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

Understand how to determine the minimum total cost needed to ensure at least one valid path exists in a grid where each cell directs movement. Explore the use of 0-1 BFS with a deque to efficiently compute costs, and learn to update paths by evaluating directional moves and their associated costs. This lesson equips you to solve grid traversal problems involving cost optimization and graph algorithms.

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 ...