3569-minimum-absolute-difference-in-sliding-submatrix.md

3884. Minimum Absolute Difference in Sliding Submatrix

Medium

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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:

  <ul>
  	<li>Starting at <code>(0, 0)</code>: <code>[[1, -2], [2, 3]]</code>.
  
  	<ul>
  		<li>Distinct values in the submatrix are <code>[1, -2, 2, 3]</code>.</li>
  		<li>The minimum absolute difference in the submatrix is <code>|1 - 2| = 1</code>.</li>
  	</ul>
  	</li>
  	<li>Starting at <code>(0, 1)</code>: <code>[[-2, 3], [3, 5]]</code>.
  	<ul>
  		<li>Distinct values in the submatrix are <code>[-2, 3, 5]</code>.</li>
  		<li>The minimum absolute difference in the submatrix is <code>|3 - 5| = 2</code>.</li>
  	</ul>
  	</li>
  </ul>
  </li>
  <li>Thus, the answer is <code>[[1, 2]]</code>.</li>
  

 

Constraints:

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