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14. Minimum Depth of Binary Tree

easyAsked at Roblox

Find the shortest root-to-leaf path length.

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 down to the nearest leaf node. A leaf is a node with no children.

Constraints

  • 0 <= number of 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. DFS

Recurse all paths and take min; explores entire tree.

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

Tradeoff:

2. BFS first-leaf

Walk levels and return the depth of the first leaf encountered.

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:

Roblox-specific tips

Roblox prefers the BFS approach since the same level-order pattern shows up when finding the closest visible neighbor in an octree.

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Output

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