Trie Search Operation in DSA Javascript - Time & Space Complexity

Time Complexity: Trie Search Operation

O(m)

Understanding Time Complexity

We want to understand how long it takes to find a word in a trie. This helps us know how fast searches are as words get longer.

The question is: How does search time grow when the word length changes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function search(root, word) {
  let node = root;
  for (let char of word) {
    if (!node.children[char]) {
      return false;
    }
    node = node.children[char];
  }
  return node.isEndOfWord === true;
}
    

This code checks if a word exists in a trie by moving through nodes for each letter.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each character of the word.
• How many times: Once for every letter in the word (word length).

How Execution Grows With Input

As the word gets longer, the search checks more letters one by one.

Input Size (word length)	Approx. Operations
10	10 checks
100	100 checks
1000	1000 checks

Pattern observation: The number of steps grows directly with the word length.

Final Time Complexity

Time Complexity: O(m)

This means the search time grows linearly with the length of the word being searched.

Common Mistake

[X] Wrong: "Searching a word in a trie takes time proportional to the number of words stored."

[OK] Correct: The search depends only on the length of the word, not how many words are in the trie.

Interview Connect

Knowing trie search time helps you explain why tries are fast for prefix searches and autocomplete features. This skill shows you understand efficient word lookups.

Self-Check

"What if the trie stored words with very long common prefixes? How would that affect the search time complexity?"

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