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

Time Complexity: Trie vs Hash Map for Prefix Matching

O(m) for Trie, O(n * m) for Hash Map

Understanding Time Complexity

We want to understand how fast we can find words that start with a certain prefix using two common data structures.

Which one works better as the list of words grows?

Scenario Under Consideration

Analyze the time complexity of prefix search using Trie and Hash Map.

// Trie prefix search
function trieStartsWith(root: TrieNode, prefix: string): boolean {
  let node = root;
  for (const char of prefix) {
    if (!node.children.has(char)) return false;
    node = node.children.get(char)!;
  }
  return true;
}

// Hash Map prefix search
function hashMapStartsWith(words: string[], prefix: string): boolean {
  for (const word of words) {
    if (word.startsWith(prefix)) return true;
  }
  return false;
}
    

The first checks prefix by walking down the Trie nodes. The second checks each word in the list one by one.

Identify Repeating Operations

Look at what repeats most in each method.

• Trie: Loop over prefix characters once.
• Hash Map: Loop over all words, then loop over prefix characters inside startsWith.
• Dominant operation: Hash Map loops over all words, which grows with number of words.

How Execution Grows With Input

Compare how work grows as we add more words or longer prefixes.

Input Size (words n)	Trie Operations	Hash Map Operations
10	Check prefix length (m) steps, e.g. 3	Check up to 10 words * prefix length
100	Still check prefix length (m) steps	Check up to 100 words * prefix length
1000	Still check prefix length (m) steps	Check up to 1000 words * prefix length

Pattern observation: Trie time depends mostly on prefix length, not number of words. Hash Map time grows with number of words.

Final Time Complexity

Time Complexity: O(m) for Trie, O(n * m) for Hash Map

Trie searches quickly by prefix length only. Hash Map checks every word, so it gets slower as word list grows.

Common Mistake

[X] Wrong: "Hash Map prefix search is always faster because hash lookups are quick."

[OK] Correct: Hash Map here stores full words, so prefix search still checks many words one by one, making it slower as list grows.

Interview Connect

Understanding these differences helps you choose the right tool for prefix search tasks, a common problem in coding interviews and real apps.

Self-Check

What if we stored all prefixes in the Hash Map instead of full words? 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. Trie, because it stores prefixes explicitly and allows fast prefix queries

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

C. Array, because it stores elements in order

D. Linked List, because it allows sequential access

Solution

1. Step 1: Understand prefix matching requirements

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

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

   Trie stores prefixes explicitly in its structure, allowing quick traversal to all words sharing a prefix. Hash Map only allows exact key lookups, not prefix searches.

3. Final Answer:

   Trie, because it stores prefixes explicitly and allows fast prefix queries -> Option A

4. Quick Check:

   Prefix matching = Trie [OK]

Hint: Trie stores prefixes; Hash Map does not support prefix search [OK]

Common Mistakes:

• Thinking Hash Map supports prefix search efficiently
• Confusing prefix matching with exact key lookup
• Assuming arrays or linked lists are efficient for prefix queries

2. Which of the following TypeScript code snippets correctly initializes a Trie node for prefix matching?

easy

A. class TrieNode { children: object = {}; isEnd: number = 0; }

B. class TrieNode { children: string[] = []; isEnd: boolean = true; }

C. class TrieNode { children: Map = new Map(); isEnd: boolean = false; }

D. class TrieNode { children: Map = new Map(); isEnd: boolean = false; }

Solution

1. Step 1: Identify correct data types for TrieNode properties

   Children should map characters (string) to TrieNode objects. isEnd should be boolean to mark word end.

2. Step 2: Check each option's correctness

   class TrieNode { children: Map = new Map(); isEnd: boolean = false; } uses Map and boolean isEnd, which is correct. Others use wrong types or incorrect isEnd values.

3. Final Answer:

   class TrieNode { children: Map = new Map(); isEnd: boolean = false; } -> Option C

4. Quick Check:

   TrieNode children = Map [OK]

Hint: Trie children map chars to nodes; isEnd is boolean [OK]

Common Mistakes:

• Using array instead of Map for children
• Setting isEnd as number instead of boolean
• Mapping children with wrong key or value types

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

const map = new Map();
map.set('app', true);
map.set('apple', true);
console.log(map.has('app'));
console.log(map.has('appl'));

medium

A. false\ntrue

B. true\ntrue

C. false\nfalse

D. true\nfalse

Solution

1. Step 1: Understand Map key lookups

   Map.has(key) returns true only if exact key exists. 'app' and 'apple' are keys, 'appl' is not.

2. Step 2: Evaluate console.log outputs

   map.has('app') is true; map.has('appl') is false because 'appl' is not a key.

3. Final Answer:

   true\nfalse -> Option D

4. Quick Check:

   Exact keys only: 'app' true, 'appl' false [OK]

Hint: Map.has checks exact keys, not prefixes [OK]

Common Mistakes:

• Assuming map.has supports prefix matching
• Confusing keys 'appl' and 'apple'
• Expecting true for partial keys

4. Consider this buggy TypeScript Trie insert method:

insert(word: string) {
  let node = this.root;
  for (let char of word) {
    if (!node.children.has(char)) {
      node.children.set(char, new TrieNode());
    }
    node = node.children.get(char);
  }
  node.isEnd = true;
}

What is the main issue causing a runtime error?

medium

A. node.children.get(char) can return undefined, causing assignment to node to fail

B. The loop variable char is not declared properly

C. The isEnd property is set before the loop

D. The root node is not initialized

Solution

1. Step 1: Analyze node.children.get(char) usage

   Even after checking node.children.has(char), node.children.get(char) can theoretically return undefined if the Map is modified concurrently or due to incorrect initialization.

2. Step 2: Identify runtime error cause

   Assigning undefined to node causes subsequent property access to fail, leading to runtime error.

3. Final Answer:

   node.children.get(char) can return undefined, causing assignment to node to fail -> Option A

4. Quick Check:

   Ensure node.children.get(char) is not undefined before assignment [OK]

Hint: Check that node.children.get(char) returns a valid TrieNode before assignment [OK]

Common Mistakes:

• Thinking Map.get() returns undefined despite prior has() check
• Overlooking need for root initialization in constructor
• Assuming object-style children access instead of Map methods

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

// Approach 1: Store all words in a Hash Map and check each key for prefix match
// Approach 2: Build a Trie from all words and traverse to prefix node to collect matches

hard

A. Approach 1 is better because Hash Map lookups are O(1) and prefix checks are fast

B. Approach 2 is better because Trie traversal to prefix node is efficient and collects matches quickly

C. Both approaches are equally efficient for prefix search

D. Neither approach works well; use a sorted array with binary search instead

Solution

1. Step 1: Evaluate Approach 1 (Hash Map with prefix checks)

   Hash Map allows O(1) exact lookups but requires checking every key for prefix, which is O(n) and inefficient for large data.

2. Step 2: Evaluate Approach 2 (Trie traversal)

   Trie stores prefixes explicitly; traversing to prefix node is O(k) where k is prefix length, then collecting matches is efficient.

3. Step 3: Compare efficiency and scalability

   Trie approach scales better for prefix search due to structured prefix storage and avoids scanning all keys.

4. Final Answer:

   Approach 2 is better because Trie traversal to prefix node is efficient and collects matches quickly -> Option B

5. Quick Check:

   Prefix search = Trie traversal [OK]

Hint: Trie stores prefixes; Hash Map needs full scan for prefix [OK]

Common Mistakes:

• Assuming Hash Map prefix checks are fast
• Ignoring Trie traversal efficiency
• Thinking both approaches perform the same