Computer Science 15-110, Fall 2010
Class Notes:  Recitation  2 (Fri 3-Sep)

1. Quiz 1
2. Practice Writing Functions
1. onesDigit and tensDigit
2. triangleArea
3. numberOfPoolBalls
4. almostEqual
5. isInteger
6. isPerfectSquare
7. isTriangular
8. fabricYards
9. fabricExcess
10. dayOfWeek
11. More Practice

Recitation 2

1. Quiz 1
   Quiz 1 will be administered at the start of recitation.
   
2. Practice Writing Functions
   
1. onesDigit and tensDigit
   These were covered via email (and will not be covered in recitation):  Writing Functions:  Annotated Examples
   
2. triangleArea
   Write a function that takes two numbers, a width and a height, and returns the area of a triangle with that width and height.  If either value is non-positive, your function should return 0.
   
   def triangleArea(width, height):
       return 42
   
   def testTriangleArea():
       print "Testing triangleArea... ",
       assert(triangleArea(1,1) == 0.5)
       assert(triangleArea(2,1) == 1)
       assert(triangleArea(0,5) == 0)
       assert(triangleArea(-5,10) == 0)
       print "Passed all tests!"
   
   testTriangleArea()
   
3. numberOfPoolBalls
   Write a function that takes the number of rows in a triangular rack of pool balls, and returns the total number of pool balls in that rack.  This just computes the sum 1 + .. .+ n, which of course is n(n+1)/2.  Simple enough.  Return 0 for negative values of n.
   
   def numberOfPoolBalls(rows):
       return 42
   
   def testNumberOfPoolBalls():
       print "Testing numberOfPoolBalls... ",
       assert(numberOfPoolBalls(0) == 0)
       assert(numberOfPoolBalls(1) == 1)
       assert(numberOfPoolBalls(2) == (1+2))
       assert(numberOfPoolBalls(3) == (1+2+3))
       assert(numberOfPoolBalls(10) == (1+2+3+4+5+6+7+8+9+10))
       assert(numberOfPoolBalls(100) == 5050)
       assert(numberOfPoolBalls(-5) == 0)
       print "Passed all tests!"
      
   testNumberOfPoolBalls()
   
4. almostEqual
   Write a function that takes two numbers and returns True if they are “almost equal” (within some very small epsilon of each other) and False otherwise.    Here, we'll use an epsilon of 0.000001.
   
   def almostEqual(d1, d2):
       epsilon = 0.000001
       return False
   
   def testAlmostEqual():
       print "Testing almostEqual... ",
       epsilon = 0.000001
       assert(almostEqual(0, 0) == True)
       assert(almostEqual(0, epsilon/2) == True)
       assert(almostEqual(epsilon/2, 0) == True)
       assert(almostEqual(0, 2*epsilon) == False)
       assert(almostEqual(2*epsilon, 0) == False)
       assert(almostEqual(-epsilon/3, +epsilon/3) == True)
       print "Passed all tests!"
      
   testAlmostEqual()
   
5. isInteger
   Write a function that takes a number and returns True if it is an integer value and False otherwise.  This is not testing whether the type is “int”, because for this question we will presume that 2.0 is an integer value, even though it is of type ‘float’.
   
   def isInteger(n):
       return False
   
   def testIsInteger():
       print "Testing isInteger... ",
       assert(isInteger(0) == True)
       assert(isInteger(5) == True)
       assert(isInteger(5.0) == True)
       assert(isInteger(-5) == True)
       assert(isInteger(-5.0) == True)
       assert(isInteger(5.1) == False)
       assert(isInteger(5.000000001) == False)
       assert(isInteger(-5.1) == False)
       assert(isInteger(-5.000000001) == False)
       print "Passed all tests!"
          
   testIsInteger()
   
6. isPerfectSquare
   Write a function that takes a number and returns True if it is a perfect square and False otherwise.
   
   def isPerfectSquare(n):
       return False
   
   def testIsPerfectSquare():
       print "Testing isPerfectSquare... ",
       assert(isPerfectSquare(0) == True)
       assert(isPerfectSquare(1) == True)
       assert(isPerfectSquare(4) == True)
       assert(isPerfectSquare(36) == True)
       assert(isPerfectSquare(12345*12345) == True)
       assert(isPerfectSquare(2) == False)
       assert(isPerfectSquare(5) == False)
       assert(isPerfectSquare(12345*12345 - 1) == False)
       assert(isPerfectSquare(-4) == False)
       print "Passed all tests!"
      
   testIsPerfectSquare()
   
7. isTriangular
   Write a function that takes a number n and returns true if it is “triangular” – that is, if it is the sum 1 + … + k for some value of k.
   
