Lab 4
Note: This lab has more problems than we expect everyone to finish during the lab time. If you do not have time to finish all problems, you can continue working on them later, or return to them in a later lab.
Reminder about CodeBench#
You can test the lab code in Codebench here using your normal uid and password combination to login. Codebench allows you to write and execute code remotely. If you submit code for an exercise, it will also allow your tutor to view the code you have written, so they can give you feedback or assistance if things are not working correctly. Finally, if you submit a solution to an exercise, Codebench will run some tests on your code and tell you if you pass or fail. This will give you some feedback in the event that you need to keep working on lab exercises after the scheduled time is complete.
It’s important to note that you are not required to use Codebench for the lab exercises (i.e. - they are not part of the course assessment scheme). It is just here as a learning tool. You can attempt the lab exercises in your normal Python development environment if you wish.
It is also worth noting that not every exercise works well in Codebench. Some modules (such as numpy) are not available, and there is no Python console. For these exercises, you will have to complete them in your normal Python development environment and ask for assistance from your tutors in Teams.
Objectives#
The purpose of this week’s lab is to:
- understand the indexing of (1-dimensional) sequences;
- do some computations over sequences that require iterating through them using loops; and
- practice reading and debugging code.
Exercise 0: Reading and debugging code#
The following are attempts to define a function that takes
three (numeric) arguments and checks if any one of them is equal to
the sum of the other two. For example, any_one_is_sum(1, 3, 2)
should return True
(because 3 == 1 + 2
), while
any_one_is_sum(0, 1, 2)
should return False
.
(a) All of the functions below are incorrect. For each of them, find examples of arguments that cause it to return the wrong answer.
Function 1#
def any_one_is_sum(a,b,c):
sum_c=a+b
sum_b=a+c
sum_a=b+c
if sum_c == a+b:
if sum_b == c+a:
if sum_a == b+c:
return True
else:
return False
Function 2#
def any_one_is_sum(a,b,c):
if b + c == a:
print(True)
if c + b == a:
print(True)
else:
print(False)
return False
Function 3#
def any_one_is_sum(a, b, c):
if a+b==c and a+c==b:
return True
else:
return False
(b) For each of the three functions above, can you work out how they are intended to work? That is, what was the idea of the programmer who wrote them? What comments would be useful to add to explain the thinking? Is it possible to fix them by making only a small change to each function?
Exercise 1: Debugging loops#
Below are two attempted solutions to the problems of summing the odd and even digits in a number (from Lab 3), respectively. Both of them, however, have some problems: For some arguments, they may return the wrong answer, or not return at all because the loop never ends.
(a) For each of the two functions, find arguments that cause it to return an incorrect answer, and arguments that cause it to get stuck in an infinite loop (either or both may be possible). Arguments to the function must (of course!) be non-negative integers.
Hint: Add print
calls inside the loop to see what is happening.
Print the variables that appear in the loop condition, so you can see
if they are changing or not (if they are not, then the loop is stuck).
def sum_odd_digits(number):
dsum = 0
# only count odd digits
while number % 2 != 0:
# add the last digit to the sum
digit = number % 10
dsum = dsum + digit
# divide by 10 (rounded down) to remove the last digit
number = number // 10
return dsum
def sum_even_digits(number):
m = 1 # the position of the next digit
dsum = 0 # the sum
while number % (10 ** m) != 0:
# get the m:th digit
digit = (number % (10 ** m)) // (10 ** (m - 1))
# only add it if even:
if digit % 2 == 0:
dsum = dsum + digit
m = m + 1
return dsum
(b) Like in the previous problem, can you work out how the functions are intended to work? That is, what was the idea of the programmer who wrote them? What comments would be useful to add to explain the thinking? Is it possible to fix the errors you uncovered in your testing by making only a small change to each function?
(c) (advanced) Here is a more complex function:
def mystery(m):
assert type(m) is int and m >= 0, "m must be a non-negative integer"
while m > 1:
i = 2
while i < m:
while m % i == 0:
m = m // i
i = i + 1
return i
(It is called mystery
because it’s not very obvious what it does.)
The mystery function is meant to work on any non-negative integer input, but some arguments will cause it to get stuck in an infinite loop. Can you find examples of arguments that will cause this?
Learning to read and debug code is a very important skill (and it will also show you the value of good naming and commenting!). There are more debugging exercises towards the end of the lab.
Sequence types#
We have already seen a number of times that all values in python
have a type, such as int
, float
, str
, etc.
To determine the type of a value we can use the function
type(_some expression_)
.
python has three built-in sequence types: lists (type list
),
strings (type str
) and tuples (type tuple
). These sequence
types are used to represent different kinds of ordered collections.
