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

Time Complexity: Autocomplete System with Trie

O(m)

Understanding Time Complexity

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

The question is: how does the time to find words grow as we add more words or type longer prefixes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class TrieNode {
  children: Map = new Map();
  isWord: boolean = false;
}

function searchPrefix(root: TrieNode, prefix: string): TrieNode | null {
  let node = root;
  for (const char of prefix) {
    if (!node.children.has(char)) return null;
    node = node.children.get(char)!;
  }
  return node;
}
    

This code finds the node in the trie that matches the given prefix, if it exists.

Identify Repeating Operations

• Primary operation: Looping over each character in the prefix string.
• How many times: Exactly once per character in the prefix (length m).

How Execution Grows With Input

As the prefix length grows, the search takes longer, but it does not depend on the total number of words stored.

Input Size (prefix length m)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: The time grows linearly with the prefix length, not with the number of stored words.

Final Time Complexity

Time Complexity: O(m)

This means the search time grows only with how long the prefix is, regardless of how many words are stored.

Common Mistake

[X] Wrong: "The search time depends on the total number of words stored in the trie."

[OK] Correct: The search only follows the prefix characters, so it depends on prefix length, not total words.

Interview Connect

Understanding this helps you explain why tries are efficient for autocomplete, showing you know how data structure choice affects speed.

Self-Check

"What if we also count the time to collect all words under the prefix node? How would the time complexity change?"

Practice

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

easy

A. To efficiently store and search prefixes of words

B. To sort words alphabetically

C. To count the frequency of words

D. To encrypt the stored words

Solution

1. Step 1: Understand the role of Trie in prefix search

   A Trie is a tree-like data structure designed to store strings by their prefixes, allowing fast prefix-based searches.

2. Step 2: Connect Trie usage to autocomplete

   Autocomplete requires quick lookup of words starting with a given prefix, which Trie supports efficiently.

3. Final Answer:

   To efficiently store and search prefixes of words -> Option A

4. Quick Check:

   Trie = prefix search [OK]

Hint: Trie is built for prefix-based fast search [OK]

Common Mistakes:

• Confusing Trie with sorting algorithms
• Thinking Trie encrypts data
• Assuming Trie counts word frequency only

2. Which of the following is the correct TypeScript syntax to define a Trie node with children as a Map of characters to Trie nodes?

easy

A. class TrieNode { children: Array<string> = []; isEnd: boolean = false; }

B. class TrieNode { children: Map = new Map(); isEnd: boolean = false; }

C. class TrieNode { children: string[] = []; isEnd: boolean = true; }

D. class TrieNode { children: Map = new Map(); isEnd: boolean = false; }

Solution

1. Step 1: Identify correct data type for children

   Children should map characters (string) to TrieNode objects, so Map is correct.

2. Step 2: Check initialization and isEnd flag

   Children initialized as new Map(), and isEnd defaults to false indicating not end of word initially.

3. Final Answer:

   class TrieNode { children: Map = new Map(); isEnd: boolean = false; } -> Option B

4. Quick Check:

   Map for children [OK]

Hint: Children map chars to nodes using Map [OK]

Common Mistakes:

• Using array instead of Map for children
• Using number keys instead of string keys
• Setting isEnd to true by default

3. Given the following TypeScript code snippet for inserting words into a Trie and searching for prefix suggestions, what will be the output of autocomplete.getSuggestions('ca')?

class TrieNode {
  children: Map = new Map();
  isEnd: boolean = false;
}

class AutocompleteSystem {
  root: TrieNode = new TrieNode();

  insert(word: string) {
    let node = this.root;
    for (const char of word) {
      if (!node.children.has(char)) {
        node.children.set(char, new TrieNode());
      }
      node = node.children.get(char)!;
    }
    node.isEnd = true;
  }

  getSuggestions(prefix: string): string[] {
    let node = this.root;
    for (const char of prefix) {
      if (!node.children.has(char)) return [];
      node = node.children.get(char)!;
    }
    const results: string[] = [];
    const dfs = (currNode: TrieNode, path: string) => {
      if (currNode.isEnd) results.push(path);
      for (const [ch, nextNode] of currNode.children) {
        dfs(nextNode, path + ch);
      }
    };
    dfs(node, prefix);
    return results;
  }
}

const autocomplete = new AutocompleteSystem();
autocomplete.insert('cat');
autocomplete.insert('car');
autocomplete.insert('cap');
autocomplete.insert('dog');
console.log(autocomplete.getSuggestions('ca'));

medium

A. ["cat", "car"]

B. ["dog"]

C. []

D. ["cat", "car", "cap"]

Solution

1. Step 1: Insert words and traverse prefix 'ca'

   Words 'cat', 'car', 'cap' are inserted. Searching prefix 'ca' finds node with children 't', 'r', 'p'.

2. Step 2: DFS collects all words starting with 'ca'

   DFS from 'ca' node collects 'cat', 'car', and 'cap' as all end nodes under that prefix.

3. Final Answer:

   ["cat", "car", "cap"] -> Option D

4. Quick Check:

   Prefix 'ca' matches cat, car, cap [OK]

Hint: DFS from prefix node collects all words [OK]

Common Mistakes:

• Returning empty list if prefix found
• Returning unrelated words like 'dog'
• Missing one or more words starting with prefix

4. The following TypeScript code for the insert method in a Trie has a bug. What is the bug?

insert(word: string) {
  let node = this.root;
  for (const char of word) {
    if (!node.children.has(char)) {
      node.children.set(char, new TrieNode());
    }
    node = node.children.get(char);
  }
  node.isEnd = true;
}

medium

A. Missing non-null assertion operator (!) when getting child node

B. Children map should be an array, not Map

C. isEnd should be set to false, not true

D. Loop should iterate over indices, not characters

Solution

1. Step 1: Identify potential null or undefined access

   node.children.get(char) can return undefined if key missing, so TypeScript requires non-null assertion or check.

2. Step 2: Fix by adding non-null assertion operator

   Adding '!' after get(char) tells TypeScript the value is not undefined, fixing the bug.

3. Final Answer:

   Missing non-null assertion operator (!) when getting child node -> Option A

4. Quick Check:

   Use get(char)! to avoid undefined [OK]

Hint: Use '!' after get() to assure non-null [OK]

Common Mistakes:

• Ignoring TypeScript undefined error
• Changing data structure unnecessarily
• Setting isEnd incorrectly

5. You want to extend the autocomplete system to return suggestions sorted by their frequency of insertion (most frequent first). Which data structure modification is best to support this efficiently?

hard

A. Store all words in a separate array and sort on each query

B. Use a binary search tree instead of a Trie

C. Add a frequency count field to each Trie node marking end of word

D. Remove the isEnd flag and rely on children count

Solution

1. Step 1: Understand frequency tracking in Trie

   Adding a frequency count to nodes marking word ends allows tracking how often each word was inserted.

2. Step 2: Use frequency to sort suggestions efficiently

   During DFS for suggestions, use frequency counts to sort or prioritize words without extra data structures.

3. Final Answer:

   Add a frequency count field to each Trie node marking end of word -> Option C

4. Quick Check:

   Frequency field in Trie nodes enables sorting [OK]

Hint: Track frequency in nodes to sort suggestions fast [OK]

Common Mistakes:

• Sorting all words on each query (slow)
• Replacing Trie with BST loses prefix efficiency
• Removing isEnd loses word boundary info