;
LL f[2][21100],gg,a[21100];
LL ans[21100],s[21100],inv[21100];
int main()
{
	n=read();gg=pow_mod(2,mod-2);
	inv[1]=s[1]=1;inv[0]=1;
	for(int i=2;i<=n;i++)a[i]=read(),s[i]=s[i-1]*a[i]%mod,inv[i]=pow_mod(s[i],mod-2);
	int nw=0;a[1]=1;
	for(int i=n;i>=1;i--)
	{
		nw^=1;memset(f[nw],0,sizeof(f[nw]));
		for(int j=2;j<=2*n-4;j++)f[nw][j+2]=f[nw^1][j]*a[i+2]%mod*a[i+2]%mod;
		for(int j=2;j<=2*n-2;j++)f[nw][j]=(f[nw][j]+s[i+j-1]*inv[i+1]%mod)%mod;
		for(int j=2;j<=2*n-2;j++)
		{
			(ans[j]+=s[i]*a[i+1]%mod*(a[i+1]-1)%mod*f[nw][j]%mod)%=mod;
			if(!(j%2)&&j/2<=n-i)ans[j]=(ans[j]-(s[i]*a[i+1]%mod*(a[i+1]-1)%mod*gg%mod*s[i+j/2]%mod*inv[i+1]%mod*s[i+j/2]%mod*inv[i+1]%mod)+mod)%mod;
		}
		for(int j=1;j<=n-i;j++)(ans[j]+=s[i+j])%=mod;
	}
	for(int i=1;i<=2*n-2;i++)printf("%lld ",ans[i]);
	puts("");
	return 0;
}