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14. Minimum Depth of Binary Tree

easyAsked at Instacart

Find the minimum depth (shortest root-to-leaf path) — Instacart uses BFS preference here to test whether you understand 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 node down to the nearest leaf node.

Constraints

  • The number of nodes in the tree is in the range [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. DFS recursion

Recurse left and right; combine carefully when one side is null.

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 with early exit

Stop at the first leaf encountered by level-order traversal.

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:

Instacart-specific tips

Instacart's interviewers love BFS here — they explicitly ask why DFS wastes work on extremely deep delivery-region trees.

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