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

Concept Flow - Trie vs Hash Map for Prefix Matching

Start Prefix Query

↓

Choose Data Structure

↓

Traverse Trie

↓

Match Prefix?

↓

Return Matches

↓

End

Shows how prefix matching starts, then splits into two paths: using a Trie or a Hash Map, each checking for prefix matches differently.

Execution Sample

DSA Typescript

class TrieNode {
  children: Map<string, TrieNode> = new Map();
  isWord: boolean = false;
}

// Insert 'cat' and 'car' into Trie
// Check prefix 'ca'

Inserts words 'cat' and 'car' into a Trie, then checks if prefix 'ca' exists.

Execution Table

Step	Operation	Nodes in Trie	Pointer Changes	Visual State
1	Create root node	root	head -> root	root: {}
2	Insert 'cat'	root -> c -> a -> t (isWord=true)	head -> root -> c -> a -> t	root: {c} c: {a} a: {t} t: {}
3	Insert 'car'	root -> c -> a -> t (isWord=true), a -> r (isWord=true)	head -> root -> c -> a -> r	root: {c} c: {a} a: {t, r} t: {} r: {}
4	Check prefix 'ca'	root -> c -> a	head -> root -> c -> a	Prefix nodes: root -> c -> a
5	Prefix 'ca' found, collect words	root -> c -> a -> t, r	head -> root -> c -> a -> t/r	Words: 'cat', 'car'
6	Hash Map keys: ['cat', 'car', 'dog']	N/A	N/A	Hash Map: {'cat': true, 'car': true, 'dog': true}
7	Check prefix 'ca' in Hash Map keys	N/A	N/A	Matches: 'cat', 'car'
8	End	N/A	N/A	Prefix matching complete

💡 All prefix matches found or no more keys to check.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	Final
Trie Nodes	{}	{root -> c -> a -> t}	{root -> c -> a -> t, r}	{root -> c -> a}	{root -> c -> a -> t, r}	N/A	N/A	N/A
Hash Map	{}	{}	{}	{}	{}	{'cat': true, 'car': true, 'dog': true}	{'cat': true, 'car': true, 'dog': true}	{'cat': true, 'car': true, 'dog': true}
Prefix Matches	[]	[]	[]	[]	['cat', 'car']	[]	['cat', 'car']	['cat', 'car']

Key Moments - 3 Insights

Why does Trie traversal stop at node 'a' when checking prefix 'ca'?

Because the prefix 'ca' corresponds to nodes root -> c -> a in the Trie, as shown in execution_table step 4. We stop traversal after matching all prefix characters.

How does Hash Map find prefix matches without a tree structure?

Hash Map checks all keys to see which start with the prefix, as in execution_table step 7. It does not traverse nodes but scans keys.

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

Trie directly follows prefix nodes without scanning all keys, shown in steps 4 and 5, while Hash Map scans all keys (step 7), which is slower for large data.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, which nodes were added to the Trie?

A Nodes for 'c', 'a', 'r'

B Nodes for 'r' only

C Nodes for 'c', 'a', 't'

D No new nodes added

💡 Hint

Check the 'Nodes in Trie' and 'Visual State' columns at step 3.

At which step does the Trie confirm the prefix 'ca' exists?

A Step 4

B Step 6

C Step 2

D Step 7

💡 Hint

Look for the step where prefix nodes root -> c -> a are identified.

If the Hash Map had 1000 keys, how would prefix matching change compared to Trie?

A Hash Map would be faster because it uses keys directly

B Trie would be slower because it traverses nodes

C Hash Map would be slower because it scans all keys

D Both would have same speed

💡 Hint

Refer to key_moments about efficiency differences.

Concept Snapshot

Trie vs Hash Map for Prefix Matching:
- Trie stores words as paths of characters (nodes).
- Prefix matching in Trie follows nodes for each prefix char.
- Hash Map stores full words as keys; prefix match scans keys.
- Trie is efficient for large datasets with many prefixes.
- Hash Map is simpler but slower for prefix queries.
- Use Trie when prefix search speed matters.

Full Transcript

This visual execution compares Trie and Hash Map for prefix matching. We start by inserting words 'cat' and 'car' into a Trie, creating nodes for each character. The Trie traversal for prefix 'ca' follows nodes root -> c -> a, confirming the prefix exists and collecting matching words. In contrast, the Hash Map stores full words as keys and checks all keys to find those starting with 'ca'. The Trie approach is more efficient for prefix matching because it directly follows prefix nodes without scanning all keys. The Hash Map approach is simpler but slower for large datasets. Key moments include understanding why Trie traversal stops at the last prefix character node and how Hash Map scans keys for prefix matches. The visual quiz tests understanding of Trie node additions, prefix confirmation steps, and efficiency differences between Trie and Hash Map.

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