# CS 61A: Homework 1

Due by 2pm on Wednesday, 9/10

Submission: See Lab 1 for submission instructions. We have provided a hw1.py starter file for the questions below.

Readings: You might find the following references useful:

### 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:
f = _____
else:
f = _____
return f(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 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
"""

### 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, a 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)
10
5
16
8
4
2
1
>>> a
7
"""

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

### Question 5: Challenge Problem (optional)

Write a one-line program that prints itself, using only the following features of the Python language:

• Number literals
• Assignment statements
• String literals that can be expressed using single or double quotes
• The arithmetic operators `+`, `-`, `*`, and `/`
• The built-in `print` function
• The built-in `eval` function, which evaluates a string as a Python expression
• The built-in `repr` function, which returns an expression that evaluates to its argument

You can concatenate two strings by adding them together with `+` and repeat a string by multipying it by an integer. Semicolons can be used to separate multiple statements on the same line. E.g.,

``````>>> c='c';print('a');print('b' + c * 2)
a
bcc``````

Hint: Explore the relationship between single quotes, double quotes, and the `repr` function applied to strings.

Place your solution in the multi-line string named `challenge_question_program` in `hw1.py`.