# Python¶

## Basic concepts¶

### Basic input and output¶

The traditional “Hello, world” program is very simple in Python. You can run the program by selecting the cell by mouse and pressing control-enter on keyboard. Try editing the string in the quotes and rerunning the program.

[1]:

print("Hello world2!")

Hello world2!


Multiple strings can be printed. By default, they are concatenated with a space:

[2]:

print("Hello,", "John!", "How are you?")

Hello, John! How are you?


In the print function, numerical expression are first evaluated and then automatically converted to strings. Subsequently the strings are concatenated with spaces:

[3]:

print(1, "plus", 2, "equals", 1+2)

1 plus 2 equals 3


Reading textual input from the user can be achieved with the input function. The input function is given a string parameter, which is printed and prompts the user to give input. In the example below, the string entered by the user is stored the variable name. Try executing the program in the interactive notebook by pressing control-enter!

[4]:

name=input("Give me your name: ")
print("Hello,", name)

Give me your name: Jarkko
Hello, Jarkko


### Indentation¶

Repetition is possible with the for loop. Note that the body of for loop is indented with a tabulator or four spaces. Unlike in some other languages, braces are not needed to denote the body of the loop. When the indentation stops, the body of the loop ends.

[5]:

for i in range(3):
print("Hello")
print("Bye!")

Hello
Hello
Hello
Bye!


Indentation applies to other compound statements as well, such as bodies of functions, different branches of an if statement, and while loops. We shall see examples of these later.

The range(3) expression above actually results with the sequence of integers 0, 1, and 2. So, the range is a half-open interval with the end point excluded from the range. In general, expression range(n) gives integers 0, 1, 2, …, n-1. Modify the above program to make it also print the value of variable i at each iteration. Rerun the code with control-enter.

Fill in the missing piece in the solution stub file hello_world.py in folder src to make it print the following:

Hello, world!

Make sure you use correct indenting. You can run it with command python3 src/hello_world.py. If the output looks good, then you can test it with command tmc test. If the tests pass, submit your solution to the server with command tmc submit.

Fill in the stub solution to make the program work as follows. The program should ask the user for an input, and the print an answer as the examples below show.

What country are you from? Sweden
I have heard that Sweden is a beautiful country.

What country are you from? Chile
I have heard that Chile is a beautiful country.


Make a program that gives the following output. You should use a for loop in your solution.

4 multiplied by 0 is 0
4 multiplied by 1 is 4
4 multiplied by 2 is 8
4 multiplied by 3 is 12
4 multiplied by 4 is 16
4 multiplied by 5 is 20
4 multiplied by 6 is 24
4 multiplied by 7 is 28
4 multiplied by 8 is 32
4 multiplied by 9 is 36
4 multiplied by 10 is 40


### Variables and data types¶

We saw already earlier that assigning a value to variable is very simple:

[6]:

a=1
print(a)

1


Note that we did not need to introduce the variable a in any way. No type was given for the variable. Python automatically detected that the type of a must be int (an integer). We can query the type of a variable with the builtin function type:

[7]:

type(a)

[7]:

int


Note also that the type of a variable is not fixed:

[8]:

a="some text"
type(a)

[8]:

str


In Python the type of a variable is not attached to the name of the variable, like in C for instance, but instead with the actual value. This is called dynamic typing.

We say that a variable is a name that refers to a value or an object, and the assignment operator binds a variable name to a value.

The basic data types in Python are: int, float, complex, str (a string), bool (a boolean with values True and False), and bytes. Below are few examples of their use.

[9]:

i=5
f=1.5
b = i==4
print("Result of the comparison:", b)
c=0+2j                                 # Note that j denotes the imaginary unit of complex numbers.
print("Complex multiplication:", c*c)
s="conca" + "tenation"
print(s)

Result of the comparison: False
Complex multiplication: (-4+0j)
concatenation


The names of the types act as conversion operators between types:

[10]:

print(int(-2.8))
print(float(2))
print(int("123"))
print(bool(-2), bool(0))  # Zero is interpreted as False
print(str(234))

-2
2.0
123
True False
234


A byte is a unit of information that can represent numbers between 0 and 255. A byte consists of 8 bits, which can in turn represent either 0 or 1. All the data that is stored on disks or transmitted across the internet are sequences of bytes. Normally we don’t have to care about bytes, since our strings and other variables are automatically converted to a sequence of bytes when needed to. An example of the correspondence between the usual data types and bytes is the characters in a string. A single character is encoded as a sequence of one or more bytes. For example, in the common UTF-8 encoding the character c corresponds to the byte with integer value 99 and the character ä corresponds to sequence of bytes [195, 164]. An example conversion between characters and bytes:

[11]:

b="ä".encode("utf-8")     # Convert character(s) to a sequence of bytes
print(b)                  # Prints bytes in hexadecimal notation
print(list(b))            # Prints bytes in decimal notation

b'\xc3\xa4'
[195, 164]

[12]:

bytes.decode(b, "utf-8")  # convert sequence of bytes to character(s)

[12]:

'ä'


During this course we don’t have to care much about bytes, but in some cases, when loading data sets, we might have to specify the encoding if it deviates from the default one.

