Laboratory Exercise on Conditionals and Loops in C

Goals

This laboratory exercise provides practice with basic elements of the C programming language. Specifically, the lab emphasizes conditional (if) and looping (for, while) constructs.

Steps for this Lab

1. Classifying Triangles:
   [This problem is based on an exercise by Darrah Chavey, Beloit College.]

   Write a C program that reads the lengths of three sides of a triangle and prints out the classification of the triangle as follows:

   • invalid input: all sides must have lengths that are strictly positive
   • not a triangle: the sum of any two sides must be less than the length of the third
   • scalene triangle: no two sides have equal length
   • isosceles triangle: two sides (but not the third) are equal
   • equilateral triangle: all three sides are equal

   In this problem, you should assume that the input values are all numbers, although error checking may indicate some numbers are negative or zero.

2. Computing the Greatest Common Divisor (Euclidean Algorithm):
   [The following is an edited and abridged version of Section 4.1 from Problems for Computer Solutions Using FORTRAN by Henry M. Walker, Winthrop Publishers, 1980 and is used with permission of the copyright holder.]

   Let N and M be two positive integers. The greatest common divisor of N and M, denoted gcd (M, N), is defined to be the positive integer D such that

   1. D divides N and M, and
   2. D is the largest integer dividing both N and M; i.e., every integer E that divides both N and M also divides D.

   For example, 2 = gcd (6, 8); 4 = gcd (4, 12); 1 = gcd (8, 9); 6 = gcd (66, 24).

   Algorithm: The algorithm proceeds by long division -- keeping track of subsequent remainders:

   • Step 1: Determine the remainder R₁, when N is divided by M.
   • Step 2: Determine the remainder R₂, when M is divided by R₁.
   • Step 3: Determine the remainder R₃, when R₁ is divided by R₂.
   • Step i: Determine the remainder R_i, when R_i-2 is divided by R_i-1.
   • Step i+1: Determine the remainder R_i+1, when R_i-1 is divided by R_i.

   This process continues until we find a remainder R_i+1 which is 0. Then R_i = gcd (M, N).

   Example:

   1. Divide 66 by 24: remainder is 18.
   2. Divide 24 by 18: remainder is 6
   3. Divide 18 by 6: remainder is 0, so we can stop.

      Thus, 6 = gcd (66, 24).

   Write a C program that reads two positive integers from the keyboard and computers and prints their greatest common divisor -- using the Euclidean Algorithm.

3. (Challenge Problem — Optional)
   A Baby Sitting Problem: A baby sitter charges $1.50 per hour until 9:00 pm (while the kids are still up), $1.00 per hour between 9:00 pm and midnight, and $1.25 per hour after midnight (since late night baby sitting interferes with morning classes).

   Write a program that reads the sitter's starting time in hours and minutes and the ending time in hours and minutes and then computes the sitter's fee. Assume all times are between 6:00 pm and 6:00 am, and hours should be entered as being between 0 and 12 (inclusive). Hours outside the range of 0 to 12 should be considered invalid.

   • The hour 6 should be considered as 6:00 pm, when it is entered as a starting time.
   • The hour 6 should be considered as 6:00 am, when it is entered as an ending time.

   The following table may clarify allowed time values for this problem.

   Starting	Starting	Ending	Ending	Starting	Ending
   Hour	Minutes	Hour	Minutes	Time	time
   8	0	3	30	8:00pm	3:30am
   6	0	0	45	6:00pm	12:45am
   12	0	6	0	12:00am (midnight)	6:00am

   Additional Notes:

   1. As illustrated in this table, an hour of 0 or 12 is interpreted the same, as midnight.
   2. You may not use a 24 hour clock for this problem.
   3. Times must be given in hours and minutes (as two nonnegative integer values).

This document is available on the World Wide Web as

     http://www.cs.grinnell.edu/~walker/courses/201.sp05/lab-intro-c.html

created 31 August 1998 last revised 8 April 2008
For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.