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

Explore how to solve the problem of finding the minimum cost to form a valid path in a grid where each cell directs movement. Understand how to implement a 0-1 BFS algorithm to prioritize zero-cost paths and efficiently determine the least costly route from the top-left to bottom-right cell by modifying directional signs.

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 ...