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14. Minimum Depth of Binary Tree

easyAsked at Etsy

Find the shallowest leaf — Etsy uses it to test that you can choose BFS for early termination.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given a binary tree, find its minimum depth — the number of nodes along the shortest path from the root down to the nearest leaf.

Constraints

  • Node count in [0, 10^5]
  • -1000 <= Node.val <= 1000

Examples

Example 1

Input
root = [3,9,20,null,null,15,7]
Output
2

Example 2

Input
root = [2,null,3,null,4,null,5,null,6]
Output
5

Approaches

1. Naive recursion

Min over both subtrees, but mishandles a single-child case unless guarded.

Time
O(n)
Space
O(h)
function minDepth(n){
  if (!n) return 0;
  if (!n.left) return 1 + minDepth(n.right);
  if (!n.right) return 1 + minDepth(n.left);
  return 1 + Math.min(minDepth(n.left), minDepth(n.right));
}

Tradeoff:

2. BFS early stop

Level-order; return depth of the first leaf encountered.

Time
O(n)
Space
O(n)
function minDepth(root) {
  if (!root) return 0;
  let q = [[root, 1]];
  while (q.length) {
    const [n, d] = q.shift();
    if (!n.left && !n.right) return d;
    if (n.left) q.push([n.left, d+1]);
    if (n.right) q.push([n.right, d+1]);
  }
}

Tradeoff:

Etsy-specific tips

Etsy will trap candidates who default to DFS for the shortest path — calling out BFS as the right tool is the bonus signal.

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