SE 504 Spring 2022
Prog. Assg.: Saddleback Search
Due: 11:59pm, Friday, May 13

For a discussion of how to employ the binary search approach when searching a two-dimensional array (whose elements are increasing along each row and column), go here.

Provided to you are the following Java components:

• GridLocation: An instance of this class represents a location in a matrix (rectangular array) via ROW and COL components.
• SaddleBackSearcher: An abstract Java class that serves as a partial implementation of a class whose objects are capable of searching for values within a matrix (i.e., a rectangular array) of integers in which the values are increasing along each row and each column.
• SaddleBackSearchByElim: A concrete child class of SaddleBackSearcher, instances of it search for values in an integer matrix using the Search-by-Elimination algorithm (discussed in class) in which each "probe" to a location results in either that location's row or column being eliminated from further consideration.

  The student's first task is to complete the findAllAux() method of this class.

• SaddleBackBinSearcher: Also a child class of SaddleBackSearcher, its search algorithm is based upon binary search, as discussed in class. The student's second task is to complete the findAllAux() method of this class.

  It would be natural for the findAllAux() method to be recursive, but, alternatively, it could use a stack to keep track of which regions of the matrix are yet to be searched.

• Stack: Interface describing the stack abstract data type.
• StackViaArray: Concrete class that implements the Stack interface. One would expect that an instance of SaddleBackBinSearcher would manage a search using either recursion or a stack. Hence, this class is provided.

For testing purposes, the following Java classes are provided:

• SB_Tester: Java application that interacts with a user to perform testing of the both SaddleBackSearchByElim and SaddleBackBinSearcher classes. The user initially chooses the size of the matrix to be searched and the seed for the pseudorandom number generator that is used in generating the values that are placed into the matrix. Then the user specifies keys for which to search. A sample user/program dialog is shown below.
• TwoDimArrayMaker: This class has static methods to create matrices whose elements are generated pseudo-randomly and such that the values therein are increasing along each row and column. It is used by the SB_Tester application.

Dialog with SB_Tester

$ java SB_Tester
Welcome to the SaddleBackSearcher tester.
Enter # rows in matrix: 10
Enter # columns in matrix: 11
Enter seed for pseudorandom # generation: 5

        0   1   2   3   4   5   6   7   8   9  10
    +--------------------------------------------
   0|   5   8  13  18  20  21  26  28  31  33  35
   1|   9  13  14  22  24  26  29  30  34  35  36
   2|  12  18  21  25  30  33  34  36  40  45  49
   3|  13  23  25  26  33  35  39  42  45  49  50
   4|  17  24  26  29  36  40  43  48  49  52  54
   5|  18  29  31  34  38  44  45  52  55  60  64
   6|  22  34  36  40  41  45  48  57  58  64  69
   7|  23  35  40  45  49  51  53  61  63  66  72
   8|  26  39  42  46  51  52  54  64  69  74  75
   9|  29  40  46  47  55  60  65  69  70  79  84

Enter a search key (or Q, or S): 30

Searching by Elimination...
The search for 30 involved 18 probes and yielded this list of locations:
[(1,7), (2,4)]

Searching by Binary Search...
The search for 30 involved 29 probes and yielded this list of locations:
[(1,7), (2,4)]

Enter a search key (or Q, or S): 22

Searching by Elimination...
The search for 22 involved 16 probes and yielded this list of locations:
[(1,3), (6,0)]

Searching by Binary Search...
The search for 22 involved 24 probes and yielded this list of locations:
[(6,0), (1,3)]

Enter a search key (or Q, or S): 59

Searching by Elimination...
The search for 59 involved 16 probes and yielded this list of locations:
[]

Searching by Binary Search...
The search for 59 involved 22 probes and yielded this list of locations:
[]

Enter a search key (or Q, or S): S

        0   1   2   3   4   5   6   7   8   9  10
    +--------------------------------------------
   0|   5   8  13  18  20  21  26  28  31  33  35
   1|   9  13  14  22  24  26  29  30  34  35  36
   2|  12  18  21  25  30  33  34  36  40  45  49
   3|  13  23  25  26  33  35  39  42  45  49  50
   4|  17  24  26  29  36  40  43  48  49  52  54
   5|  18  29  31  34  38  44  45  52  55  60  64
   6|  22  34  36  40  41  45  48  57  58  64  69
   7|  23  35  40  45  49  51  53  61  63  66  72
   8|  26  39  42  46  51  52  54  64  69  74  75
   9|  29  40  46  47  55  60  65  69  70  79  84

Enter a search key (or Q, or S): 18

Searching by Elimination...
The search for 18 involved 14 probes and yielded this list of locations:
[(0,3), (2,1), (5,0)]

Searching by Binary Search...
The search for 18 involved 21 probes and yielded this list of locations:
[(5,0), (2,1), (0,3)]

Enter a search key (or Q, or S): Q
Goodbye from the SaddleBackSearcher tester.