A home decor recommender follows a graph of room-to-room connections to find the minimum number of moves. When every edge costs the same, why does BFS guarantee the shortest path?
BFS uses a queue, so it finishes every node at distance 0, then distance 1, then distance 2, and never reaches distance k+1 before distance k is done. That's why the distance at which you first reach a node is the minimum number of edges to it.
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