python/TangDou/Topic/PrefixAndSuffix/P1719_2.cpp

#include <bits/stdc++.h>
using namespace std;
const int N = 130;
int a[N][N], s[N][N];
int main() {
    int n, res = INT_MIN;
    cin >> n;
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n; j++) {
            cin >> a[i][j];
            s[i][j] = s[i - 1][j] + a[i][j]; // 利用一维前缀和，把当前第j列前面的1~j-1列的值，累加和压缩到第j列，每列都是如此处理
        }

    // O(N^3)算法
    for (int i = 1; i <= n; i++) {
        for (int j = 0; j < i; j++) { // 前缀和需要下标从0开始
            int sum = 0;
            for (int k = 1; k <= n; k++) {
                sum = max(sum, 0) + s[i][k] - s[j][k];
                res = max(res, sum);
            }
        }
    }
    cout << res << endl;
    return 0;
}