Autocomplete System with Trie in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Trie Insert and Search

What is the output of the following C# code that inserts words into a Trie and searches for a prefix?

DSA C#

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

public class Trie {
    private TrieNode root = new TrieNode();

    public void Insert(string word) {
        var node = root;
        foreach (var ch in word) {
            if (!node.Children.ContainsKey(ch)) {
                node.Children[ch] = new TrieNode();
            }
            node = node.Children[ch];
        }
        node.IsWord = true;
    }

    public bool SearchPrefix(string prefix) {
        var node = root;
        foreach (var ch in prefix) {
            if (!node.Children.ContainsKey(ch)) {
                return false;
            }
            node = node.Children[ch];
        }
        return true;
    }
}

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

Console.WriteLine(trie.SearchPrefix("ca"));
Console.WriteLine(trie.SearchPrefix("do"));
Console.WriteLine(trie.SearchPrefix("bat"));

A

True
True
False

B

True
False
False

C

False
True
False

D

False
False
True

💡 Hint

Think about whether the prefix exists in the inserted words.

The prefixes "ca" and "do" exist in the inserted words, so SearchPrefix returns true for them. "bat" does not exist, so it returns false.

🧠 Conceptual

intermediate

Understanding Trie Node Structure

Which statement correctly describes the role of the 'IsWord' boolean in a Trie node?

A It indicates if the node has any children.

B It marks the end of a complete word stored in the Trie.

C It stores the character value of the node.

D It counts how many words pass through this node.

💡 Hint

Think about how the Trie knows a word ends.

The 'IsWord' boolean is set to true when a node represents the last character of a stored word, marking the end of that word.

🔧 Debug

advanced

Find the Bug in Trie Search Method

What error will occur when running this Trie search method code snippet?

DSA C#

public bool Search(string word) {
    var node = root;
    foreach (var ch in word) {
        if (node.Children[ch] == null) {
            return false;
        }
        node = node.Children[ch];
    }
    return node.IsWord;
}

A KeyNotFoundException at node.Children[ch] if key missing

B Returns false always

C NullReferenceException at node.Children[ch] == null check

D Compiles but returns true always

💡 Hint

Check how dictionary keys are accessed safely.

Accessing a dictionary key directly without checking if it exists causes a KeyNotFoundException if the key is missing.

🚀 Application

advanced

Autocomplete Suggestions Using Trie

Given a Trie with words inserted, which method correctly collects all words starting with a given prefix?

DSA C#

public void CollectWords(TrieNode node, string prefix, List<string> results) {
    if (node.IsWord) {
        results.Add(prefix);
    }
    foreach (var child in node.Children) {
        CollectWords(child.Value, prefix + child.Key, results);
    }
}

A Traverse children but never add words to results

B Only add words when node has no children

C Add prefix to results before recursion without checking IsWord

D Recursively traverse children, adding words when IsWord is true

💡 Hint

Think about when a word is complete in the Trie.

The method adds the prefix to results only when the node marks the end of a word, then recursively explores all children to find all words starting with that prefix.

🧠 Conceptual

expert

Trie Memory Efficiency Trade-offs

Which statement best explains a memory trade-off when using a Trie for autocomplete systems?

A Tries use less memory than linked lists because they store characters in a single node.

B Tries use less memory than arrays because they store only full words without intermediate nodes.

C Tries use more memory than hash maps because they store nodes for every character, but they allow fast prefix searches.

D Tries use the same memory as hash maps but are slower for prefix searches.

💡 Hint

Consider how Tries store characters and enable prefix queries.

Tries store nodes for each character, which can consume more memory than hash maps, but they provide efficient prefix search capabilities, which hash maps do not.

Practice

1. What is the main advantage of using a Trie over a HashSet for implementing an autocomplete system?

easy

A. Trie uses less memory than HashSet for all cases

B. Trie supports prefix-based search efficiently, while HashSet requires checking all words

C. Trie is faster for exact word lookup than HashSet

D. Trie automatically sorts words alphabetically unlike HashSet

Solution

1. Step 1: Understand autocomplete requirement

   Autocomplete needs to find all words that start with a given prefix quickly.

2. Step 2: Compare Trie vs HashSet

   Trie stores characters level by level, so prefix traversal is O(prefix length). HashSet requires scanning all words to check which ones start with the prefix.

