Diameter of Binary Tree

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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

Pseudocode

- longest path is the left most node travelling to the right most node.
    - traverse the longest path left + longest path right

Solution

var diameterOfBinaryTree = function(root) {
    let maxDistance = 0

    function walk(node) {
        // base condition
        if(!node) {
            return 0
        }


        const leftWalk = walk(node.left) 
        const rightWalk = walk(node.right) 
        maxDistance = Math.max(leftWalk + rightWalk, maxDistance)
        return Math.max(leftWalk + 1, rightWalk + 1)
    }

    walk(root)
    return maxDistance
};

Time and Space Complexity

Time

• Complete traversal of the tree - O(N)

• Total - O(N)

Space

• Memory requirements increase linearly for each recursion stack - O(N)

• Total - O(N)