1. Digression on Loop Invariants
Professor Hugh C. Lauer CS-2303, System Programming Concepts
(Slides include materials from The C Programming Language, 2nd edition, by Kernighan and Ritchie, Absolute C++, by Walter Savitch, The C++ Programming Language, Special Edition, by Bjarne Stroustrup, and from C: How to Program, 5th and 6th editions, by Deitel and Deitel)
CS-2303, A-Term 2012
Loop Invariants

2. Definition – Loop Invariant
Something that is true at a certain point of each iteration of the loop
Often at start of iteration
E.g., a relationship of the variables
Expressed as a logical statement called an assertion
Needs to be preserved from one iteration to the next
Does not necessarily remain true within loop body, but only at the specific point each time through
CS-2303, A-Term 2012
Loop Invariants 2

3. Loop Invariant Allows you to reason about a program …
… and to convince yourself (and other people) that it is correct
For many “ordinary” programs, you do this subconsciously
For seriously difficult programs, you must write out the loop invariants!
CS-2303, A-Term 2012
Loop Invariants

4. Thinking Through the Calendar Assignment
This variable is “global” to the loop. I.e., remembered from one iteration to the next.
int startingDay; /* init for your year*/ for (int month = 0; month < 12; month++) { } // for month
CS-2303, A-Term 2012
Loop Invariants 4

5. Calendar Assignment (continued)
int startingDay; /* init for your year*/ for (int month = 0; month < 12; month++) { } // for month
At beginning of each iteration, startingDay indicates the day of the week on which that particular month starts.
It is the responsibility of the loop body to update startingDay for the next month.
This is the beginning of a Loop Invariant!
CS-2303, A-Term 2012
Loop Invariants 5

6. Calendar Assignment (continued)
int month, date; int startingDay; /* init from user input*/ for (month = 0; month < 12; month++) { const int daysInMonth = …; /* set # of days */ int dayOfWeek = 0; printf(…); //month name printf(…); //days of week } // for month
CS-2303, A-Term 2012
Loop Invariants 6

7. Calendar Assignment (continued)
int month, date; int startingDay; /* init from user input*/ for (month = 0; month < 12; month++) { const int daysInMonth = …; /* set # of days */ int dayOfWeek; printf(…); //month name printf(…); //days of week for (dayOfWeek = 0; dayOfWeek<startingDay; dayOfWeek++) printf(/*blanks*/);
… } // for month
Note that dayOfWeek is global to this loop.
It is remembered outside this inner loop.
CS-2303, A-Term 2012
Loop Invariants 7

8. Calendar Assignment (continued)
int month, date; int startingDay; /* init from user input*/ for (month = 0; month < 12; month++) { const int daysInMonth = …; /* set # of days */ int dayOfWeek; printf(…); //month name printf(…); //days of week for (dayOfWeek = 0; dayOfWeek<startingDay; dayOfWeek++) printf(/*blanks*/);
… } // for month
What is the loop invariant associated with this loop?
CS-2303, A-Term 2012
Loop Invariants 8

9. Calendar Assignment (continued)
int month, date; int startingDay; /* init from user input*/ for (month = 0; month < 12; month++) { const int daysInMonth = …; /* set # of days */ int dayOfWeek; printf(…); //month name printf(…); //days of week for (dayOfWeek = 0; dayOfWeek<startingDay; dayOfWeek++) printf(/*blanks*/);
for (int date = 1; date <=
daysInMonth; date++){
} // for date
} // for month
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Loop Invariants 9

10. Calendar Assignment (continued)
int month, date; int startingDay; /* init from user input*/ for (month = 0; month < 12; month++) { const int daysInMonth = …; /* set # of days */ int dayOfWeek; printf(…); //month name printf(…); //days of week for (dayOfWeek = 0; dayOfWeek<startingDay; dayOfWeek++) printf(/*blanks*/);
for (int date = 1; date <=
daysInMonth; date++){
} // for date
} // for month
What should the loop invariant be for this loop?
Why?
CS-2303, A-Term 2012
Loop Invariants 10

11. Calendar Assignment (continued)
int month, date; int startingDay; /* init from user input*/ for (month = 0; month < 12; month++) { const int daysInMonth = …; /* set # of days */ int dayOfWeek; printf(…); //month name printf(…); //days of week for (dayOfWeek = 0; dayOfWeek<startingDay; dayOfWeek++) printf(/*blanks*/);
for (int date = 1; date <= daysInMonth; date++){ printf("…", date); if (++dayOfWeek>6) { printf("\n"); dayOfWeek = 0; }; } // for date } // for month
CS-2303, A-Term 2012
Loop Invariants 11

12. Calendar Assignment (continued)
int month, date; int startingDay; /* init from user input*/ for (month = 0; month < 12; month++) { const int daysInMonth = …; /* set # of days */ int dayOfWeek; printf(…); //month name printf(…); //days of week for (dayOfWeek = 0; dayOfWeek<startingDay; dayOfWeek++) printf(/*blanks*/);
for (int date = 1; date <=
daysInMonth; date++){
printf("…", date);
if (++dayOfWeek>6) {
printf("\n");
dayOfWeek = 0; };
} // for date
} // for month
Is loop invariant preserved by this loop? Why?
CS-2303, A-Term 2012
Loop Invariants 12

13. Calendar Assignment (continued)
int month, date; int startingDay; /* init from user input*/ for (month = 0; month < 12; month++) { const int daysInMonth = …; /* set # of days */ int dayOfWeek; printf(…); //month name printf(…); //days of week for (dayOfWeek = 0; dayOfWeek<startingDay; dayOfWeek++) printf(/*blanks*/);
for (int date = 1; date <=
daysInMonth; date++){
printf("…", date);
if (++dayOfWeek>6) {
printf("\n");
dayOfWeek = 0; };
} // for date
if (dayOfWeek != 0)
} // for month
What about the original loop invariant for this (outer) loop?
CS-2303, A-Term 2012
Loop Invariants 13

14. Calendar Assignment (continued)
int month, date; int startingDay; /* init from user input*/ for (month = 0; month < 12; month++) { const int daysInMonth = …; /* set # of days */ int dayOfWeek; printf(…); //month name printf(…); //days of week for (dayOfWeek = 0; dayOfWeek<startingDay; dayOfWeek++) printf(/*blanks*/);
for (int date = 1; date <= daysInMonth; date++) { printf("…", date); if (++dayOfWeek>6) { printf("\n"); dayOfWeek = 0; }; } // for date if (dayOfWeek !=0) startingDay = dayOfWeek; } // for month
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Loop Invariants 14

15. Questions?
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CS-2303, A-Term 2012
Loop Invariants