Diameter of Binary Tree in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the diameter of a binary tree?

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

intermediate

How do you calculate the diameter of a binary tree using recursion?

Calculate the height of left and right subtrees for each node. The diameter at that node is left height + right height. The overall diameter is the maximum of these values across all nodes.

intermediate

What is the time complexity of the naive approach to find the diameter of a binary tree?

The naive approach has O(n^2) time complexity because for each node, it calculates height which takes O(n), and there are n nodes.

advanced

How can you optimize the diameter calculation to O(n) time?

Use a single recursive function that returns both height and updates the diameter during traversal, so each node is visited once.

beginner

In the diameter calculation, why might the longest path not pass through the root?

Because the longest path can be between two nodes in the left or right subtree, not necessarily passing through the root node.

What does the diameter of a binary tree represent?

A The number of leaf nodes

B The height of the tree

C The longest path between any two nodes

D The number of nodes in the tree

The diameter is the longest path between any two nodes in the tree.

Which of the following is true about the diameter path in a binary tree?

A It always passes through the root

B It is always the path from root to a leaf

C It never passes through the root

D It may or may not pass through the root

The diameter path may or may not pass through the root node.

What is the main cause of O(n^2) time complexity in the naive diameter calculation?

A Repeated calculation of height for each node

B Using extra space for recursion

C Iterating over leaf nodes only

D Sorting nodes before calculation

Calculating height repeatedly for each node causes O(n^2) time complexity.

How can you reduce the time complexity of diameter calculation to O(n)?

A Calculate height and diameter in one traversal

B Use iterative traversal only

C Calculate diameter only at leaf nodes

D Use breadth-first search

Calculating height and updating diameter in one traversal reduces time complexity to O(n).

In diameter calculation, what does the sum of left height and right height at a node represent?

A Number of nodes in the tree

B Length of longest path through that node

C Height of the tree

D Depth of the node

Sum of left and right heights at a node gives the length of the longest path passing through that node.

Explain how to find the diameter of a binary tree using a single recursive function.

Think about combining height calculation and diameter update in one step.

Why might the longest path in a binary tree not pass through the root node?

Consider where the longest path can be located in the tree.