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What if we sort each cell of the matrix by the value?
Don't include small values in your path if you can only include large values.
Let's keep adding a possible cell to use in the path incrementally with decreasing values.
If the start and end cells are connected then we don't need to add more cells.
Use union-find data structure to check connectivity and return as answer the value of the given cell that makes start and end cells connected.
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Yes, this type of grid traversal and bottleneck path problem is common in technical interviews at companies like Amazon, Google, and Meta. It tests knowledge of graphs, priority queues, and optimization strategies.
Yes, binary search can be applied to the minimum value of the path. For each candidate value, you run a BFS or DFS to check if a valid path exists where all cells meet or exceed that value.
A priority queue (max-heap) is often the best data structure for this problem because it allows the algorithm to always process the cell with the highest value first. This ensures that promising paths with larger minimum values are explored earlier.
A common optimal approach uses a max-heap (priority queue) similar to Dijkstra’s algorithm. At each step, the algorithm expands the cell with the highest value to maximize the minimum value along the path. This greedy strategy efficiently finds the best possible bottleneck path.