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3963. Create Grid With Exactly One Path

Description

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.

Β 

Example 1:

Input: m = 2, n = 3

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

Explanation:

The only valid path is: (0,0) β†’ (0,1) β†’ (1,1) β†’ (1,2)

Example 2:

Input: m = 3, n = 3

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

Explanation:

The only valid path is: (0,0) β†’ (0,1) β†’ (1,1) β†’ (1,2) β†’ (2,2)

Example 3:

Input: m = 1, n = 4

Output: ["...."]

Explanation:

The only valid path is: (0,0) β†’ (0,1) β†’ (0,2) β†’ (0,3)

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Constraints:

  • 1 <= m, n <= 25

Solutions

Solution 1

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