Trie vs Hash Map for Prefix Matching in DSA Javascript - Complexity Comparison

Time Complexity: Trie vs Hash Map for Prefix Matching

O(m) for trie search, O(n x m) for hash map search

Understanding Time Complexity

We want to compare how fast tries and hash maps find words starting with a prefix.

How does the time to find matches grow as we add more words or longer prefixes?

Scenario Under Consideration

Analyze the time complexity of prefix search using a trie and a hash map.

// Trie prefix search
function trieSearch(root, prefix) {
  let node = root;
  for (const char of prefix) {
    if (!node.children[char]) return [];
    node = node.children[char];
  }
  return collectWords(node);
}

// Hash map prefix search
function hashMapSearch(words, prefix) {
  return words.filter(word => word.startsWith(prefix));
}
    

The trie search walks down nodes for each prefix letter. The hash map search checks every word.

Identify Repeating Operations

Look at what repeats most in each method.

• Trie search primary operation: Loop over prefix letters to go down trie nodes.
• Trie search times: Once per prefix letter (length m).
• Hash map search primary operation: Loop over all words to check prefix.
• Hash map search times: Once per word (n words), each check up to prefix length m.

How Execution Grows With Input

How does work grow as input grows?

Input Size (n words)	Trie Search (prefix length m=3)	Hash Map Search (prefix length m=3)
10	3 steps down trie	10 words x 3 chars = 30 checks
100	3 steps down trie	100 words x 3 chars = 300 checks
1000	3 steps down trie	1000 words x 3 chars = 3000 checks

Trie search time depends only on prefix length, stays small as words grow.

Hash map search time grows linearly with number of words times prefix length.

Final Time Complexity

Time Complexity: O(m) for trie search, O(n x m) for hash map search

Trie search time grows with prefix length only, hash map search grows with total words and prefix length.

Common Mistake

[X] Wrong: "Hash map search is always faster because hash maps are quick."

[OK] Correct: Hash maps are fast for exact keys, but prefix search needs checking many words, so it slows down as word list grows.

Interview Connect

Understanding these differences helps you choose the right tool for prefix search tasks in real projects.

Self-Check

What if we stored all prefixes in the hash map as keys? How would that change the time complexity?

Practice

1. Which data structure is generally more efficient for prefix matching in a large set of strings?

easy

A. Linked List, because it allows sequential access

B. Hash Map, because it stores keys with constant time lookup

C. Array, because it stores elements in order

D. Trie, because it stores prefixes explicitly and allows fast prefix search

Solution

1. Step 1: Understand prefix matching requirement

   Prefix matching means finding all strings that start with a given prefix efficiently.

2. Step 2: Compare Trie and Hash Map for prefix search

   Trie stores prefixes explicitly, allowing quick traversal to all words with that prefix. Hash Map does not store prefixes, so it requires checking all keys or additional structures.

3. Final Answer:

   Trie, because it stores prefixes explicitly and allows fast prefix search -> Option D

4. Quick Check:

   Prefix search = Trie [OK]

Hint: Trie stores prefixes explicitly, ideal for prefix search [OK]

Common Mistakes:

• Thinking hash map can do prefix search directly
• Confusing prefix matching with exact key lookup
• Assuming arrays or linked lists are efficient for prefix search

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

easy

A. if (prefix in trieNode) { ... }

B. if (trieNode.hasOwnProperty(prefix)) { ... }

C. if (trieNode[prefix]) { ... }

D. if (trieNode.contains(prefix)) { ... }

Solution

1. Step 1: Understand how to check keys in JavaScript objects

   The 'in' operator checks if a property exists in an object or its prototype chain.

2. Step 2: Compare options for checking prefix in Trie node

   if (prefix in trieNode) { ... } uses 'prefix in trieNode', which correctly checks if the prefix key exists. if (trieNode.hasOwnProperty(prefix)) { ... } uses hasOwnProperty which is valid but less common for prefix check. if (trieNode[prefix]) { ... } checks truthiness which can fail if value is falsy. if (trieNode.contains(prefix)) { ... } uses a non-existent method.