#### Creating strings¶

A string is a sequence of characters commonly used to store input or output data in a program. The characters of a string are specified either between single (') or double (") quotes. This optionality is useful if, for example, a string needs to contain a quotation mark: “I don’t want to go!”. You can also achieve this by escaping the quotation mark with the backslash: ‘I don’t want to go’.

The string can also contain other escape sequences like \n for newline and \t for a tabulator. See literals for a list of all escape sequences.

[13]:

print("One\tTwo\nThree\tFour")

One     Two
Three   Four


A string containing newlines can be easily given within triple double or triple single quotes:

[14]:

s="""A string
spanning over
several lines"""


Although we can concatenate strings using the + operator, for effiency reasons, one should use the join method to concatenate larger number of strings:

[15]:

a="first"
b="second"
print(a+b)
print(" ".join([a, b, b, a]))   # More about the join method later


firstsecond
first second second first


Sometimes printing by concatenation from pieces can be clumsy:

[16]:

print(str(1) + " plus " + str(3) + " is equal to " + str(4))
# slightly better
print(1, "plus", 3, "is equal to", 4)

1 plus 3 is equal to 4
1 plus 3 is equal to 4


The multiple catenation and quotation characters break the flow of thought. String interpolation offers somewhat easier syntax.

There are multiple ways to do sting interpolation:

• Python format strings
• the format method
• f-strings

Examples of these can be seen below:

[3]:

print("%i plus %i is equal to %i" % (1, 3, 4))     # Format syntax

print("{} plus {} is equal to {}".format(1, 3, 4)) # Format method

print(f"{1} plus {3} is equal to {4}")             # f-string

1 plus 3 is equal to 4
1 plus 3 is equal to 4
1 plus 3 is equal to 4


The i format specifier in the format syntacs corresponds to integers and the specifier f corresponds to floats. When using f-strings or the format method, integers use d instead. In format strings specifiers can usually be omitted and are generally used only when specific formatting is required. For example in f-strings f"{4:3d}" would specify the number 4 left padded with spaces to 3 digits.

It is often useful to specify the number of decimals when printing floats:

[2]:

print("%.1f %.2f %.3f" % (1.6, 1.7, 1.8))               # Old style
print("{:.1f} {:.2f} {:.3f}".format(1.6, 1.7, 1.8))     # newer style
print(f"{1.6:.1f} {1.7:.2f} {1.8:.3f}")                 # f-string

1.6 1.70 1.800
1.6 1.70 1.800
1.6 1.70 1.800


The specifier s is used for strings. An example:

[4]:

print("%s concatenated with %s produces %s" % ("water", "melon", "water"+"melon"))
print("{0} concatenated with {1} produces {0}{1}".format("water", "melon"))
print(f"{'water'} concatenated with {'melon'} produces {'water' + 'melon'}")

water concatenated with melon produces watermelon
water concatenated with melon produces watermelon
water concatenated with melon produces watermelon


Look here for more details about format specifiers, and for comparison between the old and new style of string interpolation.

Different ways of string interpolation have different strengths and weaknesses. Generally choosing which to use is a matter of personal preference. On this course examples and model solutions will predominantly use f-strings and the format method.

### Expressions¶

An expression is a piece of Python code that results in a value. It consists of values combined together with operators. Values can be literals, such as 1, 1.2, "text", or variables. Operators include arithmetics operators, comparison operators, function call, indexing, attribute references, among others. Below there are a few examples of expressions:

1+2
7/(2+0.1)
a
cos(0)
mylist[1]
c > 0 and c !=1
(1,2,3)
a<5
obj.attr
(-1)**2 == 1

Note that in Python the operator // performs integer division and operator / performs float division. The ** operator denotes exponentiation. These operators might therefore behave differently than in many other common languages.

As another example the following expression computes the kinetic energy of a non-rotating object: 0.5 * mass * velocity**2

### Statements¶

Statements are commands that have some effect. For example, a function call (that is not part of another expression) is a statement. Also, the variable assignment is a statement:

[21]:

i = 5
i = i+1    # This is a commong idiom to increment the value of i by one
i += 1     # This is a short-hand for the above


Note that in Python there are no operators ++ or -- unlike in some other languages.

It turns out that the operators + - * / // % & | ^ >> << ** have the corresponding augmented assignment operators += -= *= /= //= %= &= |= ^= >>= <<= **=

Another large set of statements is the flow-control statements such as if-else, for and while loops. We will look into these in the next sections.

In Python we have two kinds of loops: while and for. We briefly saw the for loop earlier. Let’s now look at the while loop. A while loop repeats a set of statements while a given condition holds. An example:

[22]:

i=1
while i*i < 1000:
print("Square of", i, "is", i*i)
i = i + 1
print("Finished printing all the squares below 1000.")

