Solution: Unique Paths III

Explore solving the Unique Paths III problem by applying backtracking techniques that recursively explore grid paths, ensuring every empty square is visited once. Understand how to identify the start point, count walkable squares, and use recursion with backtracking to find and count all valid four-directional paths without revisiting or crossing obstacles.

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Statement
Solution
- Time complexity
- Space complexity

Statement

You are given a $m \times n$ integer array, grid, where each cell, grid[i][j], can have one of the following values:

1 indicates the starting point. There is exactly one such square.
2 marks the ending point. There is exactly one such square.
0 represents empty squares that can be walked over.
-1 represents obstacles that cannot be crossed.

Your task is to return the total number of unique four-directional paths from the starting square (1) to the ending square (2), such that every empty square is visited exactly once during the walk.

Constraints:

$m$ $==$ grid.length
$n$ $==$ grid[i].length
$1 \leq$ ...