Programming Problem #1

Consider the following problem:
Set Cover
Input: A set I = {i1, i2, ..., in} of elements and a set S = {s1, s2, ..., sm} of subsets of I.
Output: All minimum-size set covers of I, i.e., all smallest-possible size subsets S' of S such that the union of all sets in S' is equal to I.

Write and document a Python program that uses the recursive DFS-I (no dynamic pruning) algorithm given in course lecture # 4 to print all minimum-size set covers for a given MSC instance in which the elements i1, i2, ..., ib are the integers 1, 2, ..., n. You have been given Python files myCSTMSCClasses.py and CSTMSC.py and you need to fill in the function definitions in file myCSTMSCFunctions.template according to appropriately modified versions of the specified algorithm given in Lectures #4 to create a file myCSTMSCFunctions.py such that CSTMSC.py (when run relative to given problem-description files iset1.txt, iset2.txt, iset3.txt, iset4.txt, iset5.txt, iset6.txt, iset7.txt, and iset8.txt using python3 on the CS departmental LabNet systems) can exactly reproduce the outputs in script file out.script.

You should not modify any of the code in provided files CSTMSC.py and myCSTMSCClasses.py. When modifying file myCSTMSCFunctions.template to create myCSTMSCFunctions.py, try not to

• modify the given import statements;
• add other import statements (this includes import statements added automatically by IDEs such as PyCharm);
• add, modify, or remove function definitions;
• add new class definitions or global variables (use the provided classes in file myCSTMSCClasses.py); or
• access any provided class attributes directly (use provided attribute access functions in file myCSTMSCClasses.py).

Hints

You may find it useful to progress through the given tests in the given order when debugging your code.

Additional Notes:

• July 15, 2026
  Programming Problem #1 posted.

Created: July 15, 2026
Last Modified: July 15, 2026