Extra Practice for Week 1 (Due never) Code Tracing (CT) and Reasoning Over Code (ROC) Exercises

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These problems will help you prepare for hw1 and quiz1. They are optional and you are encouraged to collaborate when working on them.

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Code Tracing (CT)
What will each of these print?

1. # CT1:
   
   def f(x):
       print('f', x)
       x += 1
       return (x**2) // 10
   
   def g(x):
       print('g', x)
       x = (7 * x) % 5
       return f(x + 3)
   
   x = 5
   print(f(g(f(x))) + x)

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2. # CT2:
   
   import math
   print(1 * 2 // 1 + 4 - 3)
   print(2**4/10 + (3 + 2**3) // 10)
   print(round(8/3) + max(8/3, math.ceil(8/3)))

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3. # CT3:
   
   def f(x, y):
       if (x > y):
           if (x > 2 * y): print('A')
           else: print('B')
       print('C')
   
   def g(x, y):
       if (abs(x % 10 - y % 10) < 2): print('D')
       elif (x % 10 > y % 10): print('E')
       else:
           if (x // 10 == y // 10): print('F')
           if (x // y > 0): print('G')
   f(3,4)
   g(1,2)

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4. # CT4:
   
   def f(x): 
       return 3 * x - 2
   
   def g(x): 
       return f(x + 3)
   
   def h(x):
       print(f(x - 2))
       x -= 2
       print(g(x))
       x %= 4
       return f(g(x) % 6) // 2
   print(3 + h(4))

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5. # CT5:
   
   def f(x): 
       return 2 * x + 1
   
   def g(x): 
       return f(x // 2)
   
   def h(x):   
       if (x % 2 == 0): 
           return f(x + g(x))   
       else:   
           return f(x) - g(x)
   def ct(x):
       print(h(x))
       print(h(x + 1))
   print(ct(5))

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Reasoning Over Code (ROC)
Find values for the parameters so the functons return True:

1. def rc1(x, y):
       return ((100 > x > y > 0) and 
               (x + y == 10) and 
               (y // x == x // y - 1))

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2. def rc2(x):
       return ((type(x) == int) and 
               (int(round(x**0.5))**2  ==  x) and 
               (x//10 == x%10 + 2))

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3. def rc3(x, y):
       return ((type(x) == type(y) == int) and
               (100 > x > y > 0) and
               (x % 10 == y // 10) and
               (y % 10 == x // 10) and
               (x - y == 9))

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4. def almostEqual(x, y):
       return abs(x - y) < 10**-9
   
   def rc4(n):
       if ((not isinstance(n, int)) or (n < 100) or (n > 999)): 
           return False
       a = n % 10
       b = n // 10
       return (almostEqual(b**0.5, a) and (a + b ==  42))

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5. def rc5(x):
       assert(type(x) == int)
       return ((x % 10 == x // 10 - 1) and (x // 9 * 9 == x))

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