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Grokking the Coding Interview Patterns in C++

Solution: Unique Paths III

Explore the backtracking approach to solve Unique Paths III, where you count all paths traversing every empty square exactly once from start to end. Understand recursive path exploration, marking visited cells, and backtracking to find all valid routes in a grid with obstacles. This lesson helps you implement and analyze the algorithm using C++.

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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 ...