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Grokking the Coding Interview Patterns

Solution: Unique Paths III

Explore the backtracking approach to solve Unique Paths III by finding all unique paths from start to end while visiting each empty square exactly once without crossing obstacles. This lesson guides you through recursive exploration, cell marking, and backtracking steps to count valid paths 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 ...