实验9: 期中复习
Lab 9: Midterm Review
Due by 11:59pm on Tuesday, October 27.
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初始文件
下载 lab09.zip。 在压缩包中,你可以找到本实验问题的初始文件,以及一份 Ok 自动评分器。
Submission
In order to facilitate midterm studying, solutions to this lab were released with the lab. We encourage you
to try out the problems and struggle for a while before looking at the solutions!
Note: You do not need to run python ok --submit
to receive
credit for this assignment.
必答题
Q1: All Questions Are Optional
Updated: The following questions in this assignment are not graded, but they are highly recommended to help you prepare for the upcoming midterm. You will receive credit for this lab even if you not complete these questions.
This question has no Ok tests.
Suggested Questions
Recursion and Tree Recursion
Q2: Subsequences
A subsequence of a sequence S
is a sequence of elements from S
, in the same
order they appear in S
, but possibly with elements missing. Thus, the lists
[]
, [1, 3]
, [2]
, and [1, 2, 3]
are some (but not all) of
the
subsequences of [1, 2, 3]
. Write a function that takes a list and returns a
list of lists, for which each individual list is a subsequence of the original
input.
In order to accomplish this, you might first want to write a function insert_into_all
that takes an item and a list of lists, adds the item to the beginning of nested list,
and returns the resulting list.
def insert_into_all(item, nested_list):
"""Assuming that nested_list is a list of lists, return a new list
consisting of all the lists in nested_list, but with item added to
the front of each.
>>> nl = [[], [1, 2], [3]]
>>> insert_into_all(0, nl)
[[0], [0, 1, 2], [0, 3]]
"""
return ______________________________
def subseqs(s):
"""Assuming that S is a list, return a nested list of all subsequences
of S (a list of lists). The subsequences can appear in any order.
>>> seqs = subseqs([1, 2, 3])
>>> sorted(seqs)
[[], [1], [1, 2], [1, 2, 3], [1, 3], [2], [2, 3], [3]]
>>> subseqs([])
[[]]
"""
if ________________:
________________
else:
________________
________________
使用 Ok 来测试你的代码:
python3 ok -q subseqs
Q3: Increasing Subsequences
Just like the last question, we want to write a function that takes a list and returns a list of lists, where each individual list is a subsequence of the original input.
This time we have another condition: we only want the subsequences for which
consecutive elements are nondecreasing. For example, [1, 3, 2]
is a
subsequence of [1, 3, 2, 4]
, but since 2 < 3, this subsequence would not
be included in our result.
Fill in the blanks to complete the implementation of the inc_subseqs
function. You may assume that the input list contains no negative elements.
You may use the provided helper function insert_into_all
, which takes in an
item
and a list of lists and inserts the item
to the front of each list.
def inc_subseqs(s):
"""Assuming that S is a list, return a nested list of all subsequences
of S (a list of lists) for which the elements of the subsequence
are strictly nondecreasing. The subsequences can appear in any order.
>>> seqs = inc_subseqs([1, 3, 2])
>>> sorted(seqs)
[[], [1], [1, 2], [1, 3], [2], [3]]
>>> inc_subseqs([])
[[]]
>>> seqs2 = inc_subseqs([1, 1, 2])
>>> sorted(seqs2)
[[], [1], [1], [1, 1], [1, 1, 2], [1, 2], [1, 2], [2]]
"""
def subseq_helper(s, prev):
if not s:
return ____________________
elif s[0] < prev:
return ____________________
else:
a = ______________________
b = ______________________
return insert_into_all(________, ______________) + ________________
return subseq_helper(____, ____)
使用 Ok 来测试你的代码:
python3 ok -q inc_subseqs
Q4: Number of Trees
A full binary tree is a tree where each node has either 2 branches or 0 branches, but never 1 branch.
How many possible full binary tree structures exist that have exactly n leaves?
For those interested in combinatorics, this problem does have a closed form solution):
def num_trees(n):
"""How many full binary trees have exactly n leaves? E.g.,
1 2 3 3 ...
