CMU 15-112: Fundamentals of Programming and Computer Science
Extra Practice for Week 1 (Due never) Code Tracing (CT) and Reasoning Over Code (ROC) Exercises

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)


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)))


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)


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))


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))

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


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


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))


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))


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