Description
PatternMatching
For this assignment you will be coding 3 different pattern matching algorithms: Brute Force, KnuthMorris-Pratt (KMP), and Boyer-Moore. For all three algorithms, you should find all occurrences of the
pattern in the text, not just the first match. The occurrences are returned as a list of integers; the
list should contain the indices of occurrences in ascending order. There is information about all three
algorithms in the javadocs with additional implementation details below. If you implement any of the
three algorithms in an unexpected manner (i.e. contrary to what the Javadocs and PDF specify), you
may receive a 0.
For all of the algorithms, make sure you check the simple failure cases as soon as possible. For example, if the pattern is longer than the text, don’t do any preprocessing on the pattern/text and just
return an empty list since there cannot be any occurrences of the pattern in the text.
Note that for pattern matching, we refer to the text length as n and the pattern length as m.
CharacterComparator
CharacterComparator is a comparator that takes in two characters and compares them. This allows
you to see how many times you have called compare(); besides this functionality, its return values are
what you’d expect a properly implemented compare() method to return. You must use this comparator
as the number of times you call compare() with it will be used when testing your assignment.
If you do not use the passed in comparator, this will cause tests to fail and will significantly lower
your grade on this assignment. You must implement the algorithms as they were taught in
class. We are expecting exact comparison counts for this homework. If you are getting fewer comparison counts than expected, it means one of two things: either you implemented the algorithm wrong
(most likely) or you are using an optimization not taught in the class (unlikely).
Brute Force
The Brute Force approach is the simplest way to do pattern matching. Align the beginning of the pattern
with the beginning of the text. Compare from left to right. If after checking the entire pattern there is
no mismatch, shift the pattern down by one. Stop early if there is a mismatch, and shift the pattern
down by one. Keep doing this until the pattern extends beyond the bounds of the text.
Knuth-Morris-Pratt
Failure Table
The Knuth-Morris-Pratt (KMP) algorithm relies on using the prefix of the pattern to determine how
much to shift the pattern by. The algorithm itself uses what is known as the failure table (also called
failure function). Before actually searching, the algorithm generates a failure table. This is an array of
length m where each index will correspond to the substring in the pattern up to that index. Each index
i of the failure table should contain the length of the longest proper prefix that matches a proper suffix
of pattern[0, …, i]. A proper prefix/suffix does not equal the string itself. There are different ways
of calculating the failure table, but we are expecting the specific format described below.
For any string pattern, have a pointer i starting at the first letter, a pointer j starting at the second letter, and an array called table that is the length of the pattern. First, set index 0 of table to 0.
Then, while j is still a valid index within pattern:
• If the characters pointed to by i and j match, then write i + 1 to index j of the table and
increment i and j.
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Homework 9: PatternMatching Due: See Canvas
• If the characters pointed to by i and j do not match:
– If i is not at 0, then change i to table[i – 1]. Do not increment j or write any value to
the table.
– If i is at 0, then write i to index j of the table. Increment only j.
For example, for the string abacab, the failure table will be:
a b a c a b
0 0 1 0 1 2
For the string ababac, the failure table will be:
a b a b a c
0 0 1 2 3 0
For the string abaababa, the failure table will be:
a b a a b a b a
0 0 1 1 2 3 2 3
For the string aaaaaa, the failure table will be:
a a a a a a
0 1 2 3 4 5
Searching Algorithm
For the main searching algorithm, the search acts like a standard brute-force search for the most part,
but in the case of a mismatch:
• If the mismatch occurs at index 0 of the pattern, then shift the pattern by 1.
• If the mismatch occurs at index j of the pattern and index i of the text, then shift the pattern
such that index failure[j-1] of the pattern lines up with index i of the text, where failure is
the failure table. Then, continue the comparisons at index i of the text (or index failure[j-1]
of the pattern). Do not restart at index 0 of the pattern.
In addition, if the whole pattern is ever matched, instead of shifting the pattern over by 1 to continue
searching for more matches, the pattern should be shifted so that the pattern at index failure[j-1],
where j is at pattern.length, aligns with the index after the match in the text. KMP treats a match as
a “mismatch” on the character immediately following the match.
Boyer-Moore
Last Occurrence Table
The Boyer-Moore algorithm, similar to KMP, relies on preprocessing the pattern. Before actually searching, the algorithm generates a last occurrence table. The table allows the algorithm to skip sections of
the text, resulting in more efficient string searching. The last occurrence table should be a mapping from
each character in the alphabet (the set of all characters that may be in the pattern or the text) to the
last index the character appears in the pattern. If the character is not in the pattern, then -1 is used as
the value, though you should not explicitly add all characters that are not in the pattern into the table.
The getOrDefault() method from Java’s Map will be useful for this.
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Homework 9: PatternMatching Due: See Canvas
Searching Algorithm
Key properties of Boyer-Moore include matching characters starting at the end of the pattern, rather
than the beginning and skipping along the text in jumps of multiple characters rather than searching
every single character in the text.
The shifting rule considers the character in the text at which the comparison process failed (assuming that a failure occurred). If the last occurrence of that character is to the left in the pattern, shift
so that the pattern occurrence aligns with the mismatched text occurrence. If the last occurrence of the
mismatched character does not occur to the left in the pattern, shift the pattern over by one (to prevent
the pattern from moving backwards). In addition, if the mismatched character does not exist in the
pattern at all (no value in last table) then pattern shifts completely past this point in the text.
For finding multiple occurrences, if you find a match, shift the pattern over by one and continue searching.
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Homework 9: PatternMatching Due: See Canvas
Grading
Here is the grading breakdown for the assignment. There are various deductions not listed that are
incurred when breaking the rules listed in this PDF and in other various circumstances.
Methods:
bruteForce 25pts
buildFailureTable 10pts
kmp 15pts
buildLastTable 10pts
boyerMoore 15pts
Other:
Checkstyle 10pts
Efficiency 15pts
Total: 100pts
Provided
The following file(s) have been provided to you. There are several, but we’ve noted the ones to edit.
1. PatternMatching.java
This is the class in which you will implement the different pattern matching algorithms. Feel
free to add private static helper methods but do not add any new public methods, new
classes, instance variables, or static variables.
2. CharacterComparator.java
This is a comparator that will be used to count the number of comparisons used. You must
use this comparator. Do not modify this file.
3. PatternMatchingStudentTests.java
This is the test class that contains a set of tests covering the basic algorithms in the PatternMatching
class. It is not intended to be exhaustive and does not guarantee any type of grade. Write your
own tests to ensure you cover all edge cases.
Deliverables
You must submit all of the following file(s). Make sure all file(s) listed below are in each submission, as
only the last submission will be graded. Make sure the filename(s) matches the filename(s) below, and
that only the following file(s) are present. The only exception is that Canvas will automatically append
a -n depending on the submission number to the file name(s). This is expected and will be handled by
the TAs when grading as long as the file name(s) before this add-on matches what is shown below. If
you resubmit, be sure only one copy of each file is present in the submission. If there are multiple files,
do not zip up the files before submitting; submit them all as separate files.
Once submitted, double check that it has uploaded properly on Canvas. To do this, download your
uploaded file(s) to a new folder, copy over the support file(s), recompile, and run. It is your sole responsibility to re-test your submission and discover editing oddities, upload issues, etc.
1. PatternMatching.java
