Q1: A Plus Abs B

Fill in the blanks in the following function definition for adding a to the absolute value of b, without calling abs.

A1

"""
Return a + abs(b), but without calling abs.

>>> a_plus_abs_b(2, 3)
5
>>> a_plus_abs_b(2, -3)
5
"""

from operator import add, sub

def a_plus_abs_b(a, b):
    if b < 0:
        f = sub
    else:
        f = add
    return f(a, b)

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Q2: Two of Three

Write a function that takes three positive numbers and returns the sum of the squares of the two largest numbers. Use only a single line for the body of the function.

A2

"""
Return x * x + y * y, where x and y are the two largest members of 
the positive numbers a, b, and c.

>>> two_of_three(1, 2, 3)
13
>>> two_of_three(5, 3, 1)
34
>>> two_of_three(10, 2, 8)
164
>>> two_of_three(5, 5, 5)
50
"""

def two_of_three(a, b, c):
    return a * a + b * b + c * c - min(a, b, c) ** 2

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Q3: Largest Factor

Write a function that takes an integer n that is greater than 1 and returns the largest integer that is smaller than n and evenly divides n.

A3

"""
Return the largest factor of n that is smaller than n.

>>> largest_factor(15) # factors are 1, 3, 5
5
>>> largest_factor(80) # factors are 1, 2, 4, 5, 8, 10, 16, 20, 40
40
>>> largest_factor(13) # factor is 1 since 13 is prime
1
"""

def largest_factor(n):
    k = n - 1
    while k != 1:
        if n % k == 0:
            return k
        k -= 1
    return 1

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Q5: If Function vs Statement

Let's try to write a function that does the same thing as an if statement.

"""
Return true_result if condition is a true value, and false_result otherwise.

>>> if_function(True, 2, 3)
2
>>> if_function(False, 2, 3)
3
>>> if_function(3==2, 3+2, 3-2)
1
>>> if_function(3>2, 3+2, 3-2)
5
"""

def if_function(condition, true_result, false_result):
    if condition:
        return true_result
    else:
        return false_result

Despite the doctests above, this function actually does not do the same thing as an if statement in all cases. To prove this fact, write functions cond, true_func, and false_func such that with_if_statement prints the number 47, but with_if_function prints both 42 and 47.

"""
>>> result = with_if_statement()
47
>>> print(result)
None
"""

def with_if_statement():
    if cond():
        return true_func()
    else:
        return false_func()

"""
>>> result = with_if_function()
42
47
>>> print(result)
None
"""

def with_if_function():
    return if_function(cond(), true_func(), false_func())

A4

def cond():
    return False

def true_func():
    print(42)

def false_func():
    print(47)

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Q5: Hailstone

Douglas Hofstadter's Pulitzer-prize-winning book, Godel, Escher, Bach, poses the following mathematical puzzle.

1. Pick a positive integer n as the start.
2. If n is even, divide it by 2.
3. If n is odd, multiply it by 3 and add 1.
4. Continue this process until n is 1.

The number n will travel up and down but eventually end at 1 (at least for all numbers that have ever been tried -- nobody has ever proved that the sequence will terminate). Analogously, a hailstone travels up and down in the atmosphere before eventually landing on earth.

This sequence of values of n is often called a Hailstone sequence, Write a function that takes a single argument with formal parameter name n, prints out the hailstone sequence starting at n, and returns the number of steps in the sequence.

A5

"""
Print the hailstone sequence starting at n and return its length.

>>> a = hailstone(10)
10
5
16
8
4
2
1
>>> a
7
"""

def hailstone(n):
    counter = 1
    while n != 1:
        print(n)
        counter += 1
        if n % 2 == 0:
            n //= 2
        else:
            n = 3 * n + 1
    print(1)
    return counter