Prefix matching with tries in Data Structures Theory - Step-by-Step Execution

Concept Flow - Prefix matching with tries

Start at root node

↓

For each character in prefix

↓

Check if character child exists

↓

Prefix not found

↓

Repeat for next character

↓

All prefix chars found

↓

Collect all words below current node

↓

Return matched words

The trie is traversed character by character for the prefix. If all prefix characters are found, all words below that node are collected as matches.

Execution Sample

Data Structures Theory

Insert words: cat, car, cart, dog
Search prefix: 'car'
Traverse trie nodes for 'c' -> 'a' -> 'r'
Collect words starting with 'car'

This example inserts words into a trie and then finds all words starting with the prefix 'car'.

Analysis Table

Step	Operation	Current Node	Character	Child Exists?	Action	Matched Words Collected
1	Start search	root	c	Yes	Move to 'c' node	[]
2	Next char	c node	a	Yes	Move to 'a' node	[]
3	Next char	a node	r	Yes	Move to 'r' node	[]
4	Prefix complete	r node	-	-	Collect words below 'r'	['car', 'cart']
5	Return result	-	-	-	Search complete	['car', 'cart']

💡 All prefix characters found; collected words starting with 'car'

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
Current Node	root	node for 'c'	node for 'a'	node for 'r'	node for 'r'	node for 'r'
Character	-	'c'	'a'	'r'	-	-
Matched Words	[]	[]	[]	[]	['car', 'cart']	['car', 'cart']

Key Insights - 3 Insights

What happens if a character in the prefix is not found in the trie?

If a character is missing, the search stops immediately and no words are matched because the prefix does not exist.

Why do we collect words only after the entire prefix is matched?

Words are collected only after confirming the prefix exists (Step 4) to ensure all returned words start with that prefix.

Can the prefix itself be a word in the trie?

Yes, if the node at the end of the prefix marks a complete word, it is included in the matched words (e.g., 'car' in the example).

Visual Quiz - 3 Questions

Look at the execution_table at Step 3. What is the current node representing?

A The node for character 'r'

B The root node

C The node for character 'a'

D No node, prefix not found

💡 Hint

Check the 'Current Node' and 'Character' columns at Step 3 in execution_table.

At which step does the algorithm confirm the prefix is fully matched?

A Step 2

B Step 4

C Step 1

D Step 5

💡 Hint

Look for the step where 'Prefix complete' is noted in the 'Operation' column.

If the prefix was 'ca' instead of 'car', what would be the matched words collected at Step 4?

A ['cat', 'car', 'cart']

B ['car', 'cart']

C ['dog']

D []

💡 Hint

Consider all words starting with 'ca' inserted in the trie and check variable_tracker for matched words.

Concept Snapshot

Prefix matching with tries:
- Start at root node
- For each prefix character, move to child node if exists
- If any character missing, prefix not found
- After full prefix matched, collect all words below current node
- Returned words all start with the prefix

Full Transcript

Prefix matching with tries works by starting at the root node and moving down the trie following each character of the prefix. If at any point a character is missing, the search stops with no matches. If all prefix characters are found, the algorithm collects all words stored below the last matched node. For example, searching prefix 'car' in a trie containing 'cat', 'car', 'cart', and 'dog' will find the node for 'r' and collect 'car' and 'cart' as matched words. This process ensures efficient retrieval of all words sharing the given prefix.

Practice

1. What is the main advantage of using a trie for prefix matching?

easy

A. It stores words in reverse order

B. It uses less memory than arrays

C. It sorts words alphabetically automatically

D. It allows fast lookup of words sharing common prefixes

Solution

1. Step 1: Understand trie structure

   A trie stores words by sharing nodes for common prefixes, reducing repeated storage.

2. Step 2: Identify prefix matching benefit

   This structure allows quick traversal to find all words starting with a given prefix.

3. Final Answer:

   It allows fast lookup of words sharing common prefixes -> Option D

4. Quick Check:

   Prefix matching speed = Fast lookup [OK]

Hint: Tries speed up prefix search by sharing nodes [OK]

Common Mistakes:

• Confusing tries with hash tables
• Thinking tries sort words automatically
• Assuming tries store words backwards

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

easy

A. Search the entire trie for the full word

B. Traverse nodes matching each prefix character until end or mismatch

C. Count all leaf nodes in the trie

D. Sort all words and do binary search

Solution

1. Step 1: Understand prefix search in tries

   To check a prefix, we walk down the trie nodes matching each character in order.

2. Step 2: Identify correct method

   If traversal completes without mismatch, prefix exists; otherwise, it does not.

3. Final Answer:

   Traverse nodes matching each prefix character until end or mismatch -> Option B

4. Quick Check:

   Prefix check = Node traversal [OK]

Hint: Walk trie nodes character by character for prefix [OK]

Common Mistakes:

• Searching entire trie instead of prefix path
• Counting leaf nodes unrelated to prefix
• Using sorting instead of trie traversal

3. Given a trie containing words: ['cat', 'car', 'cart', 'dog'], which words match the prefix 'car'?

medium

A. ['car', 'cart']

B. ['dog']

C. ['cat', 'car']

D. ['cat', 'dog']

Solution

1. Step 1: Identify words starting with 'car'

   From the list, 'car' and 'cart' start with the prefix 'car'.

2. Step 2: Exclude words not matching prefix

   'cat' starts with 'cat', not 'car'; 'dog' does not match prefix.

3. Final Answer:

   ['car', 'cart'] -> Option A

4. Quick Check:

   Words with prefix 'car' = ['car', 'cart'] [OK]

Hint: Match prefix exactly to filter words [OK]

Common Mistakes:

• Including words with similar but different prefixes
• Confusing 'cat' with 'car'
• Selecting unrelated words

4. A trie implementation returns false when checking prefix 'app' even though words ['apple', 'application'] exist. What is the most likely error?

medium

A. The trie nodes for 'app' were not linked correctly

B. The words were inserted backwards

C. The prefix check is case-insensitive

D. The trie only stores full words, not prefixes

Solution

1. Step 1: Analyze prefix check failure

   If words with prefix 'app' exist but check fails, likely the path for 'app' nodes is broken.

2. Step 2: Exclude other causes

   Words inserted backwards or case issues would cause different errors; tries store prefixes inherently.

3. Final Answer:

   The trie nodes for 'app' were not linked correctly -> Option A

4. Quick Check:

   Broken node links = prefix check fail [OK]

Hint: Check node links for prefix path [OK]

Common Mistakes:

• Assuming tries don't store prefixes
• Ignoring node linkage errors
• Confusing case sensitivity issues

5. You want to build an autocomplete feature using a trie. Which approach best improves performance when many words share prefixes?

hard

A. Use a linked list instead of trie nodes for each character

B. Store full words only at leaf nodes without intermediate nodes

C. Store a count of words passing through each node to quickly find popular prefixes

D. Sort all words and do linear search for each prefix

Solution

1. Step 1: Understand autocomplete with tries

   Autocomplete benefits from knowing how many words share a prefix to prioritize suggestions.

2. Step 2: Identify performance improvement

   Storing counts at each node helps quickly find popular prefixes without full traversal.

3. Final Answer:

   Store a count of words passing through each node to quickly find popular prefixes -> Option C

4. Quick Check:

   Node counts = faster autocomplete [OK]

Hint: Count words at nodes to speed autocomplete [OK]

Common Mistakes:

• Storing words only at leaves slows prefix search
• Using linked lists reduces trie efficiency
• Linear search ignores trie benefits