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Grokking the Coding Interview Patterns

Solution: Unique Paths III

Explore the backtracking technique to solve the Unique Paths III problem, where you find all paths from a start cell to an end cell visiting every empty cell exactly once in a grid with obstacles. Understand the recursive approach, path exploration, and backtracking steps to count valid routes efficiently.

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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 ...