* * * *
/ \ / \ / \
* * * * * *
/ \ / \
* * * *
>>> num_trees(1)
1
>>> num_trees(2)
1
>>> num_trees(3)
2
>>> num_trees(8)
429
"""
if ____________________:
return _______________
return _______________
使用 Ok 来测试你的代码:
python3 ok -q num_trees
Generators
Q5: Generators generator
Write the generator function make_generators_generator
, which takes a
zero-argument generator function g
and returns a generator that yields
generators. For each element e
yielded by the generator object returned by
calling g
, a new generator object is yielded that will generate entries 1
through e
yielded by the generator returned by g
.
def make_generators_generator(g):
"""Generates all the "sub"-generators of the generator returned by
the generator function g.
>>> def every_m_ints_to(n, m):
... i = 0
... while (i <= n):
... yield i
... i += m
...
>>> def every_3_ints_to_10():
... for item in every_m_ints_to(10, 3):
... yield item
...
>>> for gen in make_generators_generator(every_3_ints_to_10):
... print("Next Generator:")
... for item in gen:
... print(item)
...
Next Generator:
0
Next Generator:
0
3
Next Generator:
0
3
6
Next Generator:
0
3
6
9
"""
def gen(i):
for ___________ in ___________:
if _________________________:
_________________________
_______________________
_______________________
__________________________
for _________ in __________________:
______________________________
______________________________
使用 Ok 来测试你的代码:
python3 ok -q make_generators_generator
Objects
Q6: Keyboard
We'd like to create a Keyboard
class that takes in an arbitrary
number of Button
s and stores these Button
s in a dictionary. The
keys in the dictionary will be ints that represent the postition on the
Keyboard
, and the values will be the respective Button
. Fill out
the methods in the Keyboard
class according to each description,
using the doctests as a reference for the behavior of a Keyboard
.
class Button:
"""
Represents a single button
"""
def __init__(self, pos, key):
"""
Creates a button
"""
self.pos = pos
self.key = key
self.times_pressed = 0
class Keyboard:
"""A Keyboard takes in an arbitrary amount of buttons, and has a
dictionary of positions as keys, and values as Buttons.
>>> b1 = Button(0, "H")
>>> b2 = Button(1, "I")
>>> k = Keyboard(b1, b2)
>>> k.buttons[0].key
'H'
>>> k.press(1)
'I'
>>> k.press(2) #No button at this position
''
>>> k.typing([0, 1])
'HI'
>>> k.typing([1, 0])
'IH'
>>> b1.times_pressed
2
>>> b2.times_pressed
3
"""
def __init__(self, *args):
________________
for _________ in ________________:
________________
def press(self, info):
"""Takes in a position of the button pressed, and
returns that button's output"""
if ____________________:
________________
________________
________________
________________
def typing(self, typing_input):
"""Takes in a list of positions of buttons pressed, and
returns the total output"""
________________
for ________ in ____________________:
________________
________________
使用 Ok 来测试你的代码:
python3 ok -q Keyboard
Nonlocal
Q7: Advanced Counter
Complete the definition of make_advanced_counter_maker
,
which creates a function that creates counters. These counters can not
only update their personal count, but also a shared count for all
counters. They can also reset either count.
def make_advanced_counter_maker():
"""Makes a function that makes counters that understands the
messages "count", "global-count", "reset", and "global-reset".
See the examples below:
>>> make_counter = make_advanced_counter_maker()
>>> tom_counter = make_counter()
>>> tom_counter('count')
1
>>> tom_counter('count')
2
>>> tom_counter('global-count')
1
>>> jon_counter = make_counter()
>>> jon_counter('global-count')
2
>>> jon_counter('count')
1
>>> jon_counter('reset')
>>> jon_counter('count')
1
>>> tom_counter('count')
3
>>> jon_counter('global-count')
3
>>> jon_counter('global-reset')
>>> tom_counter('global-count')
1
"""
________________
def ____________(__________):
________________
def ____________(__________):
________________
"*** YOUR CODE HERE ***"
# as many lines as you want
________________
________________
使用 Ok 来测试你的代码:
python3 ok -q make_advanced_counter_maker
Mutable Lists
Q8: Trade
In the integer market, each participant has a list of positive integers to trade. When two participants meet, they trade the smallest non-empty prefix of their list of integers. A prefix is a slice that starts at index 0.