3. Final Answer:

   if (prefix in trieNode) { ... } -> Option A

4. Quick Check:

   Use 'in' operator to check keys [OK]

Hint: Use 'in' operator to check keys in objects [OK]

Common Mistakes:

• Using non-existent 'contains' method
• Checking property truthiness instead of existence
• Confusing hasOwnProperty with 'in' operator

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

const trie = {};
function insert(word) {
  let node = trie;
  for (const char of word) {
    if (!(char in node)) node[char] = {};
    node = node[char];
  }
  node.isEnd = true;
}

insert('cat');
insert('car');
insert('dog');

console.log('c' in trie, 'a' in trie['c'], 't' in trie['c']['a'], trie['c']['a']['t'].isEnd);

medium

A. true true true true

B. true true false undefined

C. true false false undefined

D. false false false undefined

Solution

1. Step 1: Trace insertions of words into the trie

   Inserting 'cat' creates nodes c -> a -> t with isEnd true at 't'. Inserting 'car' adds r under c -> a. Inserting 'dog' adds d -> o -> g separately.

2. Step 2: Check existence of keys and isEnd property

   'c' exists in trie, 'a' exists under 'c', 't' exists under 'a', and 't' node has isEnd true from 'cat' insertion.

3. Final Answer:

   true true true true -> Option A

4. Quick Check:

   All keys and isEnd exist as expected [OK]

Hint: Trace each insertion step-by-step [OK]

Common Mistakes:

• Assuming 't' node missing after insertions
• Confusing isEnd property placement
• Not updating node reference inside loop

4. The following code attempts to check if a prefix exists in a Trie but does not work correctly. What is the bug?

function startsWith(trie, prefix) {
  let node = trie;
  for (const char of prefix) {
    if (!node[char]) return false;
    node = node[char];
  }
  return true;
}

medium

A. It incorrectly returns false if a node exists but is falsy

B. It does not check if the prefix is a complete word

C. It should use 'char in node' instead of '!node[char]'

D. It does not handle empty prefix input

Solution

1. Step 1: Analyze the condition '!node[char]'

   This condition fails if node[char] exists but is falsy (like an empty object or false), causing incorrect false return.

2. Step 2: Suggest correct key existence check

   Using 'char in node' correctly checks if the key exists regardless of value truthiness.

3. Final Answer:

   It should use 'char in node' instead of '!node[char]' -> Option C

4. Quick Check:

   Use 'in' operator to check keys, not truthiness [OK]

Hint: Check key existence with 'in', not truthiness [OK]

Common Mistakes:

• Using falsy check instead of key existence
• Confusing prefix existence with complete word check
• Ignoring empty prefix edge case

5. You want to implement a prefix search that returns all words starting with a given prefix from a large dictionary. Which approach is best and why?

// Approach 1: Use a Hash Map storing all words as keys
// Approach 2: Use a Trie storing words character by character
// Approach 3: Use an array and filter words by prefix
// Approach 4: Use a sorted array and binary search for prefix

hard

A. Approach 4, because binary search on sorted array quickly finds prefix range

B. Approach 2, because Trie allows efficient prefix traversal and retrieval

C. Approach 3, because filtering arrays is simple and fast for large data

D. Approach 1, because Hash Map has constant time lookup for prefixes

Solution

1. Step 1: Evaluate each approach for prefix search

   Hash Map (Approach 1) cannot do prefix search efficiently as keys are exact. Array filter (Approach 3) is slow for large data. Sorted array with binary search (Approach 4) helps but retrieving all matches requires scanning range.

2. Step 2: Understand Trie advantages

   Trie (Approach 2) stores prefixes explicitly, allowing fast traversal to all words sharing the prefix, making it best for prefix search in large datasets.

3. Final Answer:

   Approach 2, because Trie allows efficient prefix traversal and retrieval -> Option B

4. Quick Check:

   Prefix search efficiency = Trie [OK]

Hint: Trie stores prefixes explicitly, best for prefix search [OK]

Common Mistakes:

• Assuming hash map supports prefix search
• Ignoring performance cost of filtering large arrays
• Overestimating binary search for prefix retrieval