   def isTriangular(n):
       return False
   
   def testIsTriangular():
       print "Testing isTriangular... ",
       assert(isTriangular(0) == True)
       assert(isTriangular(1) == True)
       assert(isTriangular(1+2) == True)
       assert(isTriangular(1+2+3) == True)
       assert(isTriangular(1+2+3+4+5+6+7+8+9+10) == True)
       assert(isTriangular(2) == False)
       assert(isTriangular(1+2+3+4+5+6+7+8+9+10-1) == False)
       assert(isTriangular(-1) == False)
       print "Passed all tests!"
      
   testIsTriangular()
   
8. fabricYards
   Fabric must be purchased in whole yards.  Write a function that takes the number of inches of fabric desired, and returns the smallest number of whole yards of fabric that must be purchased.
   
   def fabricYards(inches):
       return 42
   
   def testFabricYards():
       print "Testing fabricYards... ",
       assert(fabricYards(0) == 0)
       assert(fabricYards(1) == 1)
       assert(fabricYards(35) == 1)
       assert(fabricYards(36) == 1)
       assert(fabricYards(37) == 2)
       assert(fabricYards(72) == 2)
       assert(fabricYards(73) == 3)
       assert(fabricYards(108) == 3)
       assert(fabricYards(109) == 4)
       assert(fabricYards(-12345) == 0)
       print "Passed all tests!"
          
   testFabricYards()
   
9. fabricExcess
   Write a function that takes the number of inches of fabric desired and returns the number of inches of excess fabric that must be purchased (as purchases must be in whole yards).
   
   def fabricExcess(inches):
       return 42
   
   def testFabricExcess():
       print "Testing fabricExcess... ",
       assert(fabricExcess(0) == 0)
       assert(fabricExcess(1) == 35)
       assert(fabricExcess(35) == 1)
       assert(fabricExcess(36) == 0)
       assert(fabricExcess(37) == 35)
       assert(fabricExcess(72) == 0)
       assert(fabricExcess(73) == 35)
       assert(fabricExcess(108) == 0)
       assert(fabricExcess(109) == 35)
       assert(fabricExcess(-12345) == 0)
       print "Passed all tests!"
          
   testFabricExcess()
   
10. dayOfWeek
    Write a function that takes a date represented by three integers, the month (1-12), the day (1-31), and the year, and returns an integer representing the day-of-week for that date, where Sunday is 1, Monday is 2, and so on, and Saturday is 7.
    
    While there are several ways to do this, you must use this formula (from the most-excellent web site mathforum.org):
          N = d + 2m + [3(m+1)/5] + y + [y/4] - [y/100] + [y/400] + 2
    Then the remainder when you divide N by 7 is the day-of-week, where Saturday is 0 and Friday is 6.  Note that these values for the days are not quite the same as those returned by this method.
    
    Here is mathforum's description of the formula:
        "d is the number or the day of the month, m is the number
         of the month, and y is the year. The brackets around the
         divisions mean to drop the remainder and just use the
         integer part that you get.
         Also, a VERY IMPORTANT RULE is the number to use for the
         months for January and February. The numbers of these months
         are 13 and 14 of the PREVIOUS YEAR. This means that to find
         the day of the week of New Year's Day [of 1998], 1/1/98,
         you must use the date 13/1/97."
    
    Note: you must make the adjustment to the month and year when appropriate.  So, for example, the date of New Year's Day for 1998 would be obtained in the natural way:  dayOfWeek(1, 1, 1998).  You may ignore the cases where the month, day, or year are out of bounds.
    
    def testDayOfWeek():
        print "Testing dayOfWeek... ",
        # On 2/5/2006, the Steelers won Super Bowl XL on a Sunday!
        assert(dayOfWeek(2, 5, 2006) == 1)
        # On 6/15/1215, the Magna Carta was signed on a Monday!
        assert(dayOfWeek(6, 15, 1215) == 2)
        # On 3/11/1952, the author Douglas Adams was born on a Tuesday!
        assert(dayOfWeek(3, 11, 1952) == 3)
        # on 4/12/1961, Yuri Gagarin became the first man in space, on a Wednesday!
        assert(dayOfWeek(4, 12, 1961) == 4)
        # On 7/4/1776, the Declaration of Independence was signed on a Thursday!
        assert(dayOfWeek(7, 4, 1776) == 5)
        # on 1/2/1920, Isaac Asimov was born on a Friday!
        assert(dayOfWeek(1, 2, 1920) == 6)
        # on 10/11/1975, Saturday Night Live debuted on a Saturday (of course)!
        assert(dayOfWeek(10, 11, 1975) == 7)
        print "Passed all tests!"
    
11. More Practice
    See http://kosbie.net/cmu/spring-10/15-110/handouts/quiz1-practice.html#Console_Programs
    Ignore the Java references; these problems can all be done clearly in Python.

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