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Grokking the Coding Interview Patterns in Go

Solution: Unique Paths III

Explore how to apply backtracking to solve the Unique Paths III problem. Understand recursive path exploration, in-place marking, and backtracking strategies to count all valid paths that visit each empty square exactly once. This lesson covers both the algorithm and its time and space complexity analysis.

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Statement

You are given a  m×nm \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 ...