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14. Minimum Depth of Binary Tree

easyAsked at Lyft

Find the minimum depth of a binary tree.

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

Problem

Given a binary tree, find its minimum depth — the number of nodes on the shortest path from root to a leaf. A leaf is a node with no children.

Constraints

  • Number of nodes in range [0, 10^5]
  • -1000 <= node value <= 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 minimum

Recursive minimum of subtree depths with leaf check.

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

Tradeoff:

2. BFS level order

Breadth-first search and return as soon as you find any leaf — guarantees minimum depth.

Time
O(n)
Space
O(n)
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:

Lyft-specific tips

Lyft prefers BFS here — they argue the early termination is critical when scanning massive partial trees representing live driver positions in a city.

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