Diameter of Binary Tree in DSA Java - 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, then the diameter at that node is left height + right height. The overall diameter is the maximum of these values for all nodes.

intermediate

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

Because height calculation is needed repeatedly for each node to find the longest path through it. A helper function returns height and updates diameter simultaneously to avoid repeated calculations.

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 during the height and diameter calculation.

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 number of leaf nodes

B The height of the tree

C The number of nodes in the tree

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 needed to calculate the diameter at a node?

A Number of children of the node

B Only the height of the left subtree

C Sum of heights of left and right subtrees

D Only the height of the right subtree

Diameter at a node = left subtree height + right subtree height.

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

A O(n)

B O(n^2)

C O(log n)

D O(1)

Using a single traversal, diameter can be found in O(n) time.

Does the diameter path always pass through the root node?

A No, it can be anywhere in the tree

B Yes, always

C Only if the tree is balanced

D Only if the tree is a full binary tree

The diameter path can be anywhere, not necessarily through the root.

Why is a helper function useful in diameter calculation?

A To print the tree nodes

B To calculate height and update diameter in one traversal

C To count leaf nodes

D To balance the tree

Helper function calculates height and updates diameter simultaneously to optimize.

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

Think about longest path through each node.

Describe why the diameter path might not pass through the root node.

Consider a tree where one subtree is much deeper.

Practice

1. What does the diameter of a binary tree represent?

easy

A. The number of leaf nodes in the tree

B. The length of the longest path between any two nodes in the tree

C. The height of the tree

D. The total number of nodes in the tree

Solution

1. Step 1: Understand the diameter definition

   The diameter is the longest path between any two nodes, which may or may not pass through the root.

2. Step 2: Differentiate from other tree properties

   Height is the longest path from root to leaf, leaf count is number of leaves, total nodes is size, none of which define diameter.

3. Final Answer:

   The length of the longest path between any two nodes in the tree -> Option B

4. Quick Check:

   Diameter = Longest path between nodes [OK]

Hint: Diameter is longest path between any two nodes [OK]

Common Mistakes:

• Confusing diameter with height
• Thinking diameter counts nodes instead of edges
• Assuming diameter must pass through root

2. Which of the following Java method signatures correctly represents a recursive function to find the diameter of a binary tree node?

easy

A. public int diameter(int root)

B. public void diameter(TreeNode root)

C. public String diameter(TreeNode root)

D. public int diameter(TreeNode root)

Solution

1. Step 1: Identify correct parameter type

   The method must accept a TreeNode object representing the root of the tree or subtree.

2. Step 2: Identify correct return type

   Diameter is a number (int), so return type should be int, not void or String.

3. Final Answer:

   public int diameter(TreeNode root) -> Option D

4. Quick Check:

   Method returns int and takes TreeNode [OK]

Hint: Diameter method returns int and takes TreeNode [OK]

Common Mistakes:

• Using void return type for diameter
• Passing int instead of TreeNode
• Returning String instead of int

3. Given the following binary tree code snippet, what is the diameter of the tree?

class TreeNode {
  int val;
  TreeNode left, right;
  TreeNode(int x) { val = x; }
}

TreeNode root = new TreeNode(1);
root.left = new TreeNode(2);
root.right = new TreeNode(3);
root.left.left = new TreeNode(4);
root.left.right = new TreeNode(5);

// Diameter calculation code omitted for brevity

medium

A. 2

B. 5

C. 3

D. 4

Solution

1. Step 1: Visualize the tree structure

   The tree has root 1, left child 2 with children 4 and 5, and right child 3.

2. Step 2: Find longest path between any two nodes

   Longest path is from node 4 to node 3 via 2 and 1: path 4->2->1->3 = 3 edges, diameter = 3.

3. Final Answer:

   3 -> Option C

4. Quick Check:

   Longest path length = 3 edges [OK]

Hint: Count edges on longest path between two nodes [OK]

Common Mistakes:

• Counting nodes instead of edges or vice versa
• Ignoring paths not passing through root
• Miscounting edges in path

4. Identify the bug in this diameter calculation method and select the fix:

int diameter = 0;
int height(TreeNode root) {
  if (root == null) return 0;
  int left = height(root.left);
  int right = height(root.right);
  diameter = Math.max(diameter, left + right);
  return Math.max(left, right);
}

medium

A. Return Math.max(left, right) + 1 instead of Math.max(left, right)

B. Initialize diameter inside height method

C. Use diameter = Math.min(diameter, left + right)

D. Return left + right instead of Math.max(left, right)

Solution

1. Step 1: Understand height calculation

   Height of a node is 1 plus max height of its children, so must add +1.

2. Step 2: Identify bug in return statement

   Current code returns max(left, right) without +1, so height is underestimated.

3. Final Answer:

   Return Math.max(left, right) + 1 instead of Math.max(left, right) -> Option A

4. Quick Check:

   Height = max child height + 1 [OK]

Hint: Height adds 1 to max child height [OK]

Common Mistakes:

• Forgetting to add +1 in height return
• Using min instead of max for diameter update
• Returning sum of left and right as height

5. You want to find the diameter of a binary tree but also print the nodes on the longest path. Which approach is best?

hard

A. Modify the diameter function to store and return the longest path nodes along with diameter

B. Calculate diameter first, then do a separate BFS to find longest path nodes

C. Use only height function and print nodes at max height

D. Count leaf nodes and assume longest path is between two leaves

Solution

1. Step 1: Understand diameter and path relationship

   Diameter is longest path length; to print nodes, we must track path during diameter calculation.

2. Step 2: Choose approach that combines diameter and path tracking

   Modifying diameter function to store nodes on longest path is efficient and direct.

3. Final Answer:

   Modify the diameter function to store and return the longest path nodes along with diameter -> Option A

4. Quick Check:

   Track path during diameter calc for nodes [OK]

Hint: Track nodes while computing diameter for path [OK]

Common Mistakes:

• Running BFS separately wastes time
• Assuming height equals diameter path
• Counting leaves without path tracking