AcWing 796. 子矩阵的和 _

s33=s32+s23−s22+a33

抽象一下，就是：(如果感觉看代数式子不好理解，就用图理解就行啦！)

sij=si−1j+sij−1−si−1j−1+aij

#include <bits/stdc++.h>

using namespace std;
const int N = 1010;
int a[N][N];
int s[N][N];

int main() {
    int n, m, q;
    cin >> n >> m >> q;
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++) {
            cin >> a[i][j];
            s[i][j] = s[i - 1][j] + s[i][j - 1] + a[i][j] - s[i - 1][j - 1];
        }

    while (q--) {
        int x1, y1, x2, y2;
        cin >> 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;
}