2132 - Stamping the Grid.

Hard

You are given an m x n binary matrix grid where each cell is either 0 (empty) or 1 (occupied).

You are then given stamps of size stampHeight x stampWidth. We want to fit the stamps such that they follow the given restrictions and requirements:

• Cover all the empty cells.

• Do not cover any of the occupied cells.

• We can put as many stamps as we want.

• Stamps can overlap with each other.

• Stamps are not allowed to be rotated.

• Stamps must stay completely inside the grid.

Return true if it is possible to fit the stamps while following the given restrictions and requirements. Otherwise, return false.

Example 1:

Input: grid = \[\[1,0,0,0],1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0], stampHeight = 4, stampWidth = 3

Output: true

Explanation: We have two overlapping stamps (labeled 1 and 2 in the image) that are able to cover all the empty cells.

Example 2:

Input: grid = \[\[1,0,0,0],0,1,0,0,0,0,1,0,0,0,0,1], stampHeight = 2, stampWidth = 2

Output: false

Explanation: There is no way to fit the stamps onto all the empty cells without the stamps going outside the grid.

Constraints:

• m == grid.length

• n == grid[r].length

• <code>1 <= m, n <= 10⁵</code>

• <code>1 <= m * n <= 2 * 10⁵</code>

• grid[r][c] is either 0 or 1.

• <code>1 <= stampHeight, stampWidth <= 10⁵</code>