To write a list literal, write its elements, separated by commas, in a pair of square brackets:
In [1]: my_list = [1, 2, 3, 4, 5, 6]
In [2]: type(my_list)
Out [2]: ...
The elements that you write can be expressions. These are evaluated, and the resulting values become the elements of the list:
In [3]: my_list = [2, 2 + 1, 2 * 2, 2 + 3]
In [4]: my_list
Out [4]: ...
Indexing sequences#
All of list
, tuple
and string
are called sequence data types.
Every element in a sequence has an index (position). The first
element is at index 0. The length of a sequence is the number of
elements in the sequence. The index of the last element is the length
minus one. The built-in function len
returns the length of any
sequence.
Indexing a sequence selects a single element from the sequence (for
example, a character if the sequence is a string).
Python also allows indexing sequences from the end, using negative
indices. That is, -1
also refers to the last element in the sequence,
and -len(seq)
refers to the first.
Exercise 2(a)#
This exercise is to play with the list
sequence type.
Execute the following in the python shell.
For each expression, try to work out what the output will be before
you evaluate the expression.
In [1]: my_list = [1, 2, 3, 4, 5, 6]
In [2]: my_list[1]
Out [2]: ...
In [3]: my_list[4]
Out [3]: ...
In [4]: my_list[-1]
Out [4]: ...
In [5]: L = len(my_list)
In [6]: my_list[L - 1]
Out [6]: ...
In [7]: my_list[1 - L]
Out [7]: ...
They should all run without error. Is the result of each expression what you expected?
Iteration over sequences#
Python has two kinds of loop statements: the while
loop, which
repeatedly executes a suite as long as a condition is true, and the
for
loop, which executes a suite once for every element of a
sequence. (To be precise, the for
loop works not only on sequences
but on any type that is iterable. All sequences are iterable, but
later in the course we will see examples of types that are iterable
but not sequences.)
Both kinds of loop can be used to iterate over a sequence.
Which one is most appropriate to implement some function depends on
what the function needs to do with the sequence.
The for
loop is simpler to use, but only allows you to look at one
element at a time. The while
loop is more complex to use (you must
initialise and update an index variable, and specify the loop condition
correctly) but allows you greater flexibility; for example, you can
skip elements in the sequence (increment the index by more than one)
or look at elements in more than one position in each iteration.
In the lectures so far, we have mostly used while
loops, and they
are sufficient to solve all the problems in this lab. The syntax and execution of the for
loop is described in the
text books (Downey: Section “Traversal with a for loop” in Chapter 8;
Punch & Enbody: Sections 2.1.4 and 2.2.13).
Exercise 3(a)#
The following function takes one argument, a sequence, and counts the
number of elements in it that are negative. It is implemented using
a while
loop.
def count_negative(sequence):
count = 0
index = 0
while index < len(sequence):
if sequence[index] < 0:
count = count + 1
index = index + 1
return count
Note that the function will work on any sequence type (e.g., both list
and tuple
), as long as it contains only numbers.
Rewrite this function so that it uses a for
loop instead.
To test your function, you can use the following inputs:
[-1, 0, -2, 1, -3, 2]
(3 negative numbers)[i for i in range(-10, 10, 3)]
(4 negative numbers)[-1, -1, -1, -1, -1]
(5 negative numbers)[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0 negative numbers)
You can create more test cases by making variations of these, or using other list creating functions.
Exercise 3(b)#
Write a function called is_increasing
that takes a sequence (of numbers)
and returns True
iff the elements in the array are in (non-strict)
increasing order. This means that every element is less than or equal
to the next one after it.
For example,
- for
[1, 5, 9]
the function should returnTrue
- for
[3, 3, 4]
the function should returnTrue
- for
[3, 4, 2]
the function should returnFalse
Is it best to use a for
loop or a while
loop for this problem?
(Note: Downey describes different solutions to a very similar problem
in Section “Looping with Indices” in Chapter 9.)
Test your function with the examples above, and with the examples you used for exercise 3(a).
Also test your function on an empty sequence (that is, a list or
array with no elements). An empty list can be created with the
expression []
.
Does your function work? Does it work on a sequence with one element?
Exercise 3(c)#
The average (or mean) of a sequence of numbers is the sum of the numbers
divided by the length of the sequence. You can calculate the average of
a sequence of numbers using python’s built-in function sum
(which works
on any sequence type, as long as it contains numbers), or
writing your own function using a loop over the sequence.
Write a function most_average(numbers)
which finds and returns
the number in the input that is closest to the average of the
numbers. (You can assume that the argument is a sequence of numbers.)
By closest, we mean the one that has the smallest absolute difference
from the average. You can use the built-in function abs
to find the
absolute value of a difference.
For example, most_average([1, 2, 3, 4, 5])
should
return 3
(the average of the numbers in the list is 3.0
, and 3
is clearly closest to this).
most_average([3, 4, 3, 1])
should also return 3
(the average is
2.75
, and 3
is closer to 2.75
than is any other number in the
list).
