Diameter of Binary Tree in DSA C++ - 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 the sum of these heights plus two (for the edges connecting the node to its subtrees). The overall diameter is the maximum of these values across all nodes.

intermediate

Why do we use a helper function to calculate height when finding the diameter?

Because the diameter depends on the heights of subtrees, a helper function calculates height efficiently while updating the maximum diameter found so far during traversal.

intermediate

What is the time complexity of the diameter of binary tree algorithm using a single traversal?

The time complexity is O(n), where n is the number of nodes, because each node is visited once to calculate height and update diameter.

beginner

Can the diameter path pass through the root node?

Yes, the diameter path can pass through the root node, but it is not necessary. The longest path can be anywhere in the tree.

What does the diameter of a binary tree represent?

A The longest path between any two nodes

B The height of the tree

C The number of leaf 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 never passes through the root

C It may or may not pass through the root

D It is always the path from root to a leaf

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

What is the main idea to find the diameter of a binary tree efficiently?

A Calculate height and diameter in one traversal

B Calculate diameter by counting leaf nodes

C Use breadth-first search only

D Calculate diameter by summing node values

Calculating height and diameter in one traversal avoids repeated work and improves efficiency.

What is the time complexity of the optimal diameter of binary tree algorithm?

A O(n^2)

B O(n)

C O(log n)

D O(n log n)

The optimal algorithm visits each node once, so it runs in O(n) time.

In the diameter calculation, what does the sum of left and right subtree heights represent?

A The number of leaf nodes

B The number of nodes in the tree

C The height of the tree

D The length of the longest path through the current node

The sum of left and right subtree heights plus one represents the longest path through the current node.

Explain how to find the diameter of a binary tree using recursion and height calculation.

Think about how height helps find longest paths.

Describe why the diameter path may not pass through the root node in a binary tree.

Consider different shapes of trees.