(Latest Revision -- 03/24/2002)

CS 4440 Work Assignment:
Weeks Seven to Eight

Readings:

HOMEWORK to be turned in by midnight 04/19/2002

Below I have given a header comment for a program, one copy of sample input with corresponding output, and two more sets of sample input. Your assignment is to write the program and turn in source code plus test script showing how the program performs on each of the three sample inputs here, plus any other inputs you may want to test.

Make sure that the format of the test script is such that you cat the first input file, then run the program on the first input, then cat the second input file and run the program on the second input file, and then cat the third input file and run the prorgram on the third input file. 


/*

   Header comment for program
   
   This program uses dynamic programming to calculate the solution to a 0/1
   knapsack problem. (c.f. page 266 of Brassard and Bratley) You enter input
   like this:

   5
   1 1
   2 6
   5 18
   6 22
   7 28
   18
   16
   21

   Here the first number is numObjs, the number of objects that are
   available to be placed in the knapsack.  

   5

   Next come numObjs pairs of numbers.  These pairs describe the objects.

   1 1
   2 6
   5 18
   6 22
   7 28

   The first number in the i-th pair is the weight of the i-th object.  The
   second number in the i-th pair is the value (cost) of the i-th object.
   The program reads this description of the objects and then computes the
   table of solutions to the 0/1 knapsack problems for all knapsack
   capacities up to a maximum equal to the sum of the weights of all the
   objects in the data set.

   For example here the sum of the weights is 1+2+5+6+7=21.  Therefore the
   table of solutions is filled out with 22 columns, corresponding to
   knapsack capacities of 0 to 21.  The program prints out the description
   of the objects and the table.

   Finally, there comes an optional series of knapsack capacities, wtLim.

   18
   16
   21

   The program will read each value of wtLim.  For each value it prints a
   report, stating the (optimal) solution to the knapsack problem when the
   knapsack capacity is wtLim.

   The report gives the serial number, weight, and value of each object that
   should be chosen to place in the knapsack, and it also gives the total
   weight and value of the chosen solution.  How does the program know which
   objects to use to comprise the solution?  It uses the method of scanning
   backward through the table described in Brassard and Bratley.

   In this program there can be at most 20 objects, with weights that add up
   to at most 100.  It is easy to change these limits by giving certain
   constants different values.

*/

Sample Input File #1

   5
   1 1
   2 6
   5 18
   6 22
   7 28
   18
   16
   21

Output For Sample Input File #1


                   Total Weight ----->

  wt val   |   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21
____________________________________________________________________________________________________
   1   1   |   0   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1
   2   6   |   0   1   6   7   7   7   7   7   7   7   7   7   7   7   7   7   7   7   7   7   7   7
   5  18   |   0   1   6   7   7  18  19  24  25  25  25  25  25  25  25  25  25  25  25  25  25  25
   6  22   |   0   1   6   7   7  18  22  24  28  29  29  40  41  46  47  47  47  47  47  47  47  47
   7  28   |   0   1   6   7   7  18  22  28  29  34  35  40  46  50  52  56  57  57  68  69  74  75


Packing Sack with weight limit of........ 18
------------------------------------
    Object #      Weight       Value
           5           7          28
           4           6          22
           3           5          18
------------------------------------
     Totals:          18          68


Packing Sack with weight limit of........ 16
------------------------------------
    Object #      Weight       Value
           5           7          28
           4           6          22
           2           2           6
           1           1           1
------------------------------------
     Totals:          16          57


Packing Sack with weight limit of........ 21
------------------------------------
    Object #      Weight       Value
           5           7          28
           4           6          22
           3           5          18
           2           2           6
           1           1           1
------------------------------------
     Totals:          21          75


Sample Input File #2

4
2       10
4       10
6       12
9       18
0
1
2
4
6
8
16
20
21


Sample Input File #3

3
2       1
3       2
4       5
0
1
2
3
4
5
6
7
8
9