More debugging problems#
Exercise 4#
Here is a function that is meant to return the position (index) of
a given element in a sequence; if the element does not appear in the
sequence, it returns the length of the sequence.
For example, find_element([3,2,1,4], 1)
should return 2
, since
that is the index where we find a 1
.
def find_element(sequence, element):
i = 0
while sequence[i] != element:
if i < len(sequence):
i = i + 1
i = i + 1
return i
However, the function is not correct. For some inputs it will cause a runtime error. Find an example of arguments that cause an error to occur. Can you correct the error without introducing another?
Programming problems#
Note: These are more substantial programming problems. We do not expect that everyone will finish them within the lab time. If you do not have time to finish them during the lab, you should continue working on them later (at home, in the CSIT labs after teaching hours, or on one of the computers available in the university libraries or other teaching spaces).
Closest matches#
(a) Write two functions, smallest_greater(seq, value)
and
greatest_smaller(seq, value)
, that take as argument a sequence
and a value, and find the smallest element in the sequence that
is greater than the given value, and the greatest element in the
sequence that is smaller than the given value, respectively.
For example, if the sequence is [13, -3, 22, 14, 2, 18, 17, 6, 9]
and the target value is 4
, then the smallest greater element is 6
and the greatest smaller element is 2
.
- You can assume that all elements in the sequence are of the same type as the target value (that is, if the sequence is a list of numbers, then the target value is a number).
- You can not assume that the elements of the sequence are in any particular order.
- You should not assume that the sequence is of any particular type; it could be, for example, a list, or some other sequence type. Use only operations on the sequence that are valid for all sequence types.
- Does your function work if the sequence and target values are strings?
- What happens in your functions if the target value is smaller or greater than all elements in the sequence?
(b) Same as above, but assume the elements in the sequence are sorted in increasing order; can you find an algorithm that is more efficient in this case?
Counting duplicates#
If the same value appears more than once in a sequence, we say that
all copies of it except the first are duplicates. For example, in
[-1, 2, 4, 2, 0, 4]
, the second 2 and second 4 are duplicates;
in the string “Immaterium”, the ‘m’ is duplicated twice (but the ‘i’
is not a duplicate, because ‘I’ and ‘i’ are different characters).
Write a function count_duplicates(seq)
that takes as argument a
sequence and returns the number of duplicate elements (for example,
it should return 2 for both the sequences above). Your function
should work on any sequence type (for example, both lists and
strings), so use only operations that are common to all sequence
types. For the purpose of deciding if an element is a duplicate,
use standard equality, that is, the ==
operator.
Putting stuff in bins#
A histogram is way of summarising (1-dimensional) data that is often
used in descriptive statistics. Given a sequence of values, the range
of values (from smallest to greatest) is divided into a number of
sections (called “bins”) and the number of values that fall into each
bin is counted. For example, if the sequence is
[2.09, 0.5, 3.48, 1.44, 5.2, 2.86, 2.62, 6.31]
,
and we make three bins by placing the dividing lines at 2 and 4,
the resulting counts (that is, the histogram) will be the sequence
2, 4, 2
, because there are 2 elements less than 2, 4 elements
between 2 and 4, and 2 elements > 4.
(a) Write a function count_in_bin(values, lower, upper)
that
takes as argument a sequence and two values that define the lower and
upper sides of a bin, and counts the number of elements in the sequence
that fall into this bin. You should treat the bin interval as open on
the lower end and closed on the upper end; that is, use a strict
comparison lower < element
for the lower end and a non-strict
comparison element <= upper
for the upper end.
(b) Write a function histogram(values, dividers)
that takes
as argument a sequence of values and a sequence of bin dividers,
and returns the histogram as a sequence of a suitable type (say, a
list) with the counts in each bin. The number of bins is the number
of dividers + 1; the first bin has no lower limit and the last bin
has no upper limit. As in (a), elements that are equal to one of the
dividers are counted in the bin below.
For example, suppose the sequence of values is the numbers 1,..,10
and the bin dividers are [2, 5, 7]
; the histogram should be
[2, 3, 2, 3]
.
To test your function, you can create lists of random values using the random module:
In [1]: import random as rnd
In [2]: values = [rnd.randint(0, 100) for i in range(50)]
This creates a list of 50 integers between 0 and 100. The following creates 10 evenly sized bins covering the range of values:
In [2]: interval = max(values) - min(values)
In [3]: dividers = [min(values) + i * (interval / 10) for i in range(1, 10)]
As you increase the size of the value array, you should find that the histogram becomes more symmetrical and more even.
You can also test your function by comparing it with the histogram
function provided by NumPy (see help(numpy.histogram)
).