Diameter of Binary Tree in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of diameter calculation on a simple binary tree

What is the output of the following code that calculates the diameter of a binary tree?

DSA Javascript

class TreeNode {
  constructor(val, left = null, right = null) {
    this.val = val;
    this.left = left;
    this.right = right;
  }
}

function diameterOfBinaryTree(root) {
  let diameter = 0;
  function depth(node) {
    if (!node) return 0;
    const left = depth(node.left);
    const right = depth(node.right);
    diameter = Math.max(diameter, left + right);
    return Math.max(left, right) + 1;
  }
  depth(root);
  return diameter;
}

const root = new TreeNode(1, new TreeNode(2, new TreeNode(4), new TreeNode(5)), new TreeNode(3));
console.log(diameterOfBinaryTree(root));

A 2

B 5

C 4

D 3

💡 Hint

The diameter is the longest path between any two nodes, counting edges.

The longest path goes through nodes 4 -> 2 -> 1 -> 3 or 5 -> 2 -> 1 -> 3, which has 3 edges.

❓ Predict Output

intermediate

Diameter of a skewed binary tree

What is the output of the diameterOfBinaryTree function for this skewed tree?

DSA Javascript

const root = new TreeNode(1, new TreeNode(2, new TreeNode(3, new TreeNode(4))));
console.log(diameterOfBinaryTree(root));

A 3

B 4

C 0

D 1

💡 Hint

In a skewed tree, the diameter is the number of edges in the longest chain.

The tree is a straight line with 4 nodes, so the diameter is 3 edges.

🔧 Debug

advanced

Identify the error in this diameter calculation code

What error will this code produce when calculating the diameter of a binary tree?

DSA Javascript

function diameterOfBinaryTree(root) {
  let diameter = 0;
  function depth(node) {
    if (node === null) return 0;
    const left = depth(node.left);
    const right = depth(node.right);
    diameter = Math.max(diameter, left + right + 1);
    return Math.max(left, right) + 1;
  }
  depth(root);
  return diameter;
}

A TypeError because node.left might be undefined

B SyntaxError due to missing return statement

C The diameter is off by 1 (returns number of nodes, not edges)

D No error, returns correct diameter

💡 Hint

Diameter counts edges, but code adds 1 extra edge.

The code adds 1 to left + right, counting nodes instead of edges, so the diameter is one too large.

🧠 Conceptual

advanced

Understanding diameter calculation logic

Why does the diameter calculation use the sum of left and right subtree depths at each node?

A Because the longest path passes through the current node connecting left and right subtrees

B Because the diameter is the maximum depth of either subtree alone

C Because the diameter is the sum of all nodes in the tree

D Because the diameter is the height of the tree plus one

💡 Hint

Think about the longest path crossing the root of a subtree.

The diameter can be the longest path passing through a node, which is the sum of depths of left and right subtrees.

❓ Predict Output

expert

Diameter of a complex binary tree with multiple branches

What is the output of the diameterOfBinaryTree function for this tree?

DSA Javascript

const root = new TreeNode(1,
  new TreeNode(2,
    new TreeNode(4,
      new TreeNode(7),
      null
    ),
    new TreeNode(5)
  ),
  new TreeNode(3,
    null,
    new TreeNode(6,
      new TreeNode(8),
      new TreeNode(9)
    )
  )
);
console.log(diameterOfBinaryTree(root));

A 4

B 6

C 7

D 5

💡 Hint

Trace the longest path between two leaves in different branches.

The longest path is 6 edges long, for example from node 7 to node 9 passing through nodes 4, 2, 1, 3, and 6.

Practice

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

easy

A. The longest path between any two nodes in the tree

B. The height of the tree

C. The number of leaf nodes

D. The total number of nodes in the tree

Solution

1. Step 1: Understand the diameter concept

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

2. Step 2: Differentiate from height and node count

   Height is the longest path from root to leaf, and node count is total nodes, both different from diameter.

3. Final Answer:

   The longest path between any two nodes in the tree -> Option A

4. Quick Check:

   Diameter = Longest path between nodes [OK]

Hint: Diameter is longest path, not just height or node count [OK]

Common Mistakes:

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

2. Which of the following JavaScript function signatures is correct for computing the diameter of a binary tree node?

easy

A. function diameterTree() {}

B. function diameter(root, tree) {}

C. function binaryTreeDiameter(node, root) {}

D. function diameterOfBinaryTree(root) {}

Solution

1. Step 1: Check common parameter naming

   The function usually takes the root node as input, so a single parameter named root is standard.

