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

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Tree Node Levels

What is the printed level of each node after running this code?

DSA Typescript

class TreeNode {
  value: number;
  children: TreeNode[];
  level: number;
  constructor(value: number) {
    this.value = value;
    this.children = [];
    this.level = 0;
  }
}

function assignLevels(root: TreeNode, currentLevel: number = 0): void {
  root.level = currentLevel;
  for (const child of root.children) {
    assignLevels(child, currentLevel + 1);
  }
}

const root = new TreeNode(1);
const child1 = new TreeNode(2);
const child2 = new TreeNode(3);
const grandchild = new TreeNode(4);
root.children.push(child1, child2);
child1.children.push(grandchild);

assignLevels(root);

console.log(root.level, child1.level, child2.level, grandchild.level);

A 0 0 0 0

B 0 1 1 2

C 1 2 2 3

D 1 1 1 1

💡 Hint

Think about how levels increase as you go down from the root.

The root node starts at level 0. Each child node has a level one greater than its parent. So, child1 and child2 are at level 1, and grandchild is at level 2.

🧠 Conceptual

intermediate

Identify Leaf Nodes in a Tree

Which nodes are leaf nodes in the following tree structure? Root (1) ├─ Child A (2) │ └─ Grandchild A1 (4) └─ Child B (3) ├─ Grandchild B1 (5) └─ Grandchild B2 (6)

A Nodes 4, 5, 6

B Nodes 1, 2, 3

C Nodes 2, 3, 4

D Nodes 1, 5, 6

💡 Hint

Leaf nodes have no children.

Leaf nodes are nodes without any children. Here, nodes 4, 5, and 6 have no children, so they are leaves.

❓ Predict Output

advanced

Calculate Height of a Tree

What is the output of the height calculated by this code for the given tree?

DSA Typescript

class TreeNode {
  value: number;
  children: TreeNode[];
  constructor(value: number) {
    this.value = value;
    this.children = [];
  }
}

function height(node: TreeNode | null): number {
  if (!node) return -1;
  if (node.children.length === 0) return 0;
  let maxChildHeight = -1;
  for (const child of node.children) {
    const childHeight = height(child);
    if (childHeight > maxChildHeight) maxChildHeight = childHeight;
  }
  return maxChildHeight + 1;
}

const root = new TreeNode(1);
const c1 = new TreeNode(2);
const c2 = new TreeNode(3);
const gc1 = new TreeNode(4);
const gc2 = new TreeNode(5);
root.children.push(c1, c2);
c1.children.push(gc1);
c2.children.push(gc2);

console.log(height(root));

A 2

B 0

C 1

D 3

💡 Hint

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

The longest path from root to leaf is 2 edges (root->c1->gc1 or root->c2->gc2). So height is 2.

🔧 Debug

advanced

Find the Depth of a Node

What is the depth of node with value 5 after running this code?

DSA Typescript

class TreeNode {
  value: number;
  children: TreeNode[];
  constructor(value: number) {
    this.value = value;
    this.children = [];
  }
}

function findDepth(root: TreeNode, target: number, currentDepth: number = 0): number {
  if (root.value === target) return currentDepth;
  for (const child of root.children) {
    const d = findDepth(child, target, currentDepth + 1);
    if (d !== -1) return d;
  }
  return -1;
}

const root = new TreeNode(1);
const c1 = new TreeNode(2);
const c2 = new TreeNode(3);
const gc1 = new TreeNode(4);
const gc2 = new TreeNode(5);
root.children.push(c1, c2);
c1.children.push(gc1);
c2.children.push(gc2);

console.log(findDepth(root, 5));

A -1

B 3

C 2

D 1

💡 Hint

Depth counts edges from root to the node.

Node 5 is a child of node 3, which is a child of root (1). So depth is 2.

🧠 Conceptual

expert

Level vs Depth vs Height

Which statement correctly describes the difference between level, depth, and height of a node in a tree?

A Depth is the number of children; level is the distance from root to leaf; height is the distance from leaf to root.

B Height and depth are the same; level is the number of children a node has.

C Level is the number of children; depth is the number of leaves; height is the number of nodes in the tree.

D Level and depth are the same; height is the number of edges on the longest path from the node to a leaf.

💡 Hint

Think about how far a node is from the root and from the leaves.

Level and depth both mean the distance from the root to the node (counting edges). Height is the longest distance from the node down to any leaf.

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