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Grokking the Coding Interview Patterns in C++

Solution: Unique Paths III

Explore how to solve the Unique Paths III problem by applying backtracking to traverse a grid while visiting every empty cell exactly once. Understand the recursive exploration and backtracking process that finds all valid paths, handles obstacles, and ensures complete coverage. This lesson guides you through implementing an efficient solution with clear 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 ...