Square of 1 is 1
Square of 2 is 4
Square of 3 is 9
Square of 4 is 16
Square of 5 is 25
Square of 6 is 36
Square of 7 is 49
Square of 8 is 64
Square of 9 is 81
Square of 10 is 100
Square of 11 is 121
Square of 12 is 144
Square of 13 is 169
Square of 14 is 196
Square of 15 is 225
Square of 16 is 256
Square of 17 is 289
Square of 18 is 324
Square of 19 is 361
Square of 20 is 400
Square of 21 is 441
Square of 22 is 484
Square of 23 is 529
Square of 24 is 576
Square of 25 is 625
Square of 26 is 676
Square of 27 is 729
Square of 28 is 784
Square of 29 is 841
Square of 30 is 900
Square of 31 is 961
Finished printing all the squares below 1000.


Note again that the body of the while statement was marked with the indentation.

Another way of repeating statements is with the for statement. An example

[23]:

s=0
for i in [0,1,2,3,4,5,6,7,8,9]:
s = s + i
print("The sum is", s)

The sum is 45


The for loop executes the statements in the block as many times as there are elements in the given list. At each iteration the variable i refers to another value from the list in order. Instead of the giving the list explicitly as above, we could have used the generator range(10) which returns values from the sequence 0,1,…,9 as the for loop asks for a new value. In the most general form the for loop goes through all the elements in an iterable. Besides lists and generators there are other iterables. We will talk about iterables and generators later this week.

When one wants to iterate through all the elements in an iterable, then the for loop is a natural choice. But sometimes while loops offer cleaner solution. For instance, if we want to go through all Fibonacci numbers up till a given limit, then it is easier to do with a while loop.

In the main function print a multiplication table, which is shown below:

 1   2   3   4   5   6   7   8   9  10
2   4   6   8  10  12  14  16  18  20
3   6   9  12  15  18  21  24  27  30
4   8  12  16  20  24  28  32  36  40
5  10  15  20  25  30  35  40  45  50
6  12  18  24  30  36  42  48  54  60
7  14  21  28  35  42  49  56  63  70
8  16  24  32  40  48  56  64  72  80
9  18  27  36  45  54  63  72  81  90
10  20  30  40  50  60  70  80  90 100


For example at row 4 and column 9 we have 4*9=36.

Use two nested for loops to achive this. Note that you can use the following form to stop the print function from automatically starting a new line:

[24]:

print("text", end="")
print("more text")

textmore text


Print the numbers in a field with width four, so that the numbers are nicely aligned. For instructions on how adjust the field width refer to pyformat.info.

#### Decision making with the if statement¶

The if-else statement works as can be expected. Try running the below cell by pressing control+enter.

[25]:

x=input("Give an integer: ")
x=int(x)
if x >= 0:
a=x
else:
a=-x
print("The absolute value of %i is %i" % (x, a))

Give an integer: -1
The absolute value of -1 is 1


The general from of an if-else statement is

if condition1:
statement1_1
statement1_2
...
elif condition2:
statement2_1
statement2_2
...
...
else:
statementn_1
statementn_2
...


Another example:

[26]:

c=float(input("Give a number: "))
if c > 0:
print("c is positive")
elif c<0:
print("c is negative")
else:
print("c is zero")

Give a number: 3
c is positive


#### Breaking and continuing loop¶

Breaking the loop, when the wanted element is found, with the break statement:

[27]:

l=[1,3,65,3,-1,56,-10]
for x in l:
if x < 0:
break
print("The first negative list element was", x)

The first negative list element was -1


Stopping current iteration and continuing to the next one with the continue statement:

[3]:

from math import sqrt, log
l=[1,3,65,3,-1,56,-10]
for x in l:
if x < 0:
continue
print(f"Square root of {x} is {sqrt(x):.3f}")
print(f"Natural logarithm of {x} is {log(x):.4f}")

Square root of 1 is 1.000
Natural logarithm of 1 is 0.0000
Square root of 3 is 1.732
Natural logarithm of 3 is 1.0986
Square root of 65 is 8.062
Natural logarithm of 65 is 4.1744
Square root of 3 is 1.732
Natural logarithm of 3 is 1.0986
Square root of 56 is 7.483
Natural logarithm of 56 is 4.0254


Let us consider throwing two dice. (A dice can give a value between 1 and 6.) Use two nested for loops in the main function to iterate through all possible combinations the pair of dice can give. There are 36 possible combinations. Print all those combinations as (ordered) pairs that sum to 5. For example, your printout should include the pair (2,3). Print one pair per line.

### Functions¶

A function is defined with the def statement. Let’s do a doubling function.

[29]:

def double(x):
"This function multiplies its argument by two."
return x*2
print(double(4), double(1.2), double("abc")) # It even happens to work for strings!

8 2.4 abcabc


The double function takes only one parameter. Notice the docstring on the second line. It documents the purpose and usage of the function. Let’s try to access it.

[30]:

print("The docstring is:", double.__doc__)
help(double)   # Another way to access the docstring

The docstring is: This function multiplies its argument by two.
Help on function double in module __main__:

double(x)
This function multiplies its argument by two.



Most of Python’s builtin functions, classes, and modules should contain a docstring.

