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

Practice - 5 Tasks

1fill in blank

easy

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

DSA Java

TreeNode root = new TreeNode([1]);

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

A1

B0

Croot

Dnull

Attempts:

3 left

💡 Hint

Common Mistakes

Using null instead of a value for the root node.

The root node is usually created with a value, here we use 1 as the root's value.

2fill in blank

medium

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

DSA Java

boolean isLeaf = (node.left == null && node.[1] == null);

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

Achild

Bparent

Cright

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Checking parent or root instead of right child.

A leaf node has no left or right children, so both must be null.

3fill in blank

hard

Fix the error in the code to calculate the height of a node.

DSA Java

int height = 1 + Math.max(height(node.left), [1]);

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

Aheight

Bdepth

Clevel

Dheight(node.right)

Attempts:

3 left

💡 Hint

Common Mistakes

Using node.height or node.depth instead of recursive call.

To calculate height, we need the height of the right child recursively, so use height(node.right).

4fill in blank

hard

Fill both blanks to calculate the depth of a node given its parent.

DSA Java

int depth = parent.[1] + [2];

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

Adepth

B1

Cheight

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using height instead of depth.

Adding 0 instead of 1.

The depth of a node is the depth of its parent plus 1.

5fill in blank

hard

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

DSA Java

public int getLevel(TreeNode node) {
    if (node == null) return [1];
    return getLevel(node.parent) + [2]; // level is depth + 1
}

// Usage:
int level = getLevel([3]);

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

A0

B1

Cnode

Dnull

Attempts:

3 left

💡 Hint

Common Mistakes

Returning null instead of 0.

Adding 0 instead of 1.

Calling method with null instead of node.

The base case returns 0 for null node. Each recursive call adds 1 to parent's level. The method is called with the node itself.

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 concept

   The root node is the starting point of the tree and has no parent node above it.

2. Step 2: Identify the correct description

   Among the options, only the topmost node with no parent matches the root node definition.

3. Final Answer:

   The topmost node with no parent -> Option A

4. Quick Check:

   Root = topmost node with no parent [OK]

Hint: Root node has no parent, always at the top [OK]

Common Mistakes:

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

2. Which of the following is the correct way to declare a leaf node in Java if Node is a class representing tree nodes?

easy

A. Node leaf = new Node(); leaf.left = new Node();

B. Node leaf = null; // leaf nodes cannot be null

C. Node leaf = new Node(null, null); // no children

D. Node leaf = new Node(5); // with one child

Solution

1. Step 1: Understand leaf node definition

   A leaf node has no children, so its left and right child references should be null.

2. Step 2: Check each option for leaf node declaration

   Node leaf = new Node(5); // with one child: Node leaf = new Node(5); uses standard constructor which sets left = right = null, creating a leaf node. A adds a child. C likely causes syntax error (no such constructor). D is null, not a node.

3. Final Answer:

   Node leaf = new Node(5); // with no children -> Option D

4. Quick Check:

   Leaf node has no children = left and right null [OK]

Hint: Leaf nodes have no children, so child pointers are null [OK]

Common Mistakes:

• Assuming leaf nodes must have data only
• Creating children for leaf nodes
• Setting leaf node to null reference

3. Consider the following tree structure:

        1
       / \
      2   3
     /   / \
    4   5   6

What is the height of the tree?

medium

A. 5

B. 3

C. 2

D. 4

Solution

1. Step 1: Understand height of a tree

   Height is the number of edges on the longest path from root to a leaf node.

2. Step 2: Find longest path from root (1) to leaf

   Paths: 1->2->4 has 2 edges, 1->3->5 has 2 edges, 1->3->6 has 2 edges. So height = 2.

3. Final Answer:

   2 -> Option C

4. Quick Check:

   Longest path edges = 2 [OK]

Hint: Height = longest edges from root to leaf [OK]

Common Mistakes:

• Counting nodes instead of edges for height
• Confusing height with depth
• Counting root as height 1

4. Given the following code snippet, what is the error?

class Node {
  int data;
  Node left, right;
  Node(int data) {
    this.data = data;
    left = right = null;
  }
}

Node root = new Node(10);
root.left = new Node(20);
root.right = new Node(30);
root.left.left = new Node(40);
root.left.right = new Node(50);
root.right.left = new Node(60);
root.right.right = new Node(70);

System.out.println(root.left.right.data);

medium

A. NullPointerException at root.left.right

B. No error, prints 50

C. Syntax error in Node class

D. Prints 60 instead of 50

Solution

1. Step 1: Trace node assignments

   root.left.right is assigned new Node(50), so it exists and has data 50.

2. Step 2: Check print statement

   Printing root.left.right.data will print 50 without error.

3. Final Answer:

   No error, prints 50 -> Option B

4. Quick Check:

   root.left.right.data = 50 [OK]

Hint: Check if node is assigned before accessing data [OK]

Common Mistakes:

• Assuming uninitialized nodes cause error here
• Confusing left and right child nodes
• Thinking print outputs 60

5. In a tree, if the root node is at level 0, what is the depth of the node with value 6 in the tree below?

        1
       / \
      2   3
     /   / \
    4   5   6

medium

A. 2

B. 1

C. 3

D. 4

Solution

1. Step 1: Understand depth definition

   Depth is the number of edges from the root node to the target node.

2. Step 2: Trace path from root (1) to node 6

   Path: 1 -> 3 -> 6 has 2 edges, so depth is 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Edges from root to node 6 = 2 [OK]

Hint: Depth = edges from root to node [OK]

Common Mistakes:

• Counting nodes instead of edges for depth
• Confusing depth with level starting at 1
• Assuming depth equals height