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Homework 7: Overlapping Strings (use methods to break down complex problems into smaller problems)

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• Goal of this homework
  • What we want to learn from this homework:

    Break a complex task into 2 simpler tasks: Test the solution for the simpler task individually

  • When you write the 2 methods for this howework, you can use the same variable names for different local variables in the methods !!!

    Try to use the variable name i in both methods....

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• Preparation
  • Make a hw7 directory and copy over the prepared files:

    mkdir ~/cs170/hw7 cp ~cs170002/share/hw7/*.java ~/cs170/hw7 cd ~/cs170/hw7

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  • Choose your weapon..... (same choice; you should know what to do by now)

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• Overlapping strings
  • Definition:

    A string s1 overlaps another string s2 if: The characters in some suffix of the string s1 are equal to the characters in the prefix of the string s2

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  • Consider the strings s1 = "Frodo" and s2 = "odometer".

    The string s1 overlaps the string s2 in the following manners:

    1. Frodo odometer - 0 overlapping character ("trivial" overlap) 2. Frodo odometer - 1 overlapping character 3. Frodo odometer - 3 overlapping characters

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  • Maximum overlap:

    The maximum overlap of a string s1 to another string s2 is the longest overlap of s1 to s2.

    The maximum overlap of s1 = "Frodo" on s2 = "odometer" is equal to 3

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  • Consider another example: s1 = "Frodo" and s2 = "od".

    s1 can overlap s2 in the following manners:

    1. Frodo od - 0 overlapping character 2. Frodo od - 1 overlapping character Note: this is not an overlap: Frodo od Because od is not a suffix of "Frodo"

    Therefore, the maximum overlap of "Frodo" and "od" is 1 (character)

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  • Consider the last example: "Frodo" and "do".

    They can overlap in the following manners:

    1. Frodo do - 0 overlapping character 2. Frodo do - 2 overlapping character

    The maximum overlap of "Frodo" and "do" is 2 (characters)

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• Homework assignment
  • Summary:

    Write a method maxOverlap(s1, s2) that returns an integer that is equal to the maximum overlap of string s1 on string s2 (I.e., find the longest suffix of string s1 that is a prefix of string s2.)

    Example:

    maxOverlap("Frodo", "odometer") returns 3 maxOverlap("Frodo", "od") returns 1 maxOverlap("Frodo", "do") returns 2

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• How to solve this problem
  • Sketch of the algorithm with a concrete example:

    How to find maximum overlap of s1 = "abcabcab" and s2 = "abcabc" 1) Try every possible position to align a suffic of s1 to a prefix of s2: 01234567 abcabcab abcabc 01234567 abcabcab abcabc 01234567 abcabcab abcabc 01234567 abcabcab abcabc 01234567 abcabcab abcabc 01234567 abcabcab abcabc 01234567 abcabcab abcabc (You don't really need to do this case, If you don't find any match so far, you know the maximum overlap is 0) 2) For each alignment (see above), determine if the suffix of s1 is equal to the prefix of s2 (I have highlighted the results: red means there is match of the suffix of s1 and the prefix of s2, brown means mismatch) Example on how to determine if the suffix of s1 is equal to the prefix of s2: abcabcab abcabc When you compare the first pair of characters, you detects the mismatch right away; so the suffix of s1 is not equal to the prefix of s2 for this alignment. Example on how to determine if the suffix of s1 is equal to the prefix of s2: abcabcab abcabc When you compare the first pair of characters ('a' and 'a'), they are equal and you will proceed to compare the second pair, and so on. After checking the last character ('b'), you can conclude that the suffix of s1 is equal to the prefix of s2 for this alignment.

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• What can we learn from this example ?
  • Original problem:

    Write a method maxOverlap(s1, s2) that returns an integer that is equal to the maximum overlap of string s1 on string s2

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  • Suppose someone gave us a method overlap(s1, s1Start, s2) that tells us is there an overlap when the first character of string s2 is matched against the character at position s1Start in s1:

    s1.charAt(s1Start) | v s1 = "..................." ".............." ^ | s2.charAt(0)

    we can use this overlap(s1, s1Start, s2) method to find the maximum overlap easier

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• Step 1: write an algorithm to determine overlap
  • Write a method overlap(s1, s1Start, s2) that check if string s1 overlaps with string s2 starting at character s1Start in string s1:

    s1Start | V s1 = "................." s2 = "..............."

    The method overlap returns true if there is an overlap; otherwise, it returns false.

