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

Time Complexity: Autocomplete System with Trie

O(m)

Understanding Time Complexity

We want to know how fast the autocomplete system finds suggestions as we type more letters.

How does the time to get suggestions grow when the input or dictionary size changes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class TrieNode {
  constructor() {
    this.children = {};
    this.isWord = false;
  }
}

class Trie {
  constructor() {
    this.root = new TrieNode();
  }

  insert(word) {
    let node = this.root;
    for (const char of word) {
      if (!node.children[char]) node.children[char] = new TrieNode();
      node = node.children[char];
    }
    node.isWord = true;
  }

  searchPrefix(prefix) {
    let node = this.root;
    for (const char of prefix) {
      if (!node.children[char]) return null;
      node = node.children[char];
    }
    return node;
  }
}
    

This code builds a trie and finds the node matching a prefix to start autocomplete suggestions.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each character of the input word or prefix.
• How many times: Once per character in the word or prefix (length m).
• Autocomplete suggestions may involve traversing nodes below the prefix node, but this snippet focuses on prefix search.

How Execution Grows With Input

Time grows with the length of the prefix typed, not the total number of words stored.

Input Size (prefix length m)	Approx. Operations
3	3 steps to follow nodes
5	5 steps to follow nodes
10	10 steps to follow nodes

Pattern observation: The time increases linearly with prefix length, independent of dictionary size.

Final Time Complexity

Time Complexity: O(m)

This means the search time grows only with how many letters you type, not 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 nodes for the prefix letters, so it depends on prefix length, not dictionary size.

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 added a step to collect all words below the prefix node? How would that affect time complexity?"

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 quick prefix-based searches.

2. Step 2: Relate Trie to autocomplete functionality

   Autocomplete needs to find all words starting with a given prefix efficiently, which Trie supports by traversing nodes matching the prefix.

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 matching, perfect for autocomplete [OK]

Common Mistakes:

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

2. Which of the following is the correct way to insert a word "cat" into a Trie node in JavaScript?

easy

A. node.children.push('c');

B. node.children['c'] = new TrieNode();

C. node['c'] = 'cat';

D. node.add('cat');

Solution

1. Step 1: Understand Trie node structure

   Each Trie node has a children object mapping characters to child nodes, so to insert 'c', we assign a new TrieNode to node.children['c'].

2. Step 2: Check each option's correctness

   node.children['c'] = new TrieNode(); correctly assigns a new TrieNode to the character key. Options B, C, and D do not follow the standard Trie insertion method.

3. Final Answer:

   node.children['c'] = new TrieNode(); -> Option B

4. Quick Check:

   Insert char by assigning new TrieNode in children map [OK]

Hint: Use children map with character keys for Trie insertion [OK]

Common Mistakes:

• Using array push instead of map assignment
• Assigning string instead of TrieNode
• Calling undefined add method

3. Given the following code snippet for searching words with prefix "app" in a Trie, what will be the output?

const trie = new Trie();
trie.insert("apple");
trie.insert("app");
trie.insert("application");
const results = trie.searchPrefix("app");
console.log(results);

medium

A. ["apple", "application"]

B. ["app"]

C. []

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

Solution

1. Step 1: Insert words into Trie

   Words "apple", "app", and "application" are inserted, so all prefixes starting with "app" exist in the Trie.

2. Step 2: Search for prefix "app"

   The searchPrefix method returns all words starting with "app", which includes all three inserted words.

3. Final Answer:

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

4. Quick Check:

   All words with prefix "app" returned [OK]

Hint: Search prefix returns all words starting with it [OK]

Common Mistakes:

• Expecting only exact matches
• Ignoring shorter word "app" itself
• Assuming empty result if prefix is a word

4. The following code tries to insert words into a Trie but throws an error. What is the bug?

class TrieNode {
  constructor() {
    this.children = [];
    this.isEnd = false;
  }
}

class Trie {
  constructor() {
    this.root = new TrieNode();
  }
  insert(word) {
    let node = this.root;
    for (let char of word) {
      if (!node.children[char]) {
        node.children[char] = new TrieNode();
      }
      node = node.children[char];
    }
    node.isEnd = true;
  }
}

const trie = new Trie();
trie.insert("dog");

medium

A. children should be an object, not an array

B. isEnd should be initialized to true

C. Missing return statement in insert method

D. for loop should use index instead of for-of

Solution

1. Step 1: Analyze children data structure

   children is initialized as an empty array, but characters are used as keys, which are strings, not numeric indices.

2. Step 2: Identify correct data structure for children

   children should be an object (map) to use string keys like 'd', 'o', 'g'. Using array causes undefined behavior and errors.

3. Final Answer:

   children should be an object, not an array -> Option A

4. Quick Check:

   Use object for children keys [OK]

Hint: Use object for children to map chars, not array [OK]

Common Mistakes:

• Using array for children with string keys
• Setting isEnd incorrectly
• Thinking loop type causes error

5. You want to build an autocomplete system that returns the top 2 most frequent words starting with a prefix. Which modification to a Trie node helps achieve this efficiently?

hard

A. Use an array instead of object for children

B. Store only the full words at leaf nodes

C. Store a frequency count and maintain a sorted list of top words at each node

D. Store the entire dictionary at each node

Solution

1. Step 1: Understand requirement for top frequent words

   To quickly return top 2 frequent words for any prefix, each node should track frequency info and top words under it.

2. Step 2: Choose data structure modification

   Storing frequency counts and maintaining a sorted list of top words at each node allows fast retrieval without full traversal.

3. Final Answer:

   Store a frequency count and maintain a sorted list of top words at each node -> Option C

4. Quick Check:

   Frequency + top words per node = efficient autocomplete [OK]

Hint: Keep top words and frequencies at nodes for fast autocomplete [OK]

Common Mistakes:

• Storing full dictionary at each node wastes memory
• Using arrays for children slows lookup
• Ignoring frequency info for ranking