Homework 9: PatternMatching Solution

For this assignment you will be coding 3 di erent pattern matching algorithms: Brute Force, Knuth-Morris-Pratt (KMP), and Boyer-Moore. For all three algorithms, you should nd all occurrences of the pattern in the text, not just the rst 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 ex-ample, 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 signi cantly 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 com-parison 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 pre x 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 pre x that matches a proper su x of pattern[0, ..., i]. A proper pre x/su x does not equal the string itself. There are di erent ways of calculating the failure table, but we are expecting the speci c format described below.

For any string pattern, have a pointer i starting at the rst letter, a pointer j starting at the sec-ond 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 search-ing, the algorithm generates a last occurrence table. The table allows the algorithm to skip sections of the text, resulting in more e cient 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 (assum-ing 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  nding multiple occurrences, if you  nd 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


E  ciency
15pts


Total:
100pts



Provided

The following    le(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 di erent 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 le.

    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 le(s). Make sure all le(s) listed below are in each submission, as only the last submission will be graded. Make sure the lename(s) matches the lename(s) below, and that only the following le(s) are present. The only exception is that Canvas will automatically append a -n depending on the submission number to the le name(s). This is expected and will be handled by the TAs when grading as long as the le name(s) before this add-on matches what is shown below. If you resubmit, be sure only one copy of each le is present in the submission. If there are multiple les, do not zip up the les before submitting; submit them all as separate les.

Once submitted, double check that it has uploaded properly on Canvas. To do this, download your uploaded le(s) to a new folder, copy over the support le(s), recompile, and run. It is your sole respon-sibility to re-test your submission and discover editing oddities, upload issues, etc.

    1. PatternMatching.java


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