75. Shortest Path in a Grid with Obstacles Elimination

You are given an m x n integer matrix grid where each cell is either 0 (empty) or 1 (obstacle). You can move up, down, left, or right from and to an empty cell in one step.

Return the minimum number of steps to walk from the upper left corner (0, 0) to the lower right corner (m - 1, n - 1) given that you can eliminate at most k obstacles. If it is not possible to find such walk return -1.

This is a shortest path problem with a Example Usage

shortestPath([[0,0,0],[1,1,0],[0,0,0],[0,1,1],[0,0,0]], 1);  // 6
shortestPath([[0,1,1],[1,1,1],[1,0,0]], 1);                   // -1

Real-World Context

This problem models real pathfinding scenarios:

• Robot navigation: Robots that can remove obstacles with limited resources
• Game pathfinding: Finding paths in games where obstacles can be destroyed
• Network routing: Finding routes with limited ability to bypass blocked paths
• Resource-constrained pathfinding: Navigation with limited obstacle removal capability