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

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Prefix not found

↓

Repeat for next character

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All prefix chars found

↓

Collect all words below current node

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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.