Trie Node Design and Initialization in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Trie Node Initialization

What is the output of the following C# code that initializes a Trie node and prints its children count?

DSA C#

public class TrieNode {
    public Dictionary<char, TrieNode> Children = new Dictionary<char, TrieNode>();
    public bool IsEndOfWord = false;
}

class Program {
    static void Main() {
        TrieNode node = new TrieNode();
        System.Console.WriteLine(node.Children.Count);
    }
}

A 0

B 1

C null

D Throws NullReferenceException

💡 Hint

Think about what the Children dictionary contains right after initialization.

The Children dictionary is initialized empty, so its Count is 0.

❓ Predict Output

intermediate

Trie Node Children After Adding One Child

What is the output of this C# code after adding one child node to the TrieNode's Children dictionary?

DSA C#

public class TrieNode {
    public Dictionary<char, TrieNode> Children = new Dictionary<char, TrieNode>();
    public bool IsEndOfWord = false;
}

class Program {
    static void Main() {
        TrieNode root = new TrieNode();
        root.Children['a'] = new TrieNode();
        System.Console.WriteLine(root.Children.Count);
    }
}

A 0

B null

C Throws KeyNotFoundException

D 1

💡 Hint

Adding a child node increases the count of Children dictionary.

After adding one child with key 'a', the Children dictionary has one entry, so Count is 1.

🧠 Conceptual

advanced

Purpose of IsEndOfWord in Trie Node

What is the main purpose of the boolean field IsEndOfWord in a Trie node?

A To indicate if the node has any children

B To mark the node as the end of a valid word in the Trie

C To store the character value of the node

D To count the number of children nodes

💡 Hint

Think about how a Trie distinguishes complete words from prefixes.

IsEndOfWord marks nodes that represent the last character of a valid word stored in the Trie.

❓ Predict Output

advanced

Output After Adding Multiple Children to Trie Node

What is the output of this C# code snippet after adding multiple children to a Trie node?

DSA C#

public class TrieNode {
    public Dictionary<char, TrieNode> Children = new Dictionary<char, TrieNode>();
    public bool IsEndOfWord = false;
}

class Program {
    static void Main() {
        TrieNode node = new TrieNode();
        node.Children['c'] = new TrieNode();
        node.Children['a'] = new TrieNode();
        node.Children['t'] = new TrieNode();
        System.Console.WriteLine(string.Join(",", node.Children.Keys));
    }
}

A t,a,c

B a,c,t

C c,a,t

D a,t,c

💡 Hint

Dictionary keys in C# are iterated in insertion order starting from .NET Core 3.0 and later.

The keys were added in order 'c', 'a', 't', but Dictionary preserves insertion order in recent C# versions, so output is 'c,a,t'. However, in older versions order is undefined. To ensure one correct answer, assume latest C# where insertion order is preserved.

🧠 Conceptual

expert

Memory Efficiency of Trie Node Children Representation

Which data structure choice for storing children in a Trie node is generally the most memory efficient when the alphabet size is large but each node has few children?

A Dictionary<char, TrieNode>

B Linked list of child nodes

C Array of fixed size equal to alphabet size

D HashSet<char>

💡 Hint

Consider sparse vs dense storage and memory overhead.

A Dictionary stores only existing children, saving memory when few children exist compared to a large fixed array.

Practice

1. What is the primary purpose of a Trie node in a Trie data structure?

easy

A. To act as a queue for BFS traversal

B. To store integer values for sorting

C. To hold a single string value only

D. To store characters and links to child nodes representing prefixes

Solution

1. Step 1: Understand Trie node role

   A Trie node stores a character and links to child nodes representing possible next characters in words.

2. Step 2: Compare options

   Only To store characters and links to child nodes representing prefixes correctly describes this role; others describe unrelated data structures or incorrect uses.

3. Final Answer:

   To store characters and links to child nodes representing prefixes -> Option D

4. Quick Check:

   Trie node = store chars + children links [OK]

Hint: Trie nodes hold chars and children links [OK]

Common Mistakes:

• Thinking Trie nodes store full words only
• Confusing Trie nodes with array or list nodes
• Assuming Trie nodes hold integer values

2. Which of the following is the correct way to declare a Trie node class with a children array for 26 lowercase letters in C#?

easy

A. public class TrieNode { public TrieNode[] children = new TrieNode[26]; public bool isEndOfWord; }

B. public class TrieNode { public List<char> children = new List<char>(); public bool isEndOfWord; }

C. public class TrieNode { public Dictionary children = new Dictionary(); public bool isEndOfWord; }

D. public class TrieNode { public TrieNode children = null; public bool isEndOfWord; }

Solution

1. Step 1: Identify correct children storage

   For 26 lowercase letters, an array of size 26 is standard to store child nodes indexed by character.

