Homework 6
Due at 11:59:59 pm on Thursday, 10/19/2023.
Instructions
Download hw06.zip. Inside the archive, you will find starter files for the questions in this homework, along with a copy of the OK autograder.
Readings: This homework relies on following references:
Recursion
Question 1: Reduce
Write the recursive version of the function reduce
which takes
- reducer - a two-argument function that reduces elements to a single value
- seq - a sequence of values
- start - the starting value in the reduction. This is usually the identity of the reducer
If you're feeling stuck, think about the parameters of reduce
.
from operator import add, mul
def reduce(reducer, seq, start):
"""Reduce a sequence under a two-argument function starting from a start value.
>>> def add(x, y):
... return x + y
>>> def mul(x, y):
... return x*y
>>> reduce(add, [1,2,3,4], 0)
10
>>> reduce(mul, [1,2,3,4], 0)
0
>>> reduce(mul, [1,2,3,4], 1)
24
"""
"*** YOUR CODE HERE ***"
Use OK to test your code:
python3 ok -q reduce
Question 2: Remove Last from Sequence
Complete the recursive function remove_last
which creates a new list identical to the input list lst
but with the last element in the sequence that is equal to x
removed.
Hint: Remember that you can use negative indexing on lists! For example
lst[-1]
refers to the last element in a listlst
,lst[-2]
refers to the second to last element...
def remove_last(x, lst):
"""Create a new list that is identical to lst but with the last
element from the list that is equal to x removed.
>>> remove_last(1,[])
[]
>>> remove_last(1,[1])
[]
>>> remove_last(1,[1,1])
[1]
>>> remove_last(1,[2,1])
[2]
>>> remove_last(1,[3,1,2])
[3, 2]
>>> remove_last(1,[3,1,2,1])
[3, 1, 2]
>>> remove_last(5, [3, 5, 2, 5, 11])
[3, 5, 2, 11]
"""
"*** YOUR CODE HERE ***"
Illustrated here is a more complete doctest that shows good testing methodology. It is a little cumbersome as documentation, but you'll want to think about it for your projects. Test every condition that might come up. Then you won't be surprised when it does.
Use OK to test your code:
python3 ok -q remove_last
Question 3: Map
Write the recursive version of the function map
which takes
- m - a one-argument function that you want to map onto each element in the list.
- s - a sequence of values
def map(f, seq):
"""
Map a function f onto a sequence.
>>> def double(x):
... return x * 2
>>> def square(x):
... return x ** 2
>>> def toLetter(x):
... alpha = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']
... return alpha[x%26]
>>> map(double, [1,2,3,4])
[2, 4, 6, 8]
>>> map(square, [1, 2, 3, 4, 5, 10])
[1, 4, 9, 16, 25, 100]
>>> map(toLetter, [3, 0, 19, 0])
['d', 'a', 't', 'a']
"""
"*** YOUR CODE HERE ***"
Use OK to test your code:
python3 ok -q map
Question 4: Hailstone
For the hailstone
function from previously, you pick a positive
integer n
as the start. If n
is even, divide it by 2. If n
is
odd, multiply it by 3 and add 1. Repeat this process until n
is 1.
Write a recursive version of hailstone that prints out the values of
the sequence and returns the number of steps.
def hailstone_iterative(n):
"""Print out the hailstone sequence starting at n, and return the
number of elements in the sequence.
>>> a = hailstone_iterative(10)
10
5
16
8
4
2
1
>>> a
7
"""
"*** YOUR CODE HERE ***"
def hailstone_recursive(n):
"""Print out the hailstone sequence starting at n, and return the
number of elements in the sequence.
>>> a = hailstone_recursive(10)
10
5
16
8
4
2
1
>>> a
7
"""
"*** YOUR CODE HERE ***"
Use OK to test your code:
python3 ok -q hailstone_iterative
python3 ok -q hailstone_recursive
Tree Recursion
Question 5: Count Generations
Consider the following "family tree":
family_tree = [("Jordan", "Alex"), [ [("Taylor", "Morgan"), [ [("Riley", None), []], [("Avery", None), []] ]] ]]
In this family tree, we see a series of nested lists which takes the format [(parents), [children]]
. An empty list means that person has no children.
This tree represents 3 generations.
The goal is to count the maximum number of "generations" represented in the family tree. In this simple tree, there are 3 generations.
def count_generations(family_tree):
"""
Count the number of generations in a nested list-based family tree.
>>> count_generations([("A"), []])
1
>>> count_generations([("A"), [[("B"), []], [("C"), []] ] ])
2
>>> family_tree = [("Jordan", "Alex"), [
... [("Taylor", "Morgan"), [
... [("Riley", None), []],
... [("Avery", None), []]
... ]]
... ]]
>>> count_generations(family_tree)
3
>>> family_tree = [("Jordan", "Alex"), [
... [("Taylor", "Morgan"), [
... [("Riley", "Sam"), [
... [("Avery", None), []]
... ]]
... ]],
... [("Casey", "Jamie"), [
... [("Quinn", "Chris"), [
... [("Dakota", None), []],
... [("Skyler", None), []]
... ]],
... [("Jesse", "Jordan"), []]
... ]]
... ]]
>>> count_generations(family_tree)
4
"""
if not family_tree:
return 0
parents = family_tree[0]
children = family_tree[1]
"*** YOUR CODE HERE ***"
Use OK to test your code:
python3 ok -q count_generations
Submission
When you are done, submit your file to Gradescope. You only need to upload the following files:
hw06.py