# 61A Homework 1

Due by 11:59pm on Saturday, 6/28

Readings: You might find the following references useful:

Submission: See the online submission instructions. We have provided a hw1.py starter file for the questions below.

### 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 (only the TAs and Lecturers will be able to read it.)

### Question 1

We've seen that we can give 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)
5
>>> a_plus_abs_b(2, -3)
5
"""
if b < 0:
op = _____
else:
op = _____
return op(a, b)``````

### Question 2

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

### Question 3

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_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
"""
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 `c`, `t`, and `f` such that `with_if_statement` returns the number `1`, but `with_if_function` does not (it can do anything else):

``````def with_if_statement():
"""
>>> with_if_statement()
1
"""
if c():
return t()
else:
return f()

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

def c():

def t():

def f():

### Question 4

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
10
5
16
8
4
2
1
>>> a
7
"""