2. Step 2: Check syntax correctness

   public class TrieNode { public TrieNode[] children = new TrieNode[26]; public bool isEndOfWord; } declares a TrieNode array of size 26 and a boolean flag, which is correct syntax and design.

3. Final Answer:

   public class TrieNode { public TrieNode[] children = new TrieNode[26]; public bool isEndOfWord; } -> Option A

4. Quick Check:

   Children array size 26 = public class TrieNode { public TrieNode[] children = new TrieNode[26]; public bool isEndOfWord; } [OK]

Hint: Use TrieNode[] children = new TrieNode[26] for letters [OK]

Common Mistakes:

• Using List<char> instead of TrieNode array
• Using Dictionary unnecessarily
• Declaring children as single TrieNode instead of array

3. What will be the output of the following C# code snippet?

public class TrieNode {
    public TrieNode[] children = new TrieNode[26];
    public bool isEndOfWord = false;
}

public class Program {
    public static void Main() {
        TrieNode node = new TrieNode();
        Console.WriteLine(node.children[0] == null);
        Console.WriteLine(node.isEndOfWord);
    }
}

medium

A. false
False

B. true
True

C. true
False

D. false
True

Solution

1. Step 1: Check default initialization of children array

   In C#, arrays of reference types initialize elements to null by default, so children[0] is null, making the first print true.

2. Step 2: Check default value of isEndOfWord

   isEndOfWord is explicitly set to false, so printing it outputs false.

3. Final Answer:

   true False -> Option C

4. Quick Check:

   children[0] null = true, isEndOfWord false = false [OK]

Hint: Reference arrays default to null, bool defaults to false [OK]

Common Mistakes:

• Assuming children array elements are initialized to new nodes
• Confusing default bool value as true
• Misreading array initialization behavior

4. Identify the error in the following TrieNode class code and select the fix:

public class TrieNode {
    public TrieNode[] children;
    public bool isEndOfWord;

    public TrieNode() {
        children = new TrieNode[25];
        isEndOfWord = false;
    }
}

medium

A. Remove constructor and initialize fields inline

B. Change array size from 25 to 26 to cover all lowercase letters

C. Declare children as List<TrieNode> instead of array

D. Initialize isEndOfWord to true in constructor

Solution

1. Step 1: Check children array size

   For 26 lowercase English letters, children array must be size 26, not 25.

2. Step 2: Evaluate other options

   isEndOfWord should start false; List is optional but not required; constructor is fine.

3. Final Answer:

   Change array size from 25 to 26 to cover all lowercase letters -> Option B

4. Quick Check:

   Children array size must be 26 [OK]

Hint: Children array size must match alphabet count (26) [OK]

Common Mistakes:

• Using wrong array size causing index errors
• Setting isEndOfWord true by default
• Unnecessarily changing data structure type

5. You want to design a TrieNode class that supports both lowercase and uppercase English letters (52 total). Which is the best way to initialize the children array in C#?

hard

A. public Dictionary children = new Dictionary(); // dynamic keys for all letters

B. public TrieNode[] children = new TrieNode[26]; // only lowercase letters supported

C. public TrieNode[] children = new TrieNode[52]; // index 0-25 for 'a'-'z', 26-51 for 'A'-'Z'

D. public List<TrieNode> children = new List<TrieNode>(52); // list with capacity 52

Solution

1. Step 1: Consider fixed array size for 52 letters

   Using a fixed array of size 52 is possible but requires careful indexing and is error-prone.

2. Step 2: Evaluate dynamic dictionary approach

   A Dictionary with char keys allows flexible, clear mapping for both uppercase and lowercase letters without manual indexing.

3. Final Answer:

   public Dictionary children = new Dictionary(); // dynamic keys for all letters -> Option A

4. Quick Check:

   Dictionary best for mixed case letters [OK]

Hint: Use Dictionary for mixed letter sets [OK]

Common Mistakes:

• Using fixed array without clear indexing for uppercase
• Using List without key mapping
• Ignoring uppercase letters support