[Verse 1]
Multiple patterns need to find their place
In a single text we're searching through the space
Naive approach would scan from left to right
But that's inefficient, not so bright
Aho-Corasick comes to save the day
Linear time complexity, that's the way
Build a trie structure, add the patterns in
Then construct failure links where we begin
[Chorus]
Trie plus failure links, that's the key
A-C algorithm, search efficiently
When mismatch happens, don't restart from scratch
Follow failure pointers, make the perfect match
Linear time scanning, all patterns at once
Aho-Corasick never lets you down
[Verse 2]
Start with building trie from all your strings
Each character becomes a node with rings
Root connects to first chars of each word
Shared prefixes merged, that's what occurred
Then we calculate the failure function right
Longest proper suffix matching prefix tight
BFS traversal sets each failure link
To the deepest node where patterns sync
[Chorus]
Trie plus failure links, that's the key
A-C algorithm, search efficiently
When mismatch happens, don't restart from scratch
Follow failure pointers, make the perfect match
Linear time scanning, all patterns at once
Aho-Corasick never lets you down
[Bridge]
Output links point to pattern ends we've seen
Dictionary matching keeps the search clean
From any state we know exactly where
All matching patterns hiding everywhere
Preprocessing time is sum of pattern lengths
Searching time is just the text's defense
[Verse 3]
Now we scan the text from left to right
Current state guides us through the night
Character matches, move along the trie
No match found, failure link's our guide
When we reach a final state node
Pattern found, add it to our code
Output links reveal more patterns too
All occurrences come into view
[Chorus]
Trie plus failure links, that's the key
A-C algorithm, search efficiently
When mismatch happens, don't restart from scratch
Follow failure pointers, make the perfect match
Linear time scanning, all patterns at once
Aho-Corasick never lets you down
[Outro]
Finite automaton with failure transitions
Simultaneous search, no repetitions
From virus scanning to text processing tools
Aho-Corasick follows all the rules
Linear complexity, optimal and clean
Best multi-pattern search you've ever seen