Tree Terminology Root Leaf Height Depth Level in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create the root node of a tree.

DSA Javascript

const root = new TreeNode([1]);

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

Anull

B0

C1

D'root'

Attempts:

3 left

💡 Hint

Common Mistakes

Using null or 0 as the root value which may not represent the root meaningfully.

The root node usually has a value, here we assign it the string 'root'.

2fill in blank

medium

Complete the code to check if a node is a leaf (has no children).

DSA Javascript

function isLeaf(node) {
  return node.children.length [1] 0;
}

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

A===

B>

C<

D!==

Attempts:

3 left

💡 Hint

Common Mistakes

Using > or !== which would not correctly identify leaf nodes.

A leaf node has zero children, so we check if children.length is exactly 0.

3fill in blank

hard

Fix the error in the code to calculate the height of a tree node.

DSA Javascript

function height(node) {
  if (!node) return -1;
  let maxChildHeight = -1;
  for (const child of node.children) {
    maxChildHeight = Math.max(maxChildHeight, height(child));
  }
  return maxChildHeight [1] 1;
}

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication which gives wrong height values.

The height of a node is 1 plus the maximum height among its children.

4fill in blank

hard

Fill both blanks to calculate the depth of a node given its parent depth.

DSA Javascript

function depth(node, parentDepth) {
  if (!node) return -1;
  node.depth = parentDepth [1] 1;
  for (const child of node.children) {
    depth(child, node.depth [2] 0);
  }
}

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

A+

B-

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication which gives incorrect depths.

Depth of a node is parent's depth plus 1. We pass this updated depth to children.

5fill in blank

hard

Fill all three blanks to create a function that returns the level of a node in a tree.

DSA Javascript

function getLevel(node) {
  if (!node.parent) return [1];
  return getLevel(node.parent) [2] [3];
}

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

A0

B+

C1

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 as root level or subtracting which gives wrong levels.

The root node has level 0. For other nodes, level is parent's level plus 1.

Practice

1. In a tree data structure, which node is called the root?

easy

A. The topmost node with no parent

B. A node with no children

C. Any node at the bottom level

D. A node with exactly two children

Solution

1. Step 1: Understand the root node definition

   The root node is the starting point of the tree and has no parent node above it.

2. Step 2: Compare options with definition

   The topmost node with no parent matches this definition exactly; other options describe leaf or internal nodes.

3. Final Answer:

   The topmost node with no parent -> Option A

4. Quick Check:

   Root = topmost node with no parent [OK]

Hint: Root is always the very first node, no parent above it [OK]

Common Mistakes:

• Confusing root with leaf nodes
• Thinking root must have children
• Assuming root is at the bottom

2. Which of the following is the correct way to describe a leaf node in a tree?

easy

A. The root node

B. A node with at least one child

C. A node with no children

D. A node with exactly one child

Solution

1. Step 1: Define leaf node

   A leaf node is a node that does not have any children; it is at the end of a branch.

2. Step 2: Match options to definition

   Only A node with no children states the node has no children, which matches the leaf node definition.

3. Final Answer:

   A node with no children -> Option C

4. Quick Check:

   Leaf = node with no children [OK]

Hint: Leaf nodes have zero children, always at branch ends [OK]

Common Mistakes:

• Thinking leaf nodes have children
• Confusing leaf with root
• Assuming leaf nodes must have one child

3. Consider the following tree structure:

        A
       / \
      B   C
     /   / \
    D   E   F

What is the height of node B?

medium

A. 1

B. 2

C. 3

D. 0

Solution

1. Step 1: Understand height of a node

   Height is the number of edges on the longest path from the node down to a leaf.

2. Step 2: Calculate height of node B

   Node B has one child D which is a leaf. The longest path from B to leaf is B->D with 1 edge.

3. Final Answer:

   1 -> Option A

4. Quick Check:

   Height of B = 1 edge to leaf D [OK]

Hint: Height counts edges down to farthest leaf [OK]

Common Mistakes:

• Counting nodes instead of edges
• Confusing height with depth
• Counting path to root instead of leaf

4. Given this tree:

        X
       / \
      Y   Z
     / 
    W  

What is the depth of node W?
Note: Depth is the number of edges from the root to the node.

medium

A. 1

B. 2

C. 3

D. 0

Solution

1. Step 1: Understand depth definition

   Depth is the number of edges from the root node to the target node.

2. Step 2: Count edges from root X to W

   Path is X -> Y -> W, which has 2 edges.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Depth of W = 2 edges from root [OK]

Hint: Depth counts edges up from root to node [OK]

Common Mistakes:

• Counting nodes instead of edges
• Confusing depth with height
• Starting count from 1 instead of 0 edges

5. In a tree, the level of a node is defined as its depth plus one.
Given the tree:

        M
       / \
      N   O
         / \
        P   Q

What is the level of node P?

hard

A. 2

B. 1

C. 4

D. 3

Solution

1. Step 1: Calculate depth of node P

   Path from root M to P is M -> O -> P, which has 2 edges, so depth = 2.

2. Step 2: Calculate level using formula

   Level = depth + 1 = 2 + 1 = 3.

3. Final Answer:

   3 -> Option D

4. Quick Check:

   Level = depth + 1 = 3 [OK]

Hint: Level = depth + 1, count edges then add one [OK]

Common Mistakes:

• Using depth as level without adding 1
• Counting nodes incorrectly
• Confusing level with height