Maximal 2D Subarray Sum

/**
 *    author:  compounding
 *    created: 2024-12-05 21:34:33
 **/
#include <bits/stdc++.h>
using namespace std;
mt19937_64 RNG(chrono::steady_clock::now().time_since_epoch().count());
#define NeedForSpeed                  \
    ios_base::sync_with_stdio(false); \
    cin.tie(NULL);                    \
    cout.tie(NULL);
#define int long long
#define all(x) (x).begin(), (x).end()
typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<vi> vvi;
typedef vector<pair<int, int>> vpi;
#define f first
#define s second
#define yes cout << "YES" << endl
#define no cout << "NO" << endl
#define endl "\n"
const int mod = 1000000007;
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
vi a;
int kadane(vi &a)
{
    int n = a.size();
    int max_sum = INT_MIN;
    int sum = 0;
    for (int i = 0; i < n; i++)
    {
        sum += a[i];
        max_sum = max(max_sum, sum);
        if (sum < 0)
        {
            sum = 0;
        }
    }
    return max_sum;
}
void solve()
{
    // maximal sum rectangle
    int n;
    cin >> n;
    int grid[n][n];
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            cin >> grid[i][j];
        }
    }
    // fix the left and move the right
    a.resize(n);
    int ans = INT_MIN;
    for (int l = 0; l < n; l++)
    {
        for (int i = 0; i < n; i++)
        {
            // reset the array
            a[i] = 0;
        }
        for (int r = l; r < n; r++)
        {
            for (int i = 0; i < n; i++)
            {
                a[i] += grid[i][r];
            }
            ans = max(ans, kadane(a));
        }
    }
    cout << ans << endl;
    return;
}

signed main()
{
    NeedForSpeed;
    int t = 1;
    // cin >> t;
    while (t--)
    {
        solve();
    }
    return 0;
}