[31]:

help(print)

Help on built-in function print in module builtins:

print(...)
print(value, ..., sep=' ', end='\n', file=sys.stdout, flush=False)

Prints the values to a stream, or to sys.stdout by default.
Optional keyword arguments:
file:  a file-like object (stream); defaults to the current sys.stdout.
sep:   string inserted between values, default a space.
end:   string appended after the last value, default a newline.
flush: whether to forcibly flush the stream.



Here’s another example function:

[32]:

def sum_of_squares(a, b):
"Computes the sum of arguments squared"
return a**2 + b**2
print(sum_of_squares(3, 4))

25

Note the terminology: in the function definition the names a and b are called parameters of the function; in the function call, however, 3 and 4 are called arguments to the function.

It would be nice that the number of arguments could be arbitrary, not just two. We could pass a list to the function as a parameter.

[33]:

def sum_of_squares(lst):
"Computes the sum of squares of elements in the list given as parameter"
s=0
for x in lst:
s += x**2
return s
print(sum_of_squares([-2]))
print(sum_of_squares([-2,4,5]))

4
45


This works perfectly! There is however some extra typing with the brackets around the lists. Let’s see if we can do better:

[34]:

def sum_of_squares(*t):
"Computes the sum of squares of arbitrary number of arguments"
s=0
for x in t:
s += x**2
return s
print(sum_of_squares(-2))
print(sum_of_squares(-2,4,5))

4
45


The strange looking argument notation (the star) is called argument packing. It packs all the given positional arguments into a tuple t. We will encounter tuples again later, but it suffices now to say that tuples are immutable lists. With the for loop we can iterate through all the elements in the tuple.

Conversely, there is also syntax for argument unpacking. It has confusingly exactly same notation as argument packing (star), but they are separated by the location where used. Packing happens in the parameter list of the functions definition, and unpacking happens where the function is called:

[35]:

lst=[1,5,8]
print("With list unpacked as arguments to the functions:", sum_of_squares(*lst))
# print(sum_of_squares(lst))    # Does not work correctly

With list unpacked as arguments to the functions: 90


The second call failed because the function tried to raise the list of numbers to the second power. Inside the function body we have t=([1,5,8]), where the parentheses denote a tuple with one element, a list.

In addition to positional arguments we have seen so far, a function call can also have named arguments. An example will explain this concept best:

[36]:

def named(a, b, c):
print("First:", a, "Second:", b, "Third:", c)
named(5, c=7, b=8)

First: 5 Second: 8 Third: 7


Note that the named arguments didn’t need to be in the same order as in the function definition. The named arguments must come after the positional arguments. For example, the following function call is illegal named(a=5, 7, 8).

One can also specify an optional parameter by giving the parameter a default value. The parameters that have default values must come after those parameters that don’t. We saw that the parameters of the print function were of form print(value, ..., sep=' ', end='\n', file=sys.stdout, flush=False). There were four parameters with default values. If some default values don’t suit us, we can give them in the function call using the name of the parameter:

[37]:

print(1, 2, 3, end=' |', sep=' -*- ')
print("first", "second", "third", end=' |', sep=' -*- ')

1 -*- 2 -*- 3 |first -*- second -*- third |


We did not need to specify all the parameters with default values, only those we wanted to change.

Let’s go through another example of using parameters with default values:

[38]:

def length(*t, degree=2):
"""Computes the length of the vector given as parameter. By default, it computes
the Euclidean distance (degree==2)"""
s=0
for x in t:
s += abs(x)**degree
return s**(1/degree)
print(length(-4,3))
print(length(-4,3, degree=3))

5.0
4.497941445275415


With the default parameter this is the Euclidean distance, and if $$p\ne 2$$ it is called p-norm.

We saw that it was possible to use packing and unpacking of arguments with the * notation, when one wants to specify arbitrary number of positional arguments. This is also possible for arbitrary number of named arguments with the ** notation. We will talk about this more in the data structures section.

#### Visibility of variables¶

Function definition creates a new namespace (also called local scope). Variables created inside this scope are not available from outside the function definition. Also, the function parameters are only visible inside the function definition. Variables that are not defined inside any function are called global variables.

Global variable are readable also in local scopes, but an assignment creates a new local variable without rebinding the global variable. If we are inside a function, a local variable hides a global variable by the same name:

[39]:

i=2           # global variable
def f():
i=3       # this creates a new variable, it does not rebind the global i
print(i)  # This will print 3
f()
print(i)      # This will print 2

3
2


If you really need to rebind a global variable from a function, use the global statement. Example:

[40]:

i=2
def f():
global i
i=5       # rebind the global i variable
print(i)  # This will print 5
f()
print(i)      # This will print 5

5
5


Unlike languages like C or C++, Python allows defining a function inside another function. This nested function will have nested scope:

[41]:

def f():            # outer function
b=2
def g():        # inner function
#nonlocal b # Without this nonlocal statement,
b=3         # this will create a new local variable
print(b)
g()
print(b)
f()

3
2


Try first running the above cell and see the result. Then uncomment the nonlocal stamement and run the cell again. The global and nonlocal statements are similar. The first will force a variable refer to a global variable, and the second will force a variable to refer to the variable in the nearest outer scope (but not the global scope).

