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14. Minimum Depth of Binary Tree

easyAsked at Dropbox

Find the shortest root-to-leaf path length; Dropbox uses it to test BFS-vs-DFS choice for early-termination tree searches in their sync metadata layer.

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

Problem

Given the root of a binary tree, return the minimum number of nodes along the shortest root-to-leaf path. 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. Full DFS

Recurse both subtrees, take min of leaf depths (with care when one child is null).

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

Tradeoff:

2. BFS early exit

Level-order; return depth on first leaf encountered. Better for shallow leaves in tall trees.

Time
O(n)
Space
O(w)
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:

Dropbox-specific tips

Dropbox grades on whether you spot the null-child trap — when only one child exists, you must NOT take the min with the missing branch, that's the most common bug.

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