P5239 回忆京都

$Result$

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$Hyperlink$

https://www.luogu.com.cn/problem/P5239

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$Description$

求组合数的二维前缀和

数据范围：$n,m\le 10^3$

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$Solution$

随便递推一下然后二维前缀和求和就行了

时间复杂度：$O(n^2+q)$

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$Code$

#include
#include
#include
#include
#define LL long long
#define mod 19260817
using namespace std;int q,n,m;
LL C[1001][1001],S[1001][1001];
inline LL read()
{
     
	char c;LL d=1,f=0;
	while(c=getchar(),!isdigit(c)) if(c=='-') d=-1;f=(f<<3)+(f<<1)+c-48;
	while(c=getchar(),isdigit(c)) f=(f<<3)+(f<<1)+c-48;
	return d*f;
}
signed main()
{
     
	C[0][0]=1;C[1][0]=1;C[1][1]=1;
	for(register int i=2;i<=1000;i++) {
     C[i][0]=1;for(register int j=1;j<=i;j++) C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;}
	for(register int i=1;i<=1000;i++) for(register int j=1;j<=1000;j++) S[i][j]=(S[i-1][j]+S[i][j-1]-S[i-1][j-1]+C[i][j]+mod)%mod;
	q=read();
	while(q--)
	{
     
		m=read();n=read();
		printf("%lld\n",S[n][m]);
	}
}