Trie vs Hash Map for Prefix Matching in DSA Javascript - Key Differences

Recall & Review

beginner

What is a Trie data structure?

A Trie is a tree-like data structure that stores strings by sharing common prefixes. Each node represents a character, and paths from root to nodes form words.

beginner

How does a Hash Map store data for prefix matching?

A Hash Map stores key-value pairs where keys are usually full strings. It does not inherently support prefix search, so prefix matching requires checking keys manually or storing prefixes as keys.

intermediate

Why is Trie more efficient than Hash Map for prefix matching?

Trie allows direct traversal along characters of the prefix, making prefix search fast and efficient. Hash Map requires checking all keys or storing all prefixes, which is slower and uses more space.

intermediate

What is a downside of using Trie compared to Hash Map?

Trie can use more memory because it stores nodes for each character, even if some prefixes are rare. Hash Map uses memory only for stored keys but is slower for prefix queries.

intermediate

In what scenario is Hash Map preferred over Trie for prefix matching?

When the dataset is small or prefix queries are rare, Hash Map is simpler and uses less memory. Also, if only exact matches are needed, Hash Map is faster and easier to implement.

Which data structure is designed to efficiently support prefix matching?

A Stack

B Hash Map

C Trie

D Queue

Trie stores characters in a tree structure allowing fast prefix traversal.

What is a main disadvantage of using a Hash Map for prefix matching?

A No key-value pairs

B High memory usage for prefixes

C Cannot store strings

D Slow prefix search

Hash Map does not support prefix search natively, making it slow for that purpose.

Which data structure uses more memory due to storing nodes for each character?

A Trie

B Array

C Hash Map

D Linked List

Trie stores nodes for every character, which can increase memory usage.

When is Hash Map preferred over Trie?

A When only exact matches are needed

B When prefix queries are frequent

C When dataset is large

D When memory is unlimited

Hash Map is simpler and faster for exact matches without prefix queries.

What does each node in a Trie represent?

A A full word

B A character

C A number

D A key-value pair

Each node in a Trie represents a single character.

Explain how a Trie supports prefix matching compared to a Hash Map.

Think about how each data structure stores and searches strings.

List advantages and disadvantages of using Trie versus Hash Map for prefix matching.

Consider speed and memory trade-offs.

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