61A Homework 1

Due by 5pm on Wednesday, 9/11.

Due date extended. This homework was originally due Tuesday, 9/10. Due to problems with the submission system, the deadline was extended a day.

Submission. See the online submission instructions.

Readings. All problems in this homework can be solved with the subset of Python 3 introduced in sections 1.2, 1.3, 1.4, and 1.5 of the Composing Programs online text.

Welcome Survey. Please complete our welcome survey. The survey is for the instructors to get to know their students better, and your responses will be kept confidential to the staff. The survey is also due by 5pm on Tuesday, 9/10.

Q1. Recall that we can assign new names to existing functions. Fill in the blanks in the following function definition for adding a to the absolute value of b, without calling abs:

from operator import add, sub
def a_plus_abs_b(a, b):
    """Return a+abs(b), but without calling abs.

    >>> a_plus_abs_b(2, 3)
    >>> a_plus_abs_b(2, -3)
    if b < 0:
        op = _____
        op = _____
    return op(a, b)

Q2. Write a function that takes three positive numbers and returns the sum of the squares of the two largest numbers. Use only a single expression for the body of the function:

def two_of_three(a, b, c):
    """Return x*x + y*y, where x and y are the two largest of a, b, c.

    >>> two_of_three(1, 2, 3)
    >>> two_of_three(5, 3, 1)
    >>> two_of_three(10, 2, 8)
    >>> two_of_three(5, 5, 5)
    "*** YOUR CODE HERE ***"

Q3. Let's try to write a function that does the same thing as an if statement:

def if_function(condition, true_result, false_result):
    """Return true_result if condition is a true value, and false_result otherwise."""
    if condition:
        return true_result
        return false_result

This function actually does not do the same thing as an if statement in all cases. To prove this fact, write functions c, t, and f such that with_if_statement returns the number 1, but with_if_function does not:

def with_if_statement():
    if c():
        return t()
        return f()

def with_if_function():
    return if_function(c(), t(), f())

def c():
    "*** YOUR CODE HERE ***"

def t():
    "*** YOUR CODE HERE ***"

def f():
    "*** YOUR CODE HERE ***"

Q4. Douglas Hofstadter’s Pulitzer-prize-winning book, Gödel, 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, hailstone travels up and down in the atmosphere before eventually landing on earth.

The sequence of values of n is often called a Hailstone sequence, because hailstones also travel up and down in the atmosphere before falling to earth. 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:

def hailstone(n):
    """Print the hailstone sequence starting at n and return its length.

    >>> a = hailstone(10)  # Seven elements are 10, 5, 16, 8, 4, 2, 1
    >>> a
    "*** YOUR CODE HERE ***"

Hailstone sequences can get quite long! Try 27. What's the longest you can find?