Find a Safe Walk Through a Grid - Solution & Explanation

This approach uses the Breadth-First Search algorithm to find the shortest path from the top-left corner of the grid to the bottom-right corner while maintaining a positive health level. We explore all possible paths from the start, tracking the health remaining at each step. We use a queue to facilitate the level-order traversal typical of BFS and check each possible move (up, down, left, right) from the current position.

The BFS method starts at (0,0) with the given health. We use a deque for level-wise traversal of the next reachable cells, maintaining a visited set to avoid revisiting cells. We explore possible directions (up, down, left, right) and check for boundary conditions and revisit prevention. The method returns true if we reach the target cell (m-1, n-1) with positive health.

This approach applies a depth-first search strategy with memorization to explore paths from the top-left to the bottom-right of the grid. By using a stack, it simulates DFS traversal, recursively checking viable movements. Memorization avoids redundant computations by storing previously calculated results for specific grid positions with remaining health. This optimization increases efficiency and reduces unnecessary recursion.

We leverage a recursive DFS approach where each node in the recursion tree represents a grid cell with current health. We recursively explore all possible valid directions, utilizing a memoization dictionary memo to cache results and avoid redundant calculations. The base case checks if the target is reached, at which point the function returns true.