Tree Terminology Root Leaf Height Depth Level in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Tree Node Levels

What is the output of the following code that prints the level of each node in a simple tree?

DSA Javascript

class Node {
  constructor(value) {
    this.value = value;
    this.children = [];
  }
}

const root = new Node(1);
const child1 = new Node(2);
const child2 = new Node(3);
const grandchild = new Node(4);

root.children.push(child1, child2);
child1.children.push(grandchild);

function printLevels(node, level = 0) {
  console.log(`${node.value}: Level ${level}`);
  for (const child of node.children) {
    printLevels(child, level + 1);
  }
}

printLevels(root);

A

1: Level 0
2: Level 0
4: Level 1
3: Level 0

B

1: Level 0
2: Level 1
4: Level 2
3: Level 1

C

1: Level 1
2: Level 2
4: Level 3
3: Level 2

D

1: Level 1
2: Level 1
4: Level 2
3: Level 1

💡 Hint

Think about the root node level and how it increases for children.

The root node starts at level 0. Each child node is one level deeper than its parent. So, node 1 is level 0, nodes 2 and 3 are level 1, and node 4 is level 2.

🧠 Conceptual

intermediate

Identify Leaf Nodes in a Tree

Which of the following best describes a leaf node in a tree?

A A node with no children

B A node with exactly one child

C The root node of the tree

D A node with two or more children

💡 Hint

Leaf nodes do not have any branches going out.

A leaf node is a node that does not have any children. It is the end point of a branch in the tree.

❓ Predict Output

advanced

Calculate Height of a Tree

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

DSA Javascript

class Node {
  constructor(value) {
    this.value = value;
    this.children = [];
  }
}

const root = new Node(10);
const c1 = new Node(20);
const c2 = new Node(30);
const c3 = new Node(40);
const gc1 = new Node(50);
const gc2 = new Node(60);

root.children.push(c1, c2);
c1.children.push(c3);
c3.children.push(gc1, gc2);

function height(node) {
  if (node.children.length === 0) return 0;
  let maxChildHeight = 0;
  for (const child of node.children) {
    const childHeight = height(child);
    if (childHeight > maxChildHeight) maxChildHeight = childHeight;
  }
  return maxChildHeight + 1;
}

console.log(height(root));

A 3

B 4

C 2

D 5

💡 Hint

Height is the longest path from root to leaf in edges.

The longest path from root (10) to leaf is 10 -> 20 -> 40 -> 50 or 60, which has 3 edges, so height is 3.

🔧 Debug

advanced

Find the Error in Depth Calculation

The following code tries to calculate the depth of a node in a tree but produces incorrect results. What is the error?

DSA Javascript

class Node {
  constructor(value) {
    this.value = value;
    this.parent = null;
  }
}

const root = new Node(1);
const child = new Node(2);
child.parent = root;
const grandchild = new Node(3);
grandchild.parent = child;

function depth(node) {
  let d = 0;
  while (node.parent !== null) {
    d += 1;
  }
  return d;
}

console.log(depth(grandchild));

A Syntax error due to missing semicolon

B Returns 0 because parent is always null

C Returns 1 instead of 2 because of wrong increment

D Infinite loop because node is not updated inside the while loop

💡 Hint

Check if the loop changes the node variable to move up the tree.

The code never updates the node inside the while loop, so the condition never changes and causes an infinite loop.

🧠 Conceptual

expert

Understanding Tree Levels and Depths

In a tree, which statement correctly relates the level and depth of a node?

A Level and depth of a node are always equal

B Level is depth plus one

C Depth is the number of edges from root to node; level is depth plus one

D Level is the number of edges from root to node; depth is level plus one

💡 Hint

Think about how level and depth are counted starting from root.

Depth counts edges from root to node starting at 0 for root. Level counts nodes on the path starting at 1 for root. So level = depth + 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