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14. Minimum Depth of Binary Tree

easyAsked at Spotify

Find the minimum number of nodes along the shortest path from root to a leaf.

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.

Constraints

  • 0 <= nodes <= 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. Recursive DFS

Recurse both subtrees; carefully handle single-child nodes

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

Tradeoff:

2. BFS level order

First leaf encountered in BFS gives the answer. Stops immediately, perfect for unbalanced trees.

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

Tradeoff:

Spotify-specific tips

Spotify likes early-exit BFS here because their shortest-path traversals on artist-similarity graphs lean on the same idea — terminate as soon as you reach the goal layer.

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