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

Practice - 5 Tasks

1fill in blank

easy

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

DSA Typescript

const root = new TreeNode([1]);

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

Anull

B0

Cundefined

DrootValue

Attempts:

3 left

💡 Hint

Common Mistakes

Using null or undefined as the root node value.

The root node is created with a value, here represented by rootValue.

2fill in blank

medium

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

DSA Typescript

function isLeaf(node: TreeNode): boolean {
  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 < instead of === to check for zero children.

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

3fill in blank

hard

Fix the error in the function that calculates the depth of a node.

DSA Typescript

function getDepth(node: TreeNode): number {
  if (!node.parent) return [1];
  return 1 + getDepth(node.parent);
}

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

A0

Bnull

C-1

Dundefined

Attempts:

3 left

💡 Hint

Common Mistakes

Returning null or undefined instead of 0 for root depth.

The depth of the root node is 0 because it has no parent.

4fill in blank

hard

Complete the code to calculate the height of a node.

DSA Typescript

function getHeight(node: TreeNode): number {
  if (node.children.length === 0) return [1];
  return 1 + Math.max(...node.children.map(child => getHeight(child)));
}

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

A0

B1

C)

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 1 for leaf height or missing closing parenthesis.

The height of a leaf node is 0. The recursive call needs a closing parenthesis.

5fill in blank

hard

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

DSA Typescript

function getLevel(node: TreeNode): number {
  let level = 0;
  let current = node;
  while (current.[1]) {
    level [2] level + 1;
    current = current.[3];
  }
  return level;
}

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

Aparent

B=

C+=

Dchild

Attempts:

3 left

💡 Hint

Common Mistakes

Using assignment instead of increment, or wrong property name.

The level is the number of parents from the node to the root. We loop while current.parent exists, increment level with += 1, and move up to current.parent.

Practice

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

easy

A. A node with no children

B. The topmost node with no parent

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 a tree and has no parent node above it.

2. Step 2: Compare options with definition

   The topmost node with no parent matches the definition exactly. Other options describe leaf nodes or specific child counts.

3. Final Answer:

   The topmost node with no parent -> Option B

4. Quick Check:

   Root = topmost node with no parent [OK]

Hint: Root is always the top node without a parent [OK]

Common Mistakes:

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

2. Which of the following is the correct TypeScript syntax to define a simple tree node interface with a value and children array?

easy

A. interface TreeNode { value: number; children: TreeNode[]; }

B. interface TreeNode { value: number; children: TreeNode; }

C. interface TreeNode { value: number; children: number[]; }

D. interface TreeNode { value: number; child: TreeNode[]; }

Solution

1. Step 1: Check correct property names and types

   The children property should be an array of TreeNode objects, so type is TreeNode[].

2. Step 2: Validate each option

   interface TreeNode { value: number; children: TreeNode[]; } correctly uses 'children: TreeNode[]'. interface TreeNode { value: number; children: TreeNode; } uses single TreeNode, not array. interface TreeNode { value: number; children: number[]; } uses number array incorrectly. interface TreeNode { value: number; child: TreeNode[]; } uses wrong property name 'child'.

3. Final Answer:

   interface TreeNode { value: number; children: TreeNode[]; } -> Option A

4. Quick Check:

   Children is array of TreeNode objects [OK]

Hint: Children property must be an array of TreeNode [OK]

Common Mistakes:

• Using singular 'child' instead of 'children'
• Setting children as single object, not array
• Using wrong type like number[] for children

3. Given the following tree structure in TypeScript, what is the height of the tree?

const tree = {
  value: 1,
  children: [
    { value: 2, children: [] },
    { value: 3, children: [
      { value: 4, children: [] }
    ] }
  ]
};

medium

A. 1

B. 4

C. 3

D. 2

Solution

1. Step 1: Understand height definition

   Height is the longest path from root to any leaf node, counting edges.

2. Step 2: Trace longest path in given tree

   Root (1) to node (3) to node (4) is longest path with 2 edges, so height = 2. Counting nodes gives 3 levels, but height counts edges, so height = 2.

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Height = longest edge count from root to leaf = 2 [OK]

Hint: Height counts edges, not nodes, from root to deepest leaf [OK]

Common Mistakes:

• Counting nodes instead of edges for height
• Confusing height with depth
• Ignoring deeper branches

4. Consider this TypeScript code snippet for calculating the depth of a node in a tree. Identify the bug:

function getDepth(node: TreeNode, root: TreeNode, depth = 0): number {
  if (node === root) return depth;
  return getDepth(node, root.children[0], depth + 1);
}

medium

A. It always checks only the first child, missing other branches

B. It never increments depth

C. It compares node and root incorrectly

D. It should return depth + 1 instead of depth

Solution

1. Step 1: Analyze recursive call logic

   The function always calls getDepth on root.children[0], ignoring other children, so it misses nodes not in first child's subtree.

2. Step 2: Understand impact on depth calculation

   This causes incorrect depth for nodes not in first child's branch, as they are never reached.

3. Final Answer:

   It always checks only the first child, missing other branches -> Option A

4. Quick Check:

   Recursion must explore all children, not just first [OK]

Hint: Check if recursion covers all children, not just one [OK]

Common Mistakes:

• Assuming single child covers whole tree
• Not handling multiple branches in recursion
• Confusing depth increment logic

5. You have a tree where each node has a level property indicating its distance from the root (root level = 0). If a node has level 3, what is its depth and height relative to the root?

hard

A. Depth = 0, Height = 3

B. Depth = 3, Height = 3

C. Depth = 3, Height depends on subtree size

D. Depth and Height both equal to 0

Solution

1. Step 1: Understand level and depth relation

   Level and depth both measure distance from root, so depth = level = 3.

2. Step 2: Understand height meaning

   Height is longest path from node down to leaf, which depends on subtree size, so height is unknown from level alone.

3. Final Answer:

   Depth = 3, Height depends on subtree size -> Option C

4. Quick Check:

   Depth = level; height varies by subtree [OK]

Hint: Level = depth; height depends on node's subtree [OK]

Common Mistakes:

• Confusing height with depth or level
• Assuming height equals level always
• Ignoring subtree size for height