Autocomplete System with Trie in DSA C - Time & Space Complexity

Time Complexity: Autocomplete System with Trie

O(m + k)

Understanding Time Complexity

We want to understand how fast an autocomplete system using a trie can find suggestions.

Specifically, how the time grows as the number of words and prefix length increase.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Search for all words starting with prefix in trie
void autocomplete(TrieNode* root, const char* prefix) {
    TrieNode* node = root;
    for (int i = 0; prefix[i] != '\0'; i++) {
        int index = prefix[i] - 'a';
        if (!node->children[index]) return; // prefix not found
        node = node->children[index];
    }
    printAllWordsFromNode(node, prefix);
}
    

This code finds the trie node matching the prefix, then prints all words below it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Traversing prefix characters once, then recursively visiting all descendant nodes.
• How many times: Prefix traversal runs once per character (length m), recursive calls depend on number of words sharing prefix (k).

How Execution Grows With Input

The time to find the prefix node grows linearly with prefix length (m).

Then printing all words depends on how many words share that prefix (k).

Input Size (prefix length m, words k)	Approx. Operations
m=3, k=5	~3 + 5 = 8
m=5, k=50	~5 + 50 = 55
m=10, k=500	~10 + 500 = 510

Pattern observation: Time grows linearly with prefix length and number of matching words.

Final Time Complexity

Time Complexity: O(m + k)

This means the search time grows with prefix length plus the number of words found.

Common Mistake

[X] Wrong: "Autocomplete always takes constant time because tries are fast."

[OK] Correct: The time depends on prefix length and how many words share that prefix, so it can grow with input size.

Interview Connect

Understanding this complexity helps you explain how autocomplete scales and why tries are efficient for prefix searches.

Self-Check

"What if we stored word counts at each node to limit suggestions? How would that affect time complexity?"

Practice

1. What is the main purpose of using a Trie in an autocomplete system?

easy

A. To store words in a tree structure for fast prefix search

B. To sort words alphabetically before searching

C. To store words in a linked list for sequential access

D. To compress words into a hash table for quick lookup

Solution

1. Step 1: Understand the role of Trie in autocomplete

   A Trie stores words character by character in a tree, allowing quick prefix matching.

2. Step 2: Compare with other data structures

   Linked lists and hash tables do not efficiently support prefix searches like Tries do.

3. Final Answer:

   To store words in a tree structure for fast prefix search -> Option A

4. Quick Check:

   Trie = fast prefix search [OK]

Hint: Trie = tree for prefixes, perfect for autocomplete [OK]

Common Mistakes:

• Confusing Trie with hash table
• Thinking linked list is efficient for prefix search
• Assuming sorting alone solves autocomplete

2. Which of the following is the correct way to declare a Trie node structure in C for lowercase English letters?

easy

A. typedef struct TrieNode { struct TrieNode* children[26]; int isEndOfWord; } TrieNode;

B. typedef struct TrieNode { struct TrieNode* children[52]; int isEndOfWord; } TrieNode;

C. typedef struct TrieNode { struct TrieNode* children[10]; int isEndOfWord; } TrieNode;

D. typedef struct TrieNode { struct TrieNode* children; int isEndOfWord; } TrieNode;

Solution

1. Step 1: Identify the size of children array for lowercase letters

   There are 26 lowercase English letters, so children array size should be 26.

2. Step 2: Check the structure correctness

   Each node has an array of pointers to children and a flag for end of word.

3. Final Answer:

   typedef struct TrieNode { struct TrieNode* children[26]; int isEndOfWord; } TrieNode; -> Option A

4. Quick Check:

   26 children for lowercase letters [OK]

Hint: 26 children pointers for lowercase English letters [OK]

Common Mistakes:

• Using 52 for uppercase + lowercase without clarification
• Using 10 for digits only
• Not using array for children pointers

3. Given the following code snippet inserting words into a Trie and searching for prefix "app":

insert("apple");
insert("app");
insert("application");
searchPrefix("app");

What will searchPrefix("app") return?

medium

A. ["app"]

B. ["app", "apple", "application"]

C. ["apple", "application"]

D. []

Solution

1. Step 1: Understand insertion of words

   Words "apple", "app", and "application" are inserted, all sharing prefix "app".

2. Step 2: Search prefix "app" returns all words starting with "app"

   So, it returns all three words: "app", "apple", and "application".

3. Final Answer:

   ["app", "apple", "application"] -> Option B

4. Quick Check:

   Prefix "app" matches 3 words [OK]

Hint: Prefix search returns all words starting with prefix [OK]

Common Mistakes:

• Returning only exact matches
• Missing shorter word "app"
• Returning empty list incorrectly

4. Consider this buggy C code snippet for inserting a word into a Trie:

void insert(TrieNode* root, const char* word) {
  TrieNode* node = root;
  for (int i = 0; word[i] != '\0'; i++) {
    int index = word[i] - 'a';
    if (node->children[index] == NULL) {
      node->children[index] = malloc(sizeof(TrieNode));
      memset(node->children[index], 0, sizeof(TrieNode));
    }
    node = node->children[index];
  }
  node->isEndOfWord = 1;
}

What is the main bug in this code?

medium

A. Root node is not checked for NULL

B. Index calculation is incorrect

C. isEndOfWord is set before loop

D. New nodes are not initialized after malloc

Solution

1. Step 1: Analyze malloc usage for new nodes

   malloc allocates memory but does not initialize children pointers or isEndOfWord flag.

2. Step 2: Consequence of missing initialization

   Uninitialized children pointers may cause undefined behavior during traversal or insertion.

3. Final Answer:

   New nodes are not initialized after malloc -> Option D

4. Quick Check:

   malloc needs initialization [OK]

Hint: Always initialize new Trie nodes after malloc [OK]

Common Mistakes:

• Assuming malloc zeroes memory
• Thinking index calculation is wrong
• Ignoring initialization of isEndOfWord

5. You want to extend a Trie-based autocomplete system to support case-insensitive search for English letters (both uppercase and lowercase). Which modification is the best approach?

hard

A. Store words as-is and compare characters ignoring case during search only

B. Increase children array size to 52 to store uppercase and lowercase separately

C. Convert all input words to lowercase before insertion and search, keep children array size 26

D. Use a hash map instead of array for children to store any character

Solution

1. Step 1: Consider memory and complexity

   Using 52 children doubles memory; hash map adds overhead; ignoring case only during search is inefficient.

2. Step 2: Normalize input for simplicity

   Converting all words to lowercase before insertion and search simplifies Trie structure and ensures consistent matching.

3. Final Answer:

   Convert all input words to lowercase before insertion and search, keep children array size 26 -> Option C

4. Quick Check:

   Normalize case before Trie operations [OK]

Hint: Normalize case before insert/search for simpler Trie [OK]

Common Mistakes:

• Doubling children array size unnecessarily
• Ignoring case only during search causes mismatch
• Using hash map adds complexity and overhead