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14. Minimum Depth of Binary Tree

easyAsked at Glassdoor

Find the shortest path from root to any leaf — Glassdoor uses this to grade whether you correctly handle one-sided trees (often missed).

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 to the nearest leaf. A leaf is a node with no children.

Constraints

  • The number of nodes is 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 DFS

1 + min(minDepth(left), minDepth(right)) — but be careful with null children.

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

Tradeoff:

2. BFS short-circuit

First leaf encountered in level-order traversal is the answer.

Time
O(n)
Space
O(w)
function minDepth(root) {
  if (!root) return 0;
  const 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:

Glassdoor-specific tips

Glassdoor specifically watches for the one-sided null trap; mentioning BFS early-exit shows you optimize for the kind of skewed comment-tree they actually see in production.

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