Trie Node Design and Initialization in DSA C# - Time & Space Complexity

Time Complexity: Trie Node Design and Initialization

O(1)

Understanding Time Complexity

We want to understand how much work it takes to create a single node in a trie.

This helps us see how initialization cost grows when building tries.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public class TrieNode {
    public TrieNode[] Children = new TrieNode[26];
    public bool IsWordEnd = false;

    public TrieNode() {
        for (int i = 0; i < 26; i++) {
            Children[i] = null;
        }
        IsWordEnd = false;
    }
}

This code creates a trie node with 26 children slots and marks it as not ending a word.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that sets each child slot to null.
• How many times: Exactly 26 times, once for each letter slot.

How Execution Grows With Input

Each node initialization always sets 26 children slots, no matter what.

Input Size (n)	Approx. Operations
1 node	26 operations
10 nodes	260 operations
100 nodes	2600 operations

Pattern observation: The work grows linearly with the number of nodes created.

Final Time Complexity

Time Complexity: O(1)

This means creating one node always takes the same fixed amount of time, regardless of input size.

Common Mistake

[X] Wrong: "Initializing a node takes longer if the trie is bigger."

[OK] Correct: Each node is created independently with a fixed 26-slot array, so the time does not depend on trie size.

Interview Connect

Understanding this fixed cost helps you explain how tries manage memory and speed when building or searching.

Self-Check

"What if we changed the children array size from 26 to 52? How would the time complexity change?"

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