Autocomplete System with Trie in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Trie data structure?

A Trie is a tree-like data structure that stores a dynamic set of strings, where each node represents a character. It is used to quickly find words with common prefixes.

beginner

How does a Trie help in implementing an autocomplete system?

A Trie allows fast lookup of all words that start with a given prefix by traversing nodes corresponding to the prefix characters, then collecting all descendant words.

intermediate

What is the time complexity to insert a word of length n into a Trie?

The time complexity is O(n), where n is the length of the word, because each character is inserted one by one along the path in the Trie.

intermediate

Explain how to search for all words with a given prefix in a Trie.

First, traverse the Trie nodes for each character in the prefix. If the prefix exists, perform a depth-first search from that node to collect all complete words below it.

beginner

What is a common way to store children nodes in a Trie node in JavaScript?

Children nodes are often stored in a JavaScript Map or an object where keys are characters and values are child nodes, allowing quick access to next characters.

What does each node in a Trie represent?

A A number

B A whole word

C A character of a word

D A sentence

Each node in a Trie represents a single character of a word.

What is the main advantage of using a Trie for autocomplete?

A Fast prefix search

B Uses less memory than arrays

C Sorts words automatically

D Stores only numbers

Trie allows fast search for words starting with a given prefix, which is key for autocomplete.

Which data structure is commonly used to store children in a Trie node in JavaScript?

A Stack

B Array

C Set

D Map

A Map is commonly used to store children nodes keyed by characters for quick access.

What is the time complexity to search for a prefix of length n in a Trie?

A O(n)

B O(1)

C O(n^2)

D O(log n)

Searching for a prefix of length n requires traversing n nodes, so O(n).

After finding the prefix node in a Trie, what is the next step to get autocomplete suggestions?

A Delete the prefix node

B Perform a depth-first search to collect all words

C Insert new words

D Sort the prefix node

We perform a depth-first search from the prefix node to find all complete words below it.

Describe how to build an autocomplete system using a Trie.

Think about storing words and searching by prefix.

Explain the process to find all words starting with a given prefix in a Trie.

Focus on prefix traversal and collecting words.

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