minimum-absolute-difference-in-sliding-submatrix

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.

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)