    Examples:

    s1 = "abcabcab"; s2 = "abcabc"; Example1: overlap( s1, 2, s2 ): s1Start | v 01234567 abcabcab abcabc You must compare: s1.charAt(2) <-> s2.charAt(0) s1.charAt(3) <-> s2.charAt(1) ... Can you see 2 running indices ? first index: 2, 3, ...., last character in s1 second index: 0, 1, .... What is the last character in s1 ??? When do you stop (Hint: 2 ways to stop, on first mismatch and when all characters have been tested) Example 2: overlap( s1, 6, s2 ): s1Start | v 01234567 abcabcab abcabc You must compare: s1.charAt(6) <-> s2.charAt(0) s1.charAt(7) <-> s2.charAt(1) Can you see 2 running indices ? first index: 6, 7 (= last character in s1) second index: 0, 1 What is the last character in s1 ??? When do you stop (Hint: 2 ways to stop, on first mismatch and when all characters have been tested)

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  • Task 1:

    Write the method overlap(s1, s1Start, s2) inside the program TestOverlap.java.

    The TestOverlap.java contains a main() method that let you test the overlap(s1, s1Start, s2) before using it to solve the "find maximum overlap" problem.

    public class TestOverlap { // Write the overlap() method here public static void main(String[] args) { String x1, x2; int i, j; x1 = "abcabcab"; x2 = "abcabc"; for ( i = 2; i < 8; i++ ) { System.out.println( "\n" + x1 ); for ( j = 0; j < i; j++ ) System.out.print( " " ); System.out.println( x2 ); System.out.print( "Overlap: " ); if ( overlap( x1, i, x2 ) ) System.out.println( " **** YES ! " ); else System.out.println( " no " ); } } }

    Note:

    Look careful at how the method overlap() is used. What are the type of each parameter What is the type of the return value (it's used in an if-statement, what is the type of such expression) Define the overlap() using the exact type of parameters and the exact type of return value.

    Compile and run the test.

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  • If your overlap() is correct, it will print the following result:

    abcabcab abcabc Overlap: no abcabcab abcabc Overlap: **** YES ! abcabcab abcabc Overlap: no abcabcab abcabc Overlap: no abcabcab abcabc Overlap: **** YES ! abcabcab abcabc Overlap: no

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• Step 2: find the maximum overlap
  • Use the overlap() method that you have developed in Step 1 and write a method named maxOverlap(s1, s2) that return the maximum number of characters that the string s1 overlaps the string s2.

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  • How to solve this problem:

    1. Start matching s2 against s1 from the left and run to the end: First position | v s1 = "............" "........" <----- this is s2 Second position | v s1 = "............" "........" <----- this is s2 ... Last position | v s1 = "............" "........" <----- this is s2 What's the first position ? What's the last position ? (What kind of statement would you use to instruct the computer to perform this ???) Warning: The first position is computed differently when s1 is longer than s2 and s1 is shorter than s2 You must handle both cases (because my test program uses s1 that is longer and shorter than s2). 2. For each starting position above: What should you do if there is a match ? What should you do if there is a mismatch ? (What kind of statement would you use to instruct the computer to perform this ???)

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  • Task 2:

    Cut and paste the overlap() method that you have written in task 1 into the program Overlap.java (Now you should not change anything in this method, you will only be using this method to solve the original problem.) Write the method maxOverlap(s1, s2) inside the program Overlap.java. The maxOverlap(s1, s2) should use (invoke) the overlap() method with specific parameters to solve the maximum overlap problem !!! (So don't start from scratch !!!)

  • The Overlap.java program contains a main() method that test the correctness of the maxOverlap(s1, s2) method:

    public class Overlap { // Cut and paste your overlap() method definition here // Write the maxOverlap() method here public static void main(String[] args) { String x1, x2; x1 = "abcabcabc"; x2 = "bcabcxx"; System.out.println( x1 + " " + x2 + " = " + maxOverlap(x1, x2) ); x1 = "Frodo"; x2 = "odometer"; System.out.println( x1 + " " + x2 + " = " + maxOverlap(x1, x2) ); x1 = "Frodo"; x2 = "Odometer"; System.out.println( x1 + " " + x2 + " = " + maxOverlap(x1, x2) ); x1 = "Frodo"; x2 = "od"; System.out.println( x1 + " " + x2 + " = " + maxOverlap(x1, x2) ); x1 = "Frodo"; x2 = "do"; System.out.println( x1 + " " + x2 + " = " + maxOverlap(x1, x2) ); } }

    Note:

    Look careful at how the method maxOverlap() is used. What are the type of each parameter What is the type of the return value (it must return the maximum number of overlapping characters, what is the type of this number ?) Define the maxOverlap() using the exact type of parameters and the exact type of return value.

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  • If your maxOverlap() is correct, the program will print:

    abcabcabc bcabcxx = 5 Frodo odometer = 3 Frodo Odometer = 0 Frodo od = 1 Frodo do = 2

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• Turnin
  • Turn in your TestOverlap.java and Overlap.java as follows:

    /home/cs170002/turnin-hw Overlap.java hw7 /home/cs170002/turnin-hw TestOverlap.java hw7a