Write two functions: triple and square. Function triple multiplies its parameter by three. Function square raises its parameter to the power of two. For example, we have equalities triple(5)==15 and square(5)==25.

Part 1.

In the main function write a for loop that iterates through values 1 to 10, and for each value prints its triple and its square. The output should be as follows:

triple(1)==3 square(1)==1
triple(2)==6 square(2)==4
...


Part 2.

Now modify this for loop so that it stops iteration when the square of a value is larger than the triple of the value, without printing anything in the last iteration.

Note that the test cases check that both functions triple and square are called exactly once per iteration.

Create a program that can compute the areas of three shapes, triangles, rectangles and circles, when their dimensions are given.

An endless loop should ask for which shape you want the area be calculated. An empty string as input will exit the loop. If the user gives a string that is none of the given shapes, the message “unknown shape!” should be printed. Then it will ask for dimensions for that particular shape. When all the necessary dimensions are given, it prints the area, and starts the loop all over again. Use format specifier f for the area.

What happens if you give incorrect dimensions, like giving string “aa” as radius? You don’t have to check for errors in the input.

Example interaction:

Choose a shape (triangle, rectangle, circle): triangle
Give base of the triangle: 20
Give height of the triangle: 5
The area is 50.000000
Choose a shape (triangle, rectangle, circle): rectangel
Unknown shape!
Choose a shape (triangle, rectangle, circle): rectangle
Give width of the rectangle: 20
Give height of the rectangle: 4
The area is 80.000000
Choose a shape (triangle, rectangle, circle): circle
Give radius of the circle: 10
The area is 314.159265
Choose a shape (triangle, rectangle, circle):


### Data structures¶

The main data structures in Python are strings, lists, tuples, dictionaries, and sets. We saw some examples of lists, when we discussed for loops. And we saw briefly tuples when we introduced argument packing and unpacking. Let’s get into more details now.

#### Sequences¶

A list contains arbitrary number of elements (even zero) that are stored in sequential order. The elements are separated by commas and written between brackets. The elements don’t need to be of the same type. An example of a list with four values:

[42]:

[2, 100, "hello", 1.0]

[42]:

[2, 100, 'hello', 1.0]


A tuple is fixed length, immutable, and ordered container. Elements of tuple are separated by commas and written between parentheses. Examples of tuples:

[43]:

(3,)               # a singleton
(1,3)              # a pair
(1, "hello", 1.0); # a triple

Note the difference between (3) and (3,). Because the parentheses can also be used to group expressions, the first one defines an integer, but the second one defines a tuple with single element.

As we can see, both lists and tuples can contain values of different type.

List, tuples, and strings are called sequences in Python, and they have several commonalities:

• their length can be queried with the len function
• min and max function find the minimum and maximum element of a sequence, and sum adds all the elements of numbers together
• Sequences can be concatenated with the + operator, and repeated with the * operator: "hi"*3=="hihihi"
• Since sequences are ordered, we can refer to the elements of a sequences by integers using the indexing notation: "abcd"[2] == "c"
• Note that the indexing begins from 0
• Negative integers start indexing from the end: -1 refers to the last element, -2 refers to the second last, and so on

Above we saw that we can access a single element of a sequence using indexing. If we want a subsequence of a sequence, we can use the slicing syntax. A slice consists of elements of the original sequence, and it is itself a sequence as well. A simple slice is a range of elements:

[44]:

s="abcdefg"
s[1:4]

[44]:

'bcd'


Note that Python ranges exclude the last index. The generic form of a slice is sequence[first:last:step]. If any of the three parameters are left out, they are set to default values as follows: first=0, last=len(L), step=1. So, for instance “abcde”[1:]==”bcde”. The step parameter selects elements that are step distance apart from each other. For example:

[45]:

print([0,1,2,3,4,5,6,7,8,9][::3])

[0, 3, 6, 9]


In mathematics, the quadratic equation $$ax^2+bx+c=0$$ can be solved with the formula $$x=\frac{-b\pm \sqrt{b^2 -4ac}}{2a}$$.

Write a function solve_quadratic, that returns both solutions of a generic quadratic as a pair (2-tuple) when the coefficients are given as parameters. It should work like this:

print(solve_quadratic(1,-3,2))
(2.0,1.0)
(-1.0,-1.0)


You may want to use the math.sqrt function from the math module in your solution. Test that your function works in the main function!

#### Modifying lists¶

We can assign values to elements of a list by indexing or by slicing. An example:

[46]:

L=[11,13,22,32]
L[2]=10          # Changes the third element
print(L)

[11, 13, 10, 32]


Or we can assign a list to a slice:

[47]:

L[1:3]=[4]
print(L)

[11, 4, 32]


We can also modify a list by using mutating methods of the list class, namely the methods append, extend, insert, remove, pop, reverse, and sort. Try Python’s help functionality to find more about these methods: e.g. help(list.extend) or help(list).

