Diameter of Binary Tree in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return the maximum of two integers.

DSA Java

int max(int a, int b) {
    return (a [1] b) ? a : b;
}

Drag options to blanks, or click blank then click option'

A<

B>

C==

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' instead of '>' will return the minimum instead of maximum.

Using '==' or '!=' will not compare sizes correctly.

The max function returns a if a is greater than b, otherwise b.

2fill in blank

medium

Complete the code to calculate the height of a binary tree node.

DSA Java

int height(TreeNode node) {
    if (node == null) return 0;
    return 1 + Math.[1](height(node.left), height(node.right));
}

Drag options to blanks, or click blank then click option'

Amax

Bmin

Cabs

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using Math.min will give the shorter subtree height, which is incorrect.

Using Math.abs or Math.sum are not valid methods for this purpose.

The height of a node is 1 plus the maximum height of its left or right subtree.

3fill in blank

hard

Fix the error in updating the diameter during recursion.

DSA Java

int diameter = 0;

int height(TreeNode node) {
    if (node == null) return 0;
    int leftHeight = height(node.left);
    int rightHeight = height(node.right);
    diameter = Math.[1](diameter, leftHeight + rightHeight);
    return 1 + Math.max(leftHeight, rightHeight);
}

Drag options to blanks, or click blank then click option'

Amin

Babs

Cmax

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using Math.min will incorrectly reduce the diameter.

Using Math.abs or Math.sum are not valid for this update.

We update diameter to the maximum of current diameter and sum of left and right heights.

4fill in blank

hard

Fill both blanks to complete the diameterOfBinaryTree method.

DSA Java

public int diameterOfBinaryTree(TreeNode root) {
    diameter = 0;
    [1](root);
    return [2];
}

Drag options to blanks, or click blank then click option'

Aheight

Bdiameter

CmaxDepth

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Calling maxDepth instead of height will cause errors if maxDepth is undefined.

Returning root instead of diameter will return the wrong value.

We call height to compute heights and update diameter, then return diameter.

5fill in blank

hard

Fill all three blanks to complete the height method with diameter update.

DSA Java

int height(TreeNode node) {
    if (node == null) return 0;
    int leftHeight = [1](node.left);
    int rightHeight = [2](node.right);
    diameter = Math.[3](diameter, leftHeight + rightHeight);
    return 1 + Math.max(leftHeight, rightHeight);
}

Drag options to blanks, or click blank then click option'

Aheight

Bmax

Cmin

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using min instead of max for diameter update.

Calling max or sum instead of height for subtree heights.

We recursively call height on left and right children, then update diameter with max.

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