Word Search in Trie in DSA C# - Time & Space Complexity

Time Complexity: Word Search in Trie

O(m)

Understanding Time Complexity

We want to understand how long it takes to find a word in a Trie data structure.

How does the search time change as the word length or Trie size grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public bool Search(string word) {
    TrieNode current = root;
    foreach (char c in word) {
        if (!current.Children.ContainsKey(c)) {
            return false;
        }
        current = current.Children[c];
    }
    return current.IsEndOfWord;
}
    

This code checks if a given word exists in the Trie by following each character step-by-step.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each character of the word.
• How many times: Exactly once per character in the word (word length).

How Execution Grows With Input

As the word gets longer, the search checks more characters one by one.

Input Size (word length)	Approx. Operations
10	10 character checks
100	100 character checks
1000	1000 character checks

Pattern observation: The number of operations grows directly with the word length.

Final Time Complexity

Time Complexity: O(m)

This means the search time grows linearly with the length of the word being searched.

Common Mistake

[X] Wrong: "Searching a word depends on the total number of words in the Trie."

[OK] Correct: The search only follows the characters of the word, so it depends on word length, not how many words are stored.

Interview Connect

Knowing how Trie search scales helps you explain efficient word lookups clearly and confidently in interviews.

Self-Check

"What if we changed the search to find all words with a given prefix? How would the time complexity change?"

Practice

1. What is the main purpose of using a Trie data structure in word search problems?

easy

A. To efficiently store and search words by their prefixes

B. To sort words alphabetically

C. To store words in a linked list

D. To perform arithmetic operations on words

Solution

1. Step 1: Understand Trie structure

   A Trie stores characters of words in a tree-like structure where each node represents a character.

2. Step 2: Identify Trie usage in word search

   It allows quick prefix-based search, making it efficient to find words starting with given letters.

3. Final Answer:

   To efficiently store and search words by their prefixes -> Option A

4. Quick Check:

   Trie = prefix search [OK]

Hint: Trie is best for prefix-based word searches [OK]

Common Mistakes:

• Confusing Trie with sorting structures
• Thinking Trie stores words linearly
• Assuming Trie is for arithmetic

2. Which of the following is the correct way to declare a Trie node class in C#?

easy

A. public class TrieNode { public Dictionary Children = new Dictionary(); public bool IsWordEnd = false; }

B. public class TrieNode { public List<int> Children; public bool IsWordEnd; }

C. public class TrieNode { public string Children; public int IsWordEnd; }

D. public class TrieNode { public int Children; public bool IsWordEnd; }

Solution

1. Step 1: Check data types for children

   Trie children should map characters to TrieNode objects, so Dictionary is correct.

2. Step 2: Check word end marker

   Boolean flag IsWordEnd indicates if node ends a word, so bool is correct type.

3. Final Answer:

   public class TrieNode { public Dictionary Children = new Dictionary(); public bool IsWordEnd = false; } -> Option A

4. Quick Check:

   Children dictionary + bool flag = public class TrieNode { public Dictionary Children = new Dictionary(); public bool IsWordEnd = false; } [OK]

Hint: Trie node children map chars to nodes with bool end flag [OK]

Common Mistakes:

• Using List<int> instead of Dictionary
• Using string or int for children
• Using int instead of bool for IsWordEnd

3. Given the following C# code snippet for searching a word in a Trie, what will be the output?

Trie trie = new Trie();
trie.Insert("cat");
trie.Insert("car");
trie.Insert("dog");

bool result = trie.Search("cap");
Console.WriteLine(result);

medium

A. True

B. False

C. Compilation error

D. Runtime exception

Solution

1. Step 1: Understand inserted words

   Words "cat", "car", and "dog" are inserted into the Trie.

2. Step 2: Search for "cap"

   "cap" shares prefix "ca" but 'p' is not inserted after 'a', so search returns false.

3. Final Answer:

   False -> Option B

4. Quick Check:

   Word not found = False [OK]

Hint: Search returns false if full word path missing [OK]

Common Mistakes:

• Assuming prefix match means word found
• Expecting true for partial matches
• Confusing compilation/runtime errors

4. Identify the error in the following C# Trie search method:

public bool Search(string word) {
    TrieNode node = root;
    foreach (char c in word) {
        if (!node.Children.ContainsKey(c))
            return false;
        node = node.Children[c];
    }
    return true;
}

medium

A. It does not check for null root

B. It throws NullReferenceException if word is empty

C. It returns true even if the word is only a prefix, not a complete word

D. It uses wrong data type for node

Solution

1. Step 1: Analyze search logic

   The method checks if all characters exist in Trie nodes but does not check if last node marks end of a word.

2. Step 2: Identify missing condition

   Without checking node.IsWordEnd, it returns true for prefixes that are not complete words.

3. Final Answer:

   It returns true even if the word is only a prefix, not a complete word -> Option C

4. Quick Check:

   Missing IsWordEnd check = It returns true even if the word is only a prefix, not a complete word [OK]

Hint: Always check IsWordEnd after traversal [OK]

Common Mistakes:

• Ignoring IsWordEnd flag
• Assuming prefix means word found
• Not handling empty strings

5. You want to find all words in a Trie that start with the prefix "pre". Which approach correctly uses the Trie to achieve this?

hard

A. Use a hash set to store all words and filter those starting with "pre"

B. Search each word in the Trie individually to check if it starts with "pre"

C. Insert all words starting with "pre" into a new Trie and search there

D. Traverse the Trie to the node representing 'e' in "pre", then perform a DFS to collect all words below

Solution

1. Step 1: Locate prefix node in Trie

   Traverse characters 'p', 'r', 'e' to reach the node representing last prefix character.

2. Step 2: Collect words using DFS

   From this node, perform depth-first search to find all complete words that start with "pre".

3. Final Answer:

   Traverse the Trie to the node representing 'e' in "pre", then perform a DFS to collect all words below -> Option D

4. Quick Check:

   Prefix node + DFS = Traverse the Trie to the node representing 'e' in "pre", then perform a DFS to collect all words below [OK]

Hint: Find prefix node, then DFS for words [OK]

Common Mistakes:

• Checking all words individually
• Using unrelated data structures
• Rebuilding Trie unnecessarily