Minimum Depth of Binary Tree

To solve the Minimum Depth problem efficiently, I would prioritize a Breadth-First Search approach over Depth-First Search. The core reason is that BFS naturally explores the tree layer by layer. This means the very first leaf node we encounter during the traversal is guaranteed to be at the shallowest possible depth, allowing us to return immediately without processing the rest of the tree. In contrast, a standard DFS might visit deep nodes before finding a shallow leaf, resulting in unnecessary computation. My implementation would use a queue to store nodes along with their current depth. First, I'd check if the root is null; if so, the depth is zero. Then, I enqueue the root with a depth of one. While the queue isn't empty, I dequeue a node. If this node has no left or right children, it is a leaf, and I immediately return its recorded depth. If it has children, I enqueue them with an incremented depth. For Amazon's focus on efficiency, this approach ensures an average time complexity of O(N) but often performs significantly better on skewed trees since we stop early. A common pitfall to avoid is treating a node with only one child as a leaf. We must strictly verify that both left and right pointers are null before considering it a terminal node for the minimum path calculation.