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

Challenge - 5 Problems

🧠 Conceptual

intermediate

Identify the root node in a tree

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

A The node with the highest depth

B The node with no children

C The node with the lowest height

D The node with no parent

💡 Hint

Think about where the tree starts growing from.

The root node is the topmost node in a tree and has no parent node.

❓ Predict Output

intermediate

Output the leaf nodes of a tree

Given the following tree structure, which nodes are leaves?

DSA Go

type Node struct {
    Value int
    Children []*Node
}

// Tree:
//       1
//     /   \
//    2     3
//   / \     \
//  4   5     6

// Leaves are nodes with no children.

A [4, 5, 6]

B [1, 2, 3]

C [2, 3, 6]

D [1, 4, 5]

💡 Hint

Leaves have no children nodes.

Nodes 4, 5, and 6 have no children, so they are leaves.

❓ Predict Output

advanced

Calculate the height of a node in a tree

What is the height of node 2 in the following tree? // Tree: // 1 // / \ // 2 3 // / \ \ // 4 5 6 // Height is the number of edges on the longest path from the node to a leaf.

A 0

B 3

C 1

D 2

💡 Hint

Count edges from node 2 down to its farthest leaf.

Node 2 has children 4 and 5 which are leaves. The longest path from 2 to a leaf has 1 edge (to 4 or 5), so height is 1.

🧠 Conceptual

advanced

Understanding depth and level of a node

Which statement correctly describes the depth and level of a node in a tree?

A Depth is the number of leaves under the node; level is the number of ancestors

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

C Depth and level are always equal to the height of the node

D Depth is the number of children of the node; level is the number of siblings

💡 Hint

Think about how far a node is from the root.

Depth counts edges from root to node; level counts nodes from root (starting at 1). So level = depth + 1.

🔧 Debug

expert

Find the error in height calculation code

What error will this Go code produce when calculating the height of a tree node? func height(node *Node) int { if node == nil { return -1 } maxHeight := -1 for _, child := range node.Children { h := height(child) if h > maxHeight { maxHeight = h } } return maxHeight + 1 } // Node struct has Children slice.

A Returns incorrect height for leaf nodes

B Causes infinite recursion

C Returns -1 for empty tree correctly

D Panics due to nil pointer dereference

💡 Hint

Check base case and initial maxHeight value.

For leaf nodes (no children), maxHeight is initialized to -1 and remains -1, so the function returns 0. This correctly represents the height of a leaf node. The original code initialized maxHeight to 0, causing the function to return 1 for leaf nodes, which is incorrect.

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 lowest 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: Differentiate root from other nodes

   Leaf nodes have no children, but root specifically has no parent. Lowest level nodes are leaves or internal nodes, not necessarily root.

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 top node without a parent [OK]

Common Mistakes:

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

2. Which of the following is the correct way to declare a tree node struct in Go with integer data and pointers to left and right children?

easy

A. type Node struct { data int, left &Node, right &Node }

B. type Node struct { data int, left *Node, right *Node }

C. type Node struct { data int, left Node, right Node }

D. type Node struct { data int, left Node*, right Node* }

Solution

1. Step 1: Recall Go pointer syntax

   In Go, pointers are declared with * before the type, e.g., *Node.

2. Step 2: Check each option's pointer usage

   type Node struct { data int, left *Node, right *Node } uses *Node correctly. type Node struct { data int, left Node, right Node } uses Node (value, not pointer). type Node struct { data int, left &Node, right &Node } uses &Node which is invalid syntax. type Node struct { data int, left Node*, right Node* } uses Node* which is invalid in Go.

3. Final Answer:

   type Node struct { data int, left *Node, right *Node } -> Option B

4. Quick Check:

   Pointer syntax in Go = *Type [OK]

Hint: Use *Type for pointers in Go structs [OK]

Common Mistakes:

• Using value type instead of pointer for children
• Using &Type or Type* which are invalid in Go
• Using semicolons instead of commas in struct fields

3. Given the following tree structure in Go, what is the depth of node with value 5?

type Node struct {
  data  int
  left  *Node
  right *Node
}

root := &Node{data: 1}
root.left = &Node{data: 2}
root.right = &Node{data: 3}
root.left.left = &Node{data: 4}
root.left.right = &Node{data: 5}

medium

A. 2

B. 1

C. 3

D. 4

Solution

1. Step 1: Understand depth definition

   Depth of a node is the number of edges from the root to that node.

2. Step 2: Trace path from root to node 5

   Path: 1 (root) -> 2 -> 5. Number of edges = 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Depth = edges from root = 2 [OK]

Hint: Count edges from root to node for depth [OK]

Common Mistakes:

• Counting nodes instead of edges
• Confusing depth with height
• Miscounting path length

4. Consider this Go code snippet for a binary tree node:

type Node struct {
  data  int
  left  *Node
  right *Node
}

func isLeaf(n *Node) bool {
  return n.left == nil && n.right == nil
}

root := &Node{data: 10}
root.left = &Node{data: 20}
root.right = &Node{data: 30}
root.left.left = &Node{data: 40}

fmt.Println(isLeaf(root.left))

What is the output and why?

medium

A. true

B. Runtime panic

C. Compilation error

D. false

Solution

1. Step 1: Understand isLeaf function

   It returns true if both left and right children are nil (no children).

2. Step 2: Check root.left node children

   root.left has left child (40) but no right child, so left != nil, right == nil.

3. Step 3: Evaluate isLeaf(root.left)

   Since left is not nil, isLeaf returns false.

4. Final Answer:

   false -> Option D

5. Quick Check:

   Leaf = no children, root.left has left child [OK]

Hint: Leaf nodes have no children; check both left and right nil [OK]

Common Mistakes:

• Assuming node with one child is leaf
• Confusing nil checks causing panic
• Expecting true without checking both children

5. You have a binary tree where the root is at level 0. If a node is at level 3, what is its height assuming the tree height is 5? Also, which node is at level 0? Choose the correct pair of answers.

hard

A. Height = 5; Root node is at level 0

B. Height = 3; Leaf node is at level 0

C. Height = 2; Root node is at level 0

D. Height = 2; Leaf node is at level 0

Solution

1. Step 1: Calculate height of node at level 3

   Height = total tree height - node level = 5 - 3 = 2.

2. Step 2: Identify node at level 0

   By definition, root node is at level 0.

3. Final Answer:

   Height = 2; Root node is at level 0 -> Option C

4. Quick Check:

   Height = 5 - 3 = 2; Root at level 0 [OK]

Hint: Height = tree height - level; root always level 0 [OK]

Common Mistakes:

• Confusing height with level
• Assuming leaf node at level 0
• Calculating height as level number