二维前缀和

 

 由图1，二维前缀和的递推公式是：$s[i][j] = s[i-1][j] + s[i][j-1] -s[i-1][j-1] + a[i][j]$。

由图2，二维前缀和的查询公式是：前缀和 = $s[x_2][y_2] - s[x_1 - 1][y_2] - s[x_2][y_1-1] + s[x_1-1][y_1-1]$。 

#include <iostream>
#include <cstdio>

using namespace std;

const int N = 1010;

int n, m, q;
int 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];

    while (q -- )
    {
        int x1, y1, x2, y2;
        scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
        printf("%d\n", s[x2][y2] - s[x1 - 1][y2] - s[x2][y1 - 1] + s[x1 - 1][y1 - 1]);
    }

    return 0;
}