Write a function trade
that exchanges the first m
elements of list
first
with the first n
elements of list second
, such that the sums of those
elements are equal, and the sum is as small as possible. If no such prefix
exists, return the string 'No deal!'
and do not change either list. Otherwise
change both lists and return 'Deal!'
. A partial implementation is provided.
Hint: You can mutate a slice of a list using slice assignment. To do so, specify a slice of the list
[i:j]
on the left-hand side of an assignment statement and another list on the right-hand side of the assignment statement. The operation will replace the entire given slice of the list fromi
inclusive toj
exclusive with the elements from the given list. The slice and the given list need not be the same length.>>> a = [1, 2, 3, 4, 5, 6] >>> b = a >>> a[2:5] = [10, 11, 12, 13] >>> a [1, 2, 10, 11, 12, 13, 6] >>> b [1, 2, 10, 11, 12, 13, 6]
Additionally, recall that the starting and ending indices for a slice can be left out and Python will use a default value.
lst[i:]
is the same aslst[i:len(lst)]
, andlst[:j]
is the same aslst[0:j]
.
def trade(first, second):
"""Exchange the smallest prefixes of first and second that have equal sum.
>>> a = [1, 1, 3, 2, 1, 1, 4]
>>> b = [4, 3, 2, 7]
>>> trade(a, b) # Trades 1+1+3+2=7 for 4+3=7
'Deal!'
>>> a
[4, 3, 1, 1, 4]
>>> b
[1, 1, 3, 2, 2, 7]
>>> c = [3, 3, 2, 4, 1]
>>> trade(b, c)
'No deal!'
>>> b
[1, 1, 3, 2, 2, 7]
>>> c
[3, 3, 2, 4, 1]
>>> trade(a, c)
'Deal!'
>>> a
[3, 3, 2, 1, 4]
>>> b
[1, 1, 3, 2, 2, 7]
>>> c
[4, 3, 1, 4, 1]
"""
m, n = 1, 1
equal_prefix = lambda: ______________________
while _______________________________:
if __________________:
m += 1
else:
n += 1
if equal_prefix():
first[:m], second[:n] = second[:n], first[:m]
return 'Deal!'
else:
return 'No deal!'
使用 Ok 来测试你的代码:
python3 ok -q trade
Q9: Shuffle
Define a function shuffle
that takes a sequence with an even number of
elements (cards) and creates a new list that interleaves the elements
of the first half with the elements of the second half.
def card(n):
"""Return the playing card numeral as a string for a positive n <= 13."""
assert type(n) == int and n > 0 and n <= 13, "Bad card n"
specials = {1: 'A', 11: 'J', 12: 'Q', 13: 'K'}
return specials.get(n, str(n))
def shuffle(cards):
"""Return a shuffled list that interleaves the two halves of cards.
>>> shuffle(range(6))
[0, 3, 1, 4, 2, 5]
>>> suits = ['♡', '♢', '♤', '♧']
>>> cards = [card(n) + suit for n in range(1,14) for suit in suits]
>>> cards[:12]
['A♡', 'A♢', 'A♤', 'A♧', '2♡', '2♢', '2♤', '2♧', '3♡', '3♢', '3♤', '3♧']
>>> cards[26:30]
['7♤', '7♧', '8♡', '8♢']
>>> shuffle(cards)[:12]
['A♡', '7♤', 'A♢', '7♧', 'A♤', '8♡', 'A♧', '8♢', '2♡', '8♤', '2♢', '8♧']
>>> shuffle(shuffle(cards))[:12]
['A♡', '4♢', '7♤', '10♧', 'A♢', '4♤', '7♧', 'J♡', 'A♤', '4♧', '8♡', 'J♢']
>>> cards[:12] # Should not be changed
['A♡', 'A♢', 'A♤', 'A♧', '2♡', '2♢', '2♤', '2♧', '3♡', '3♢', '3♤', '3♧']
"""
assert len(cards) % 2 == 0, 'len(cards) must be even'
half = _______________
shuffled = []
for i in _____________:
_________________
_________________
return shuffled
使用 Ok 来测试你的代码:
python3 ok -q shuffle
Linked Lists
Q10: Insert
Implement a function insert
that takes a Link
, a value
, and an
index
, and inserts the value
into the Link
at the given
index
.
