Trie Search Operation in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Trie data structure?

A Trie is a tree-like data structure used to store a dynamic set of strings where keys are usually strings. Each node represents a character, and paths from root to leaves represent words.

beginner

How does the search operation work in a Trie?

The search operation checks each character of the word in the Trie by moving from the root node through child nodes. If all characters are found and the last node marks the end of a word, the search returns true; otherwise, false.

intermediate

What does it mean if a node's 'endOfWord' flag is false during a Trie search?

It means that although the prefix exists in the Trie, the exact word being searched for does not exist as a complete word in the Trie.

intermediate

Why is Trie search efficient for prefix-based queries?

Trie search is efficient because it shares common prefixes among words, allowing quick traversal to the node representing the prefix without checking all words individually.

intermediate

What is the time complexity of searching a word in a Trie?

The time complexity is O(m), where m is the length of the word being searched, because each character is checked once along the path.

In a Trie search, what happens if a character is not found among the current node's children?

A The search returns false immediately

B The search continues to the next character

C The search restarts from the root

D The search returns true immediately

If a character is missing in the current node's children, the word cannot be in the Trie, so the search returns false immediately.

What does the 'endOfWord' flag indicate in a Trie node?

A The node is the root

B The node is a leaf node

C The node has no children

D The node marks the end of a valid word

The 'endOfWord' flag shows that the path to this node forms a complete valid word stored in the Trie.

What is the main advantage of using a Trie for searching words?

A It allows fast prefix-based search

B It compresses words

C It sorts words automatically

D It uses less memory than arrays

Trie allows fast prefix-based search by sharing common prefixes among words.

If you search for 'cat' in a Trie and find nodes for 'c' and 'a' but not 't', what is the result?

A Partial match

B True

C False

D Error

Since 't' is missing, the word 'cat' does not exist in the Trie, so the search returns false.

What is the worst-case time complexity to search a word of length m in a Trie?

A O(1)

B O(m)

C O(log m)

D O(m^2)

The search checks each character once, so the time complexity is O(m).

Explain how the Trie search operation works step-by-step for the word 'dog'.

Think about moving through nodes for each letter and checking if the word ends there.

What is the role of the 'endOfWord' flag in Trie search, and why is it important?

Consider what happens if a prefix is found but the word is not complete.

Practice

1. What does the search operation in a Trie data structure primarily check for?

easy

A. The length of the longest word in the Trie

B. If the Trie is empty

C. If a given word exists in the Trie

D. The number of words stored in the Trie

Solution

1. Step 1: Understand the purpose of Trie search

   The search operation in a Trie is designed to check if a specific word is present in the Trie by traversing nodes corresponding to each character.

2. Step 2: Identify what the search confirms

   It confirms the presence or absence of the entire word, not the count or length of words stored.

3. Final Answer:

   If a given word exists in the Trie -> Option C

4. Quick Check:

   Trie search checks word existence [OK]

Hint: Search checks full word presence in Trie nodes [OK]

Common Mistakes:

• Confusing search with counting words
• Thinking search returns word length
• Assuming search checks if Trie is empty

2. Which of the following is the correct way to check if a character node exists in a Trie during search in JavaScript?

easy

A. if (node.char !== null)

B. if (node[char] !== undefined)

C. if (node.has(char))

D. if (node.char === true)

Solution

1. Step 1: Understand Trie node structure in JavaScript

   Trie nodes are usually objects where keys are characters. Checking if a character exists uses property access and undefined check.

2. Step 2: Identify correct syntax for existence check

   Using node[char] !== undefined correctly checks if the character key exists in the node object.

3. Final Answer:

   if (node[char] !== undefined) -> Option B

4. Quick Check:

   Check node property with !== undefined [OK]

Hint: Use node[char] !== undefined to check character node [OK]

Common Mistakes:

• Using dot notation with variable char
• Using incorrect method like has() on object
• Checking for null instead of undefined

3. What will be the output of the following JavaScript code snippet?

class TrieNode {
  constructor() {
    this.children = {};
    this.isEnd = 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.isEnd = true;
  }

  search(word) {
    let node = this.root;
    for (const char of word) {
      if (!node.children[char]) return false;
      node = node.children[char];
    }
    return node.isEnd;
  }
}

const trie = new Trie();
trie.insert('cat');
trie.insert('car');
console.log(trie.search('cat'));
console.log(trie.search('cap'));

medium

A. true false

B. false true

C. true true

D. false false

Solution

1. Step 1: Insert words 'cat' and 'car' into Trie

   Both words are inserted by creating nodes for each character and marking the last node's isEnd as true.

2. Step 2: Search for 'cat' and 'cap'

   'cat' exists fully with isEnd true, so search returns true. 'cap' is missing 'p' node, so search returns false.

3. Final Answer:

   true false -> Option A

4. Quick Check:

   Search 'cat' = true, 'cap' = false [OK]

Hint: Search returns true only if full word and isEnd true [OK]

Common Mistakes:

• Assuming partial matches return true
• Not setting isEnd flag on insert
• Confusing children object access

4. Identify the bug in the following Trie search method and select the correct fix:

search(word) {
  let node = this.root;
  for (const char of word) {
    if (node.children[char] === undefined) return false;
    node = node.children[char];
  }
  return true;
}

medium

A. Use 'for (let i=0; i

B. Change '===' to '!==' in the if condition

C. Initialize node with a new TrieNode inside the method

D. Return node.isEnd instead of true at the end

Solution

1. Step 1: Analyze the search method's return value

   The method returns true after traversing all characters without checking if the last node marks the end of a word.

2. Step 2: Correct the return to check word completion

   Return node.isEnd to confirm the word ends here, not just prefix exists.

3. Final Answer:

   Return node.isEnd instead of true at the end -> Option D

4. Quick Check:

   Check isEnd flag to confirm full word [OK]

Hint: Always check isEnd flag after traversal [OK]

Common Mistakes:

• Returning true without isEnd check
• Changing comparison operator incorrectly
• Unnecessary loop syntax changes

5. Given a Trie containing the words ['apple', 'app', 'bat', 'bath'], which of the following search queries will return true? Assume the search method correctly checks for full word presence. Select the correct combination.

hard

A. search('app'), search('bat'), search('bath')

B. search('appl'), search('bat'), search('bath')

C. search('apple'), search('bat'), search('batman')

D. search('app'), search('bath'), search('batman')

Solution

1. Step 1: Identify words present in the Trie

   The Trie contains 'apple', 'app', 'bat', and 'bath'. Only these exact words return true on search.

2. Step 2: Check each option's search queries

   search('app'), search('bat'), search('bath') searches 'app', 'bat', 'bath' all present. Others include partial or missing words like 'appl' or 'batman' which return false.

3. Final Answer:

   search('app'), search('bat'), search('bath') -> Option A

4. Quick Check:

   Only full words in Trie return true [OK]

Hint: Search true only for full words inserted in Trie [OK]

Common Mistakes:

• Assuming partial words return true
• Confusing prefixes with full words
• Including words not inserted in Trie