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.