public int MaxSumSubmatrix(int[][] matrix, int k)
{
// Inspired by https://leetcode.com/problems/max-sum-of-rectangle-no-larger-than-k/discuss/83599/Accepted-C%2B%2B-codes-with-explanation-and-references
// This problem can be converted to sub-problems of a problem similar to "53. Maximum Subarray".
// Each number in the 1-dimension array represents a subarray of a row, because this number
// is accumulated from the numbers in that subarray.
// The problem becomes "Find the subarray which has the largest sum but less than k".
// We can use the "prefix sum" technique. For each current sum j so far, find a previous minimum
// sum i such that j - i <= k.
int m = matrix.Length;
int n = matrix[0].Length;
int result = int.MinValue;
// Time complexity is O[n^2 * m * log(m)], so if n is larger than m, we'd better swap m and n.
for (int left = 0; left < n; left++)
{
int[] nums = new int[m];
for (int right = left; right < n; right++)
{
for (int i = 0; i < m; i++)
{
nums[i] += matrix[i][right];
}
var set = new TreeSet <int>()
{
0
};
int j = 0;
foreach (int num in nums)
{
// Find the minimum i such that num[j] - num[i] <= k.
j += num;
if (set.Ceiling(j - k, out int i))
{
result = Math.Max(result, j - i);
}
set.Add(j);
}
}
}
return(result);
}
