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.
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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)
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
"""
"*** YOUR CODE HERE ***"
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():
"*** YOUR CODE HERE ***"
def t():
"*** YOUR CODE HERE ***"
def f():
"*** YOUR CODE HERE ***"
Douglas Hofstadter’s Pulitzer-prize-winning book, Gödel, Escher, Bach, poses the following mathematical puzzle.
n
as the start.n
is even, divide it by 2.n
is odd, multiply it by 3 and add 1.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
"""
"*** YOUR CODE HERE ***"
Hailstone sequences can get quite long! Try 27. What's the longest you can find?