create-grid-with-exactly-one-path

You are given two integers m and n, representing the number of rows and columns of a grid.

Construct any m x n grid consisting only of the characters '.' and '#', where:

• '.' represents a free cell.


• '#' represents an obstacle cell.

A valid path is a sequence of free cells that:

• Starts at the top-left cell (0, 0).


• Ends at the bottom-right cell (m - 1, n - 1).


• Moves only:
  
  
  
  • Right, from (i, j) to (i, j + 1), or
  
  
  • Down, from (i, j) to (i + 1, j).
  
  
  
  

Return any grid such that there is exactly one valid path from the top-left cell to the bottom-right cell.

Example 1:

Input: m = 2, n = 3

Output: ["..#","#.."]

Explanation:

The only valid path is: (0,0) → (0,1) → (1,1) → (1,2)

Example 2:

Input: m = 3, n = 3

Output: ["..#","#..","##."]

Explanation:

The only valid path is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2)

Example 3:

Input: m = 1, n = 4

Output: ["...."]

Explanation:

The only valid path is: (0,0) → (0,1) → (0,2) → (0,3)

Constraints:

• 1 <= m, n <= 25