AcWing 796. Sub-matrix sum (two-dimensional prefix sum)

The
meaning of the title: the time has changed from n^3 to n^2. When adding the s[] array, pay attention to the repeated adding part, and the excessively subtracting part when outputting.
formula:

S[i, j] = 第i行j列格子左上部分所有元素的和
s[i][j]+=s[i-1][j]+s[i][j-1]-s[i-1][j-1]
以(x1, y1)为左上角，(x2, y2)为右下角的子矩阵的和为：
S[x2, y2] - S[x1 - 1, y2] - S[x2, y1 - 1] + S[x1 - 1, y1 - 1]

Code:

#include<iostream>

using namespace std;

const int N=1010;
int n,m,q,s[N][N];

int main()
{
    
    
	scanf("%d%d%d",&n,&m,&q);
	for(int i=1;i<=n;i++)
		for(int j=1;j<=m;j++)
			scanf("%d",&s[i][j]);
	for(int i=1;i<=n;i++)
		for(int j=1;j<=m;j++)
			s[i][j]+=s[i-1][j]+s[i][j-1]-s[i-1][j-1];//将其变为前n项和的形式 
	while(q--)
	{
    
    
		int x1,y1,x2,y2;
		scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
		printf("%d\n",s[x2][y2]-s[x2][y1-1]-s[x1-1][y2]+s[x1-1][y1-1]);//用二维前n项和进行求解 
	}
	return 0;
}