Note that we cannot perform these modifications on tuples or strings since they are immutable

#### Generating numerical sequences¶

Trivial lists can be tedious to write: [0,1,2,3,4,5,6]. The function range creates numeric ranges automatically. The above sequence can be generated with the function call range(7). Note again that then end value is not included in the sequence. An example of using the range function:

[48]:

L=range(3)
for i in L:
print(i)
# Note that L is not a list!
print(L)

0
1
2
range(0, 3)


So L is not a list, but it is a sequence. We can for instace access its last element with L[-1]. If really needed, then it can be converted to a list with the list constructor:

[49]:

L=range(10)
print(list(L))

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Note that using a range consumes less memory than the corresponding list. This is because in a list all the elements are stored in the memory, whereas the range generates the requested elements only when needed. For example, when the for loop asks for the next element from the range at each iteration, only a single element from the range exists in memory at the same time. This makes a big difference when using large ranges, like range(1000000).

The range function works in similar fashion as slices. So, for instance the step of the sequence can be given:

[50]:

print(list(range(0, 7, 2)))

[0, 2, 4, 6]


#### Sorting sequences¶

In Python there are two ways to sort sequences. The sort method modifies the original list, whereas the sorted function returns a new sorted list and leaves the original intact. A couple of examples will demonstrate this:

[51]:

L=[5,3,7,1]
L.sort()      # here we call the sort method of the object L
print(L)
L2=[6,1,7,3,6]
print(sorted(L2))
print(L2)

[1, 3, 5, 7]
[1, 3, 6, 6, 7]
[6, 1, 7, 3, 6]


The parameter reverse=True can be given (both to sort and sorted) to get descending order of elements:

[52]:

L=[5,3,7,1]
print(sorted(L, reverse=True))

[7, 5, 3, 1]


Suppose we have two lists L1 and L2 that contain integers which are sorted in ascending order. Create a function merge that gets these lists as parameters and returns a new sorted list L that has all the elements of L1 and L2. So, len(L) should equal to len(L1)+len(L2). Do this using the fact that both lists are already sorted. You can’t use the sorted function or the sort method in implementing the merge method. You can however use these functions in the main function for creating inputs to the merge function. Test with a couple of examples in the main function that your solution works correctly.

Note: In Python argument lists are passed by reference to the function, they are not copied! Make sure you don’t modify the original lists of the caller.

Create a function named detect_ranges that gets a list of integers as a parameter. The function should then sort this list, and transform the list into another list where pairs are used for all the detected intervals. So 3,4,5,6 is replaced by the pair (3,7). Numbers that are not part of any interval result just single numbers. The resulting list consists of these numbers and pairs, separated by commas. An example of how this function works:

print(detect_ranges([2,5,4,8,12,6,7,10,13]))
[2,(4,9),10,(12,14)]


Note that the second element of the pair does not belong to the range. This is consistent with the way Python’s range function works. You may assume that no element in the input list appears multiple times.

#### Zipping sequences¶

The zip function combines two (or more) sequences into one sequence. If, for example, two sequences are zipped together, the resulting sequence contains pairs. In general, if n sequences are zipped together, the elements of the resulting sequence contains n-tuples. An example of this:

[53]:

L1=[1,2,3]
L2=["first", "second", "third"]
print(zip(L1, L2))               # Note that zip does not return a list, like range
print(list(zip(L1, L2)))         # Convert to a list

<zip object at 0x7fb8141907c8>
[(1, 'first'), (2, 'second'), (3, 'third')]


Here’s another example of using the zip function.

[7]:

days="Monday Tuesday Wednesday Thursday Friday Saturday Sunday".split()
weathers="rainy rainy sunny cloudy rainy sunny sunny".split()
temperatures=[10,12,12,9,9,11,11]
for day, weather, temperature in zip(days,weathers,temperatures):
print(f"On {day} it was {weather} and the temperature was {temperature} degrees celsius.")

# Or equivalently:
#for t in zip(days,weathers,temperatures):
#    print("On {} it was {} and the temperature was {} degrees celsius.".format(*t))

On Monday it was rainy and the temperature was 10 degrees celsius.
On Tuesday it was rainy and the temperature was 12 degrees celsius.
On Wednesday it was sunny and the temperature was 12 degrees celsius.
On Thursday it was cloudy and the temperature was 9 degrees celsius.
On Friday it was rainy and the temperature was 9 degrees celsius.
On Saturday it was sunny and the temperature was 11 degrees celsius.
On Sunday it was sunny and the temperature was 11 degrees celsius.


If the sequences are not of equal length, then the resulting sequence will be as long as the shortest input sequence is.

Write function interleave that gets arbitrary number of lists as parameters. You may assume that all the lists have equal length. The function should return one list containing all the elements from the input lists interleaved. Test your function from the main function of the program.

Example: interleave([1,2,3], [20,30,40], ['a', 'b', 'c']) should return [1, 20, 'a', 2, 30, 'b', 3, 40, 'c']. Use the zip function to implement interleave. Remember the extend method of list objects.

#### Enumerating sequences¶

In some other programming languages one iterates through the elements using their indices (0,1, …) in the sequence. In Python we normally don’t need to think about indices when iterating, because the for loop allows simpler iteration through the elements. But sometimes you really need to know the index of the current element in the sequence. In this case one uses Python’s enumerate function. In the next example we would like find the second occurrence of integer 5 in a list.

