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

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of the tree traversal showing root and leaf nodes?

Given the following Java code that builds a simple tree and prints root and leaf nodes, what is the printed output?

DSA Java

class Node {
    int value;
    Node left, right;
    Node(int val) { value = val; left = right = null; }
}

public class TreeTest {
    public static void main(String[] args) {
        Node root = new Node(10);
        root.left = new Node(5);
        root.right = new Node(15);
        root.left.left = new Node(3);
        root.left.right = new Node(7);
        root.right.right = new Node(18);

        System.out.print("Root: " + root.value + "\n");
        System.out.print("Leaf nodes: ");
        printLeaves(root);
    }

    static void printLeaves(Node node) {
        if (node == null) return;
        if (node.left == null && node.right == null) {
            System.out.print(node.value + " ");
        }
        printLeaves(node.left);
        printLeaves(node.right);
    }
}

A

Root: 10
Leaf nodes: 3 7 15 18 

B

Root: 10
Leaf nodes: 5 15 

C

Root: 10
Leaf nodes: 3 7 18 

D

Root: 10
Leaf nodes: 3 7 

💡 Hint

Leaf nodes have no children (left and right are null).

The root node is 10. Leaf nodes are nodes with no children: 3, 7, and 18.

❓ Predict Output

intermediate

What is the height of the given binary tree?

Consider the binary tree constructed below. What is the height of the tree?

DSA Java

class Node {
    int value;
    Node left, right;
    Node(int val) { value = val; left = right = null; }
}

public class TreeHeight {
    public static void main(String[] args) {
        Node root = new Node(1);
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.left = new Node(4);
        root.left.left.left = new Node(5);

        System.out.println(height(root));
    }

    static int height(Node node) {
        if (node == null) return -1;
        int leftHeight = height(node.left);
        int rightHeight = height(node.right);
        return 1 + Math.max(leftHeight, rightHeight);
    }

A 3

B 4

C 5

D 2

💡 Hint

Height counts edges on longest path from node to leaf.

Height is number of edges on longest path from root to leaf. Here path is 1->2->4->5 with 3 edges.

❓ Predict Output

advanced

What is the depth of node with value 7 in the tree?

Given the tree below, what is the depth of the node with value 7?

DSA Java

class Node {
    int value;
    Node left, right;
    Node(int val) { value = val; left = right = null; }
}

public class TreeDepth {
    public static void main(String[] args) {
        Node root = new Node(10);
        root.left = new Node(5);
        root.right = new Node(15);
        root.left.left = new Node(3);
        root.left.right = new Node(7);

        System.out.println(depth(root, 7, 0));
    }

    static int depth(Node node, int val, int currentDepth) {
        if (node == null) return -1;
        if (node.value == val) return currentDepth;
        int left = depth(node.left, val, currentDepth + 1);
        if (left != -1) return left;
        return depth(node.right, val, currentDepth + 1);
    }

A 1

B 0

C 3

D 2

💡 Hint

Depth counts edges from root to the node.

Node 7 is two edges away from root: 10->5->7, so depth is 2.

🧠 Conceptual

advanced

Which statement correctly describes the level of nodes in a tree?

Select the correct statement about the level of nodes in a tree.

A Level of root node is 1, and level decreases by 1 for each step down the tree.

B Level of root node is 0, and level increases by 1 for each step down the tree.

C Level of root node is 0, and level decreases by 1 for each step down the tree.

D Level of root node is 1, and level remains the same for all nodes.

💡 Hint

Level counts how far a node is from the root in steps.

Level starts at 0 for root and increases by 1 for each child level down.

🧠 Conceptual

expert

Which node is both a leaf and has height 0 in a tree?

In a tree, which node is guaranteed to be both a leaf and have height 0?

A A node with no children

B The root node

C A node with one child

D A node with two children

💡 Hint

Height 0 means no edges below the node.

Leaf nodes have no children and thus height 0 because no edges go down from them.

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