# 104. Maximum Depth of Binary Tree

## The Problem

Link to original problem on Leetcode

Given a binary tree, find its maximum depth.

The maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

Note: A leaf is a node with no children.

Example:

Given binary tree [3,9,20,null,null,15,7],

    3
/ \
9  20
/  \
15   7


return its depth = 3.

## My Solution

This solution uses recursion. It beat 91.16% of submissions in runtime and 82.15% in memory usage.

const maxDepth = (root) => {    // Terminate immediately if there is no node provided    // This is handy when called on a non-existant child.    if (!root) {        return 0;    }    // Recursively call this function on the children of the node.    // Add a 1, because if this is a leaf, you'd get Math.max(0, 0).    // The 1 represents this level, which will serve as the starting    // point to count each level back to the root.    return Math.max(maxDepth(root.left), maxDepth(root.right)) + 1;}

## Best Solution

Solutions page locked, but here is another JS answer that is roughly equivalent to mine. Could be a one-liner, but I find it easier to read as three.

const maxDepth = (root) => !root  ? 0  : 1 + Math.max(maxDepth(root.left), maxDepth(root.right));

Another solution that uses iteration instead of recursion:

const maxDepth = (root) => {    if (!root) return 0;    // Initialize a queue with the root node.    const queue = [root];    // Initialize the tree's depth at 0.    let depth = 0;    while (queue.length !== 0) {        const len = queue.length;        // Iterates over each item in the queue, adding all child nodes        // to the queue. So in the original example, the queue starts at        // [3] and becomes [9, 20]. Then the depth is iterated by 1.        // Next would be [9, 20] to [15, 7].        // Loop ended when there's nothing left to add to the queue.        for (let i = 0; i < len; i++) {            let item = queue.shift()            if (item.left) queue.push(item.left);            if (item.right) queue.push(item.right);        }        depth++;    }    // Return the deepest level you could hit.    return depth;};