15-112 Spring 2013 Practice Quiz 1

* No calculators, no notes, no books, no computers.
SHOW YOUR WORK, CIRCLE YOUR ANSWERS.

1. Quick Answers.

   For positive int values x, y, and z:

   1. For any fixed value of y, what is the largest value of (x%y) where (x < y)?  where (x > y)?  where (x == y)?

   2. Is it true that (x % y % y) always equals (x % y)?  Why (or why not)?

   3. Under what conditions is this true:   x/y*y < x

   4. Give an expression equivalent to (x % y) that does not use the % operator.
       

2. Code Tracing

   Indicate what each will print:

   def f(x):
       print "f", x
       return 2*x
   
   def g(x,y,z):
       print "g", x, y, z
       y += f(x+f(z))
       print "g", x, y, z
   
   print g(2, f(2), 6)

   ############################################
   
   def h(x,y):
       print x/y, y/x, (x/y or y/x or 42)
   h(5, 23)

3. Reasoning Over Code

   Find arguments for the following functions that make them return True.

   def f(x,y):
       return ((type(x) == type(y) == int) and
               (100 > x > y > 0) and
               (x + y > 50) and
               (x == y+y*y**y))

   ############################################
   
   def g(x):
       a = int(x)
       b = int(round(10*(x%1)))
       print a,b
       return ((type(x) == type(x*1.0)) and
               (a != b) and
               (a == 4*b) and
               (10 >= a+b > 5))

4. Free Response

   Here you would be expected to write any of the functions from hw1, or from practice-thru-week1, or any variant of those, or anything similarly challenging.  For example:
   
   fourDigits(x,y)
   Write a function that takes two values which may or may not be numbers, and returns True if the two values are both integers, both between 0 and 99 (inclusive), and such that no digit occurs more than once in the two numbers (including leading zeros).  Your function may not crash even on non-integer inputs.