Problem

Given the root of a binary tree, return **the length of the *diameter* of the tree**.

The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.

The length of a path between two nodes is represented by the number of edges between them.

  Example 1:

Input: root = [1,2,3,4,5]
Output: 3
Explanation: 3 is the length of the path [4,2,1,3] or [5,2,1,3].

Example 2:

Input: root = [1,2]
Output: 1

  Constraints:

• The number of nodes in the tree is in the range [1, 104].

• -100 <= Node.val <= 100

Solution

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @return {number}
 */
var diameterOfBinaryTree = function(root) {
    return dfs(root)[0];
};

var dfs = function(node) {
    if (!node) return [0, 0];
    var left = dfs(node.left);
    var right = dfs(node.right);
    var child = Math.max(
        node.left ? left[1] + 1 : 0,
        node.right ? right[1] + 1 : 0,
    );
    var branch = (node.left ? left[1] + 1 : 0) +
        (node.right ? right[1] + 1 : 0);
    return [
        Math.max(
            left[0],
            right[0],
            branch,
        ),
        child,
    ];
};

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(1).