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.