Diameter of Binary Tree in DSA Typescript - 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 to the children). The overall diameter is the maximum of all such values.

beginner

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

Because the longest path can be between two nodes in the same subtree, not necessarily involving the root node.

intermediate

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

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

beginner

In the diameter calculation, what does the height of a node represent?

The height of a node is the number of edges on the longest path from that node down to a leaf node.

What does the diameter of a binary tree measure?

A The number of nodes in the tree

B The height of the tree

C The number of leaf nodes

D The longest path between any two nodes

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

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

A It always passes through the root

B It equals the height of the tree

C It can be entirely in one subtree

D It is the shortest path between two nodes

The diameter path can be inside one subtree and not pass through the root.

What is the key step in calculating the diameter at each node?

A Sum of heights of left and right subtrees plus two

B Sum of number of nodes in left and right subtrees

C Maximum depth of the tree

D Number of leaf nodes

Diameter at a node = height(left subtree) + height(right subtree) + 2.

What is the time complexity of the optimal diameter calculation algorithm?

A O(n^2)

B O(n)

C O(n log n)

D O(log n)

Each node is visited once, so time complexity is O(n).

What does the height of a node in a binary tree represent?

A Number of edges from node to deepest leaf

B Number of edges from node to root

C Number of child nodes

D Number of sibling nodes

Height is the longest path from the node down to a leaf node.

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

Think about how height and diameter relate at each node.

Why can the longest path in a binary tree not pass through the root? Give an example scenario.

Consider a tree where one side is much deeper than the other.