Minimum Depth of Binary Tree

Problem

Return the minimum depth — the number of nodes along the shortest root-to-leaf path.

Constraints

• 0 ≤ nodes ≤ 10⁵

Approach — Tree Traversal

This is a Tree Traversal problem. The idea: traverse the tree — DFS recursively, or BFS level by level — and combine the results from each subtree. Work through the reference code below line by line, then re-derive it yourself in the editor — that's how the pattern sticks.

Complexity: O(n) time.

Solution code

Python

class Solution:
    def minDepth(self, root):
        if not root:
            return 0
        if not root.left:
            return 1 + self.minDepth(root.right)
        if not root.right:
            return 1 + self.minDepth(root.left)
        return 1 + min(self.minDepth(root.left), self.minDepth(root.right))

Java

class Solution {
    public int minDepth(TreeNode root) {
        if (root == null) return 0;
        // Layered BFS — the FIRST leaf we meet is the shallowest one,
        // so we can stop immediately (DFS would walk the whole tree).
        Queue<TreeNode> q = new ArrayDeque<>();
        q.add(root);
        int depth = 1;
        while (!q.isEmpty()) {
            int size = q.size();              // freeze one whole layer
            for (int i = 0; i < size; i++) {
                TreeNode cur = q.poll();
                if (cur.left == null && cur.right == null) return depth;
                if (cur.left != null)  q.add(cur.left);
                if (cur.right != null) q.add(cur.right);
            }
            depth++;
        }
        return depth;

        // DFS alternative (watch the trap — a node with ONE child is
        // not a leaf, so you can't just take min of both sides):
        //   if (root.left == null)  return 1 + minDepth(root.right);
        //   if (root.right == null) return 1 + minDepth(root.left);
        //   return 1 + Math.min(minDepth(root.left), minDepth(root.right));
    }
}

Practice it

Reading a solution isn't the same as being able to write it under pressure. Open this problem in the in-browser editor, hide the solution, and solve it from scratch — your code runs against real test cases instantly.