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14. Minimum Depth of Binary Tree

easyAsked at Ola

Find the shortest path from the root to any leaf in a binary tree.

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. A leaf is a node with no children.

Constraints

  • 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. DFS full traversal

Recurse all paths and track min.

Time
O(n)
Space
O(h)
const go = n => {
  if (!n) return Infinity;
  if (!n.left && !n.right) return 1;
  return 1 + Math.min(go(n.left), go(n.right));
};
return root ? go(root) : 0;

Tradeoff:

2. BFS shortest path

Level-order; return depth on the first leaf encountered. Exits early on shallow leaves.

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:

Ola-specific tips

Ola interviewers ask why BFS beats DFS here when most leaves sit at the top of the tree; tie it to early-stopping on shallow shortest-supply matches.

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