3. Final Answer:

   Trie supports prefix-based search efficiently, while HashSet requires checking all words -> Option B

4. Quick Check:

   Trie = prefix search in O(m), HashSet = O(n*m) for prefix [OK]

Hint: Trie shares common prefixes among words - natural fit for autocomplete [OK]

Common Mistakes:

• Assuming Trie always uses less memory - it can use more for sparse word sets
• Thinking exact lookup is why Trie beats HashSet - HashSet is actually faster for exact lookup
• Assuming Trie sorts automatically - it doesn't sort, traversal order depends on children insertion

2. Which C# code correctly inserts a word into a Trie node structure where each node has a Dictionary<char, TrieNode> Children and a bool IsEndOfWord?

easy

A. node.Children[c] = new TrieNode(); node = node.Children[c];

B. if (!node.Children.ContainsKey(c)) node.Children[c] = new TrieNode(); node = node.Children[c];

C. node.Children.Add(c); node = node.Children[c];

D. node.Children[c] = c; node = node.Children[c];

Solution

1. Step 1: Check if child exists

   Before creating a new node, check if the character key already exists in Children to avoid overwriting existing subtrees.

2. Step 2: Create only if missing

   Using ContainsKey check ensures we reuse existing nodes and only create new ones when the character path doesn't exist yet.

3. Final Answer:

   if (!node.Children.ContainsKey(c)) node.Children[c] = new TrieNode(); node = node.Children[c]; -> Option B

4. Quick Check:

   Always check ContainsKey before adding to avoid overwriting existing paths [OK]

Hint: Always guard with ContainsKey before inserting a new Trie node [OK]

Common Mistakes:

• Option A overwrites existing children, destroying previously inserted words
• Option C uses Add which throws if key already exists
• Option D stores char as value instead of TrieNode

3. What will the following C# Trie prefix search return when searching for prefix "ca" in a Trie containing ["cat", "car", "card", "dog"]?

List<string> results = new List<string>();
void DFS(TrieNode node, string current) {
    if (node.IsEndOfWord) results.Add(current);
    foreach (var kvp in node.Children)
        DFS(kvp.Value, current + kvp.Key);
}
TrieNode prefixNode = GetPrefixNode("ca");
if (prefixNode != null) DFS(prefixNode, "ca");

medium

A. ["cat", "car", "card", "dog"]

B. ["ca"]

C. ["cat", "car", "card"]

D. []

Solution

1. Step 1: Find prefix node

   GetPrefixNode("ca") traverses c→a and returns the node at 'a'. "dog" is unreachable from this node.

2. Step 2: DFS from prefix node

   DFS explores all children from 'a': t (cat), r (car), r→d (card). All three have IsEndOfWord=true.

3. Final Answer:

   ["cat", "car", "card"] -> Option C

4. Quick Check:

   Only words under prefix "ca" subtree are returned, "dog" excluded [OK]

Hint: DFS from prefix node returns only words in that subtree - "dog" is in a different branch [OK]

Common Mistakes:

• Including 'dog' - it's in a completely separate Trie branch
• Returning only 'ca' - 'ca' itself is not marked IsEndOfWord
• Returning empty - prefix 'ca' exists in the Trie so DFS finds words

4. Identify the bug in this C# autocomplete prefix search:

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

medium

A. Should return false when character not found, and true at the end

B. Should use a List instead of Dictionary for Children

C. Should check IsEndOfWord instead of ContainsKey

D. Should start from the last character of the prefix

Solution

1. Step 1: Trace the logic

   When a character is not found in Children, it means the prefix doesn't exist - should return false, not true. And after traversing all prefix characters successfully, the prefix exists - should return true.

2. Step 2: Identify the swap

   The return values are swapped: 'return true' and 'return false' are in each other's place.

3. Final Answer:

   Should return false when character not found, and true at the end -> Option A

4. Quick Check:

   Missing prefix char = false, full prefix traversed = true [OK]

Hint: If you can't follow the path, prefix is absent = false; if path complete = true [OK]

Common Mistakes:

• Thinking Dictionary is wrong - Dictionary is correct for Children
• Checking IsEndOfWord - StartsWith only checks if prefix path exists, not word end
• Starting from last character - prefix traversal always goes left to right

5. In a Trie-based autocomplete system with 100,000 words averaging 8 characters each, what is the time complexity to retrieve all words matching a prefix of length p, where k is the number of matching words and m is the average word length?

hard

A. O(n) where n is total number of words

B. O(p + k * m) - traverse prefix then DFS over matching words

C. O(p * n) - check prefix against each word

D. O(1) - Trie provides constant time autocomplete

Solution

1. Step 1: Cost of reaching prefix node

   Traversing p characters to reach the prefix node costs O(p).

2. Step 2: Cost of DFS to collect results

   DFS visits all nodes under the prefix subtree. With k matching words of average length m, this costs O(k * m) in the worst case.

3. Final Answer:

   O(p + k * m) -> Option B

4. Quick Check:

   Prefix traversal O(p) + result collection O(k*m) = O(p + k*m) [OK]

Hint: Trie autocomplete = prefix path O(p) + collect results O(k*m), independent of total word count n [OK]

Common Mistakes:

• O(n) - Trie doesn't scan all words, only the prefix subtree
• O(1) - result collection depends on number and length of matching words
• O(p*n) - that's the HashSet approach, not Trie