题解 | 最大子矩阵

#include <bits/stdc++.h>
using namespace std;

int main() {
    int n;
    cin >> n;
    vector<vector<int>> a(n, vector<int>(n));
    for (int i = 0; i < n; ++i)
        for (int j = 0; j < n; ++j)
            cin >> a[i][j];

    int best = INT_MIN;

    for (int L = 0; L < n; ++L) {
        vector<int> sum(n, 0);              // 行累计和
        for (int R = L; R < n; ++R) {
            for (int i = 0; i < n; ++i)     // 把第 R 列加入
                sum[i] += a[i][R];

            // Kadane: 一维最大子段和
            int cur = sum[0], mx = sum[0];
            for (int i = 1; i < n; ++i) {
                cur = max(sum[i], cur + sum[i]);
                mx = max(mx, cur);
            }
            best = max(best, mx);
        }
    }

    cout << best << '\n';
    return 0;
}