前缀和 (Acwing_796 子矩阵的和）

题目

1.S[i,j]即为图1红框中所有数的的和为:
S[i,j]=S[i,j−1]+S[i−1,j]−S[i−1,j−1]+a[i,j]

2.(x1,y1),(x2,y2)这一子矩阵中的所有数之和为:
S[x2,y2]−S[x1−1,y2]−S[x2,y1−1]+S[x1−1,y1−1]

#include <iostream>

using namespace std;

const int N = 1e3 + 10;

int main()
{
    int n, m, q;
    cin >> n >> m >> q;
    int s[N][N];
    
    for(int i = 1; i <= n; i ++ )
        for(int j = 1; j <= m; j ++ )
            cin >> 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;
        cin >> x1 >> y1 >> x2 >> y2;
        cout << s[x2][y2] - s[x2][y1 - 1] - s[x1 - 1][y2] + s[x1 - 1][y1 - 1] << endl;
    }
    return 0;
}