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14. Minimum Depth of Binary Tree

easyAsked at TripAdvisor

Find the minimum depth of a binary tree from root to nearest leaf.

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

Problem

Given a binary tree, find its minimum depth. The minimum depth is the number of nodes along the shortest path from the root node down to the nearest leaf node. Note that a leaf is a node with no children.

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 min

1 + min of subtrees, but careful about single-child nodes.

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 first leaf

BFS level by level; return depth as soon as the first leaf is dequeued.

Time
O(n)
Space
O(w)
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:

TripAdvisor-specific tips

TripAdvisor uses min-depth questions to test if you exit search early when finding the closest reviewer in a moderation tree.

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Output

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