Minimum Absolute Difference in Sliding Submatrix

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3567. Minimum Absolute Difference in Sliding Submatrix

Medium

You are given an m x n integer matrix grid and an integer k.

For every contiguous k x k submatrix of grid, compute the minimum absolute difference between any two distinct values within that submatrix.

Return a 2D array ans of size (m - k + 1) x (n - k + 1), where ans[i][j] is the minimum absolute difference in the submatrix whose top-left corner is (i, j) in grid.

Note: If all elements in the submatrix have the same value, the answer will be 0.

A submatrix (x1, y1, x2, y2) is a matrix that is formed by choosing all cells matrix[x][y] where x1 <= x <= x2 and y1 <= y <= y2.

Example 1:

Input: grid = [[1,8],[3,-2]], k = 2

Output: [[2]]

Explanation:

There is only one possible k x k submatrix: [[1, 8], [3, -2]].
Distinct values in the submatrix are [1, 8, 3, -2].
The minimum absolute difference in the submatrix is |1 - 3| = 2. Thus, the answer is [[2]].

Example 2:

Input: grid = [[3,-1]], k = 1

Output: [[0,0]]

Explanation:

Both k x k submatrix has only one distinct element.
Thus, the answer is [[0, 0]].

Example 3:

Input: grid = [[1,-2,3],[2,3,5]], k = 2

Output: [[1,2]]

Explanation:

There are two possible k × k submatrix:
- Starting at (0, 0): [[1, -2], [2, 3]].
  - Distinct values in the submatrix are [1, -2, 2, 3].
  - The minimum absolute difference in the submatrix is |1 - 2| = 1.
- Starting at (0, 1): [[-2, 3], [3, 5]].
  - Distinct values in the submatrix are [-2, 3, 5].
  - The minimum absolute difference in the submatrix is |3 - 5| = 2.
Thus, the answer is [[1, 2]].

Constraints:

1 <= m == grid.length <= 30
1 <= n == grid[i].length <= 30
-10⁵ <= grid[i][j] <= 10⁵
1 <= k <= min(m, n)

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