You can assume the linked list already has at least one element. Do not
return anything -- insert
should mutate the linked list.
Note: If the index is out of bounds, you can raise an
IndexError
with:raise IndexError
def insert(link, value, index):
"""Insert a value into a Link at the given index.
>>> link = Link(1, Link(2, Link(3)))
>>> print(link)
<1 2 3>
>>> insert(link, 9001, 0)
>>> print(link)
<9001 1 2 3>
>>> insert(link, 100, 2)
>>> print(link)
<9001 1 100 2 3>
>>> insert(link, 4, 5)
IndexError
"""
if ____________________:
____________________
____________________
____________________
elif ____________________:
____________________
else:
____________________
使用 Ok 来测试你的代码:
python3 ok -q insert
Q11: Deep Linked List Length
A linked list that contains one or more linked lists as elements is called a
deep linked list. Write a function deep_len
that takes in a (possibly deep)
linked list and returns the deep length of that linked list. The deep length of
a linked list is the total number of non-link elements in the list, as well as the
total number of elements contained in all contained lists. See the function's doctests
for examples of the deep length of linked lists.
Hint: Use
isinstance
to check if something is an instance of an object.
def deep_len(lnk):
""" Returns the deep length of a possibly deep linked list.
>>> deep_len(Link(1, Link(2, Link(3))))
3
>>> deep_len(Link(Link(1, Link(2)), Link(3, Link(4))))
4
>>> levels = Link(Link(Link(1, Link(2)), \
Link(3)), Link(Link(4), Link(5)))
>>> print(levels)
<<<1 2> 3> <4> 5>
>>> deep_len(levels)
5
"""
if ______________:
return 0
elif ______________:
return 1
else:
return _________________________
使用 Ok 来测试你的代码:
python3 ok -q deep_len
Q12: Linked Lists as Strings
Kevin and Jerry like different ways of displaying the linked list
structure in Python. While Kevin likes box and pointer diagrams,
Jerry prefers a more futuristic way. Write a function
make_to_string
that returns a function that converts the
linked list to a string in their preferred style.
Hint: You can convert numbers to strings using the str
function,
and you can combine strings together using +
.
>>> str(4)
'4'
>>> 'cs ' + str(61) + 'a'
'cs 61a'
def make_to_string(front, mid, back, empty_repr):
""" Returns a function that turns linked lists to strings.
>>> kevins_to_string = make_to_string("[", "|-]-->", "", "[]")
>>> jerrys_to_string = make_to_string("(", " . ", ")", "()")
>>> lst = Link(1, Link(2, Link(3, Link(4))))
>>> kevins_to_string(lst)
'[1|-]-->[2|-]-->[3|-]-->[4|-]-->[]'
>>> kevins_to_string(Link.empty)
'[]'
>>> jerrys_to_string(lst)
'(1 . (2 . (3 . (4 . ()))))'
>>> jerrys_to_string(Link.empty)
'()'
"""
def printer(lnk):
if ______________:
return _________________________
else:
return _________________________
return printer
使用 Ok 来测试你的代码:
python3 ok -q make_to_string
Trees
Q13: Prune Small
Complete the function prune_small
that takes in a Tree
t
and a
number n
and prunes t
mutatively. If t
or any of its branches
has more than n
branches, the n
branches with the smallest labels
should be kept and any other branches should be pruned, or removed,
from the tree.
def prune_small(t, n):
"""Prune the tree mutatively, keeping only the n branches
of each node with the smallest label.
>>> t1 = Tree(6)
>>> prune_small(t1, 2)
>>> t1
Tree(6)
>>> t2 = Tree(6, [Tree(3), Tree(4)])
>>> prune_small(t2, 1)
>>> t2
Tree(6, [Tree(3)])
>>> t3 = Tree(6, [Tree(1), Tree(3, [Tree(1), Tree(2), Tree(3)]), Tree(5, [Tree(3), Tree(4)])])
>>> prune_small(t3, 2)
>>> t3
Tree(6, [Tree(1), Tree(3, [Tree(1), Tree(2)])])
"""
while ___________________________:
largest = max(_______________, key=____________________)
_________________________
for __ in _____________:
___________________
使用 Ok 来测试你的代码:
python3 ok -q prune_small