[55]:

L=[1,2,98,5,-1,2,0,5,10]
counter = 0
for i, x in enumerate(L):
if x == 5:
counter += 1
if counter == 2:
break
print(i)

7


The enumerate(L) function call can be thought to be equivalent to zip(range(len(L)), L).

#### Dictionaries¶

A dictionary is a dynamic, unordered container. Instead of using integers to access the elements of the container, the dictionary uses keys to access the stored values. The dictionary can be created by listing the comma separated key-value pairs in braces. Keys and values are separated by a colon. A tuple (key,value) is called an item of the dictionary.

Let’s demonstrate the dictionary creation and usage:

[56]:

d={"key1":"value1", "key2":"value2"}
print(d["key1"])
print(d["key2"])

value1
value2


Keys can have different types even in the same container. So the following code is legal: d={1:"a", "z":1}. The only restriction is that the keys must be hashable. That is, there has to be a mapping from keys to integers. Lists are not hashable, but tuples are!

There are alternative syntaxes for dictionary creation:

[57]:

dict([("key1", "value1"), ("key2", "value2"), ("key3", "value3")]) # list of items
dict(key1="value1", key2="value2", key3="value3");


If a key is not found in a dictionary, the indexing d[key] results in an error (exception KeyError). But an assignment with a non-existing key causes the key to be added in the dictionary associated with the corresponding value:

[58]:

d={}
d[2]="value"
print(d)

{2: 'value'}

[59]:

# d[1]   # This would cause an error


Dictionary object contains several non-mutating methods:

d.copy()
d.items()
d.keys()
d.values()
d.get(k[,x])


Some methods mutate the dictionary:

d.clear()
d.update(d1)
d.setdefault(k[,x])
d.pop(k[,x])
d.popitem()


Try out some of these in the below cell. You can find more info with help(dict) or help(dict.keys).

[60]:

d=dict(a=1, b=2, c=3, d=4, e=5)
d.values()

[60]:

dict_values([1, 2, 3, 4, 5])


#### Sets¶

Set is a dynamic, unordered container. It works a bit like dictionary, but only the keys are stored. And each key can be stored only once. The set requires that the keys to be stored are hashable. Below are a few ways of creating a set:

[61]:

s={1,1,1}
print(s)
s=set([1,2,2,'a'])
print(s)
s=set()  # empty set
print(s)
print(s)

{1}
{1, 2, 'a'}
set()
{7}


A more useful example:

[8]:

s="mississippi"
print(f"There are {len(set(s))} distinct characters in {s}")

There are 4 distinct characters in mississippi


The set provides the following non-mutating methods:

[63]:

s=set()
s1=set()
s.copy()
s.issubset(s1)
s.issuperset(s1)
s.union(s1)
s.intersection(s1)
s.difference(s1)
s.symmetric_difference(s1);


The last four operation can be tedious to write to create a more complicated expression. The alternative is to use the corresponding operator forms: |, &, -, and ^. An example of these:

[64]:

s=set([1,2,7])
t=set([2,8,9])
print("Union:", s|t)
print("Intersection:", s&t)
print("Difference:", s-t)
print("Symmetric difference", s^t)

Union: {1, 2, 7, 8, 9}
Intersection: {2}
Difference: {1, 7}
Symmetric difference {1, 7, 8, 9}


There are also the following mutating methods:

s.add(x)
s.clear()
s.pop()
s.remove(x)


And the set operators |, &, -, and ^ have the corresponding mutating, augmented assignment forms: |=, &=, -=, and ^=.

Write function distinct_characters that gets a list of strings as a parameter. It should return a dictionary whose keys are the strings of the input list and the corresponding values are the numbers of distinct characters in the key.

Use the set container to temporarily store the distinct characters in a string. Example of usage: distinct_characters(["check", "look", "try", "pop"]) should return { "check" : 4, "look" : 3, "try" : 3, "pop" : 2}.

#### Miscellaneous stuff¶

To find out whether a container includes an element, the in operator can be used. The operator returns a truth value. Some examples of the usage:

[65]:

print(1 in [1,2])
d=dict(a=1, b=3)
print("b" in d)
s=set()
print(1 in s)
print("x" in "text")

True
True
False
True


As a special case, for strings the in operator can be used to check whether a string is part of another string:

[66]:

print("issi" in "mississippi")
print("issp" in "mississippi")

True
False


Elements of a container can be unpacked into variables:

[10]:

first, second = [4,5]
a,b,c = "bye"
print(c)
d=dict(a=1, b=3)
key1, key2 = d
print(key1, key2)

e
a b


In membership testing and unpacking only the keys of a dictionary are used, unless either values or items (like below) are explicitly asked.

[11]:

for key, value in d.items():
print(f"For key '{key}' value {value} was stored")

For key 'a' value 1 was stored
For key 'b' value 3 was stored


To remove the binding of a variable, use the del statement. For example:

[69]:

s="hello"
del s
# print(s)    # This would cause an error


To delete an item from a container, the del statement can again be applied:

[70]:

L=[13,23,40,100]
del L[1]
print(L)

[13, 40, 100]


In similar fashion del can be used to delete a slice. Later we will see that del can delete attributes from an object.