2. Step 2: Validate function signature correctness

   function diameterOfBinaryTree(root) {} uses a clear, single parameter 'root' and a descriptive function name, matching common practice.

3. Final Answer:

   function diameterOfBinaryTree(root) {} -> Option D

4. Quick Check:

   Correct function signature uses root parameter [OK]

Hint: Function usually takes root node as single parameter [OK]

Common Mistakes:

• Using multiple unrelated parameters
• Incorrect or unclear function names
• Missing parameters for the tree root

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

class TreeNode {
  constructor(val, left = null, right = null) {
    this.val = val;
    this.left = left;
    this.right = right;
  }
}

const root = new TreeNode(1,
  new TreeNode(2,
    new TreeNode(4),
    new TreeNode(5)
  ),
  new TreeNode(3)
);

function diameterOfBinaryTree(root) {
  let diameter = 0;
  function depth(node) {
    if (!node) return 0;
    const left = depth(node.left);
    const right = depth(node.right);
    diameter = Math.max(diameter, left + right);
    return Math.max(left, right) + 1;
  }
  depth(root);
  return diameter;
}

console.log(diameterOfBinaryTree(root));

medium

A. 4

B. 3

C. 2

D. 5

Solution

1. Step 1: Analyze the tree structure

   The tree has root 1, left subtree with nodes 2,4,5 and right subtree with node 3. The longest path is from node 4 to node 3 through 2 and 1 (4->2->1->3), which has length 3 edges.

2. Step 2: Trace the code logic

   The code calculates diameter as max sum of left and right depths at each node. At node 2, left and right depths are 1 each, so diameter updates to 2. At root, left depth is 2, right depth is 1, so diameter updates to 3.

3. Final Answer:

   3 -> Option B

4. Quick Check:

   Longest path edges = 3 [OK]

Hint: Diameter = max sum of left and right subtree depths [OK]

Common Mistakes:

• Counting nodes instead of edges for diameter
• Ignoring paths not passing through root
• Misreading tree structure

4. The following code attempts to compute the diameter of a binary tree but returns incorrect results. What is the bug?

function diameterOfBinaryTree(root) {
  let diameter = 0;
  function depth(node) {
    if (!node) return 0;
    const left = depth(node.left);
    const right = depth(node.right);
    diameter = Math.max(diameter, left * right);
    return Math.max(left, right) + 1;
  }
  depth(root);
  return diameter;
}

medium

A. Using multiplication instead of addition for diameter update

B. Returning max depth instead of sum of depths

C. Not handling null nodes correctly

D. Missing base case for leaf nodes

Solution

1. Step 1: Identify diameter update logic

   The code updates diameter using left * right, which multiplies depths instead of adding them.

2. Step 2: Correct diameter calculation

   Diameter should be updated with left + right, representing the longest path through the node.

3. Final Answer:

   Using multiplication instead of addition for diameter update -> Option A

4. Quick Check:

   Diameter update uses addition, not multiplication [OK]

Hint: Diameter update = left depth + right depth, not multiplication [OK]

Common Mistakes:

• Multiplying depths instead of adding
• Confusing depth return with diameter update
• Ignoring base case for null nodes

5. You want to find the diameter of a binary tree but also return the path nodes that form this diameter. Which approach correctly extends the diameter calculation to return the path?

hard

A. Use breadth-first search to find the longest path from root to any leaf

B. Only compute the height of the tree and return the nodes at the deepest level

C. Track left and right subtree depths and their paths; update diameter and store combined path when a longer diameter is found

D. Count total nodes and return all leaf nodes as the diameter path

Solution

1. Step 1: Understand diameter path requirements

   Diameter path is the longest path between any two nodes, so we must track paths from left and right subtrees.

2. Step 2: Extend depth function to track paths

   Along with depths, store paths for left and right subtrees. When diameter updates, combine these paths to form the diameter path.

3. Step 3: Reject incorrect approaches

   Height alone or BFS from root won't find longest path between any two nodes. Counting leaf nodes is unrelated.

4. Final Answer:

   Track left and right subtree depths and their paths; update diameter and store combined path when a longer diameter is found -> Option C

5. Quick Check:

   Track depths and paths to get diameter path [OK]

Hint: Store paths with depths; update when diameter increases [OK]

Common Mistakes:

• Only tracking height or BFS from root
• Ignoring path storage during recursion
• Assuming diameter path is always root to leaf