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Grokking the Coding Interview Patterns in C++

Solution: Minimum Cost to Make at Least One Valid Path in a Grid

Explore how to determine the minimum total cost to ensure at least one valid path exists from the top-left to bottom-right in a grid where each cell points to a direction. Learn to implement a 0-1 BFS algorithm that efficiently prioritizes moves matching cell directions with zero cost and changes with cost one, updating the cost grid to find the optimal path under grid constraints.

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Statement

You are given an m×nm \times n grid, where each cell contains a directional sign indicating which neighboring cell to move to next. The sign in a cell grid[i][j] can be:

  • 1: Move right, i.e., from grid[i][j] to grid[i][j + 1].

  • 2 ...