Let d be a dictionary that has English words as keys and a list of Finnish words as values. So, the dictionary can be used to find out the Finnish equivalents of an English word in the following way:

d["move"]
["liikuttaa"]
d["hide"]
["piilottaa", "salata"]


Make a function reverse_dictionary that creates a Finnish to English dictionary based on a English to Finnish dictionary given as a parameter. The values of the created dictionary should be lists of words. It should work like this:

d={'move': ['liikuttaa'], 'hide': ['piilottaa', 'salata'], 'six': ['kuusi'], 'fir': ['kuusi']}
reverse_dictionary(d)
{'liikuttaa': ['move'], 'piilottaa': ['hide'], 'salata': ['hide'], 'kuusi': ['six', 'fir']}


Be careful with synonyms and homonyms!

Write function find_matching that gets a list of strings and a search string as parameters. The function should return the indices to those elements in the input list that contain the search string. Use the function enumerate.

An example: find_matching(["sensitive", "engine", "rubbish", "comment"], "en") should return the list [0, 1, 3].

### Compact way of creating data structures¶

We can now easily create complicated data structures using for loops:

[71]:

L=[]
for i in range(10):
L.append(i**2)
print(L)

[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]


Because this kind of pattern is often used, Python offers a short-hand for this. A list comprehension is an expression that allows creating complicated lists on one line. The notation is familiar from mathematics:

$$\{a^3 : a \in \{1,2, \ldots, 10\}\}$$

The same written in Python as a list comprehension:

[72]:

L=[ a**3 for a in range(1,11)]
print(L)

[1, 8, 27, 64, 125, 216, 343, 512, 729, 1000]


The generic form of a list comprehension is: [ expression for element in iterable lc-clauses ]. Let’s break this syntax into pieces. The iterable can be any sequence (or something more general). The lc-clauses consists of zero or more of the following clauses:

• for elem in iterable
• if expression

A more complicated example. How would you describe these numbers?

[73]:

L=[ 100*a + 10*b +c for a in range(0,10)
for b in range(0,10)
for c in range(0,10)
if a <= b <= c]
print(L)

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 66, 67, 68, 69, 77, 78, 79, 88, 89, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 133, 134, 135, 136, 137, 138, 139, 144, 145, 146, 147, 148, 149, 155, 156, 157, 158, 159, 166, 167, 168, 169, 177, 178, 179, 188, 189, 199, 222, 223, 224, 225, 226, 227, 228, 229, 233, 234, 235, 236, 237, 238, 239, 244, 245, 246, 247, 248, 249, 255, 256, 257, 258, 259, 266, 267, 268, 269, 277, 278, 279, 288, 289, 299, 333, 334, 335, 336, 337, 338, 339, 344, 345, 346, 347, 348, 349, 355, 356, 357, 358, 359, 366, 367, 368, 369, 377, 378, 379, 388, 389, 399, 444, 445, 446, 447, 448, 449, 455, 456, 457, 458, 459, 466, 467, 468, 469, 477, 478, 479, 488, 489, 499, 555, 556, 557, 558, 559, 566, 567, 568, 569, 577, 578, 579, 588, 589, 599, 666, 667, 668, 669, 677, 678, 679, 688, 689, 699, 777, 778, 779, 788, 789, 799, 888, 889, 899, 999]


If one needs only to iterate through the list once, it is more memory efficient to use a generator expression instead. The only thing that changes syntactically is that the surrounding brackets are replaced by parentheses:

[74]:

G = ( 100*a + 10*b + c for a in range(0,10)
for b in range(0,10)
for c in range(0,10)
if a <= b <= c )
print(sum(G))   # This iterates through all the elements from the generator
print(sum(G))   # It doesn't restart from the beginning, so all elements are already consumed

60885
0

Note above that one can only iterate through the generator once.

Similary a dictionary comprehension creates a dictionary:

[75]:

d={ k : k**2 for k in range(10)}
print(d)

{0: 0, 1: 1, 2: 4, 3: 9, 4: 16, 5: 25, 6: 36, 7: 49, 8: 64, 9: 81}


And a set comprehension creates a set:

[76]:

s={ i*j for i in range(10) for j in range(10)}
print(s)

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 54, 56, 63, 64, 72, 81}


Redo the earlier exercise which printed all the pairs of two dice results that sum to 5. But this time use a list comprehension. Print one pair per line.

### Processing sequences¶

In this section we will go through some useful tools, that are maybe familiar to you from some functional programming language like lisp or haskell. These functions rely on functions being first-class objects in Python, that is, you can

• pass a function as a parameter to another function
• return a function as a return value from some function
• store a function in a data structure or a variable

We will talk about map, filter, and reduce functions. We will also cover how to create functions with no name using the lambda expressions.

#### Map and lambda functions¶

The map function gets a list and a function as parameters, and it returns a new list whose elements are elements of the original list