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

Explore how to determine the minimum cost required to make at least one valid path in a directional grid. Understand the use of 0-1 BFS with a deque for efficient graph traversal, and learn to apply cost updates strategically for solving grid-based path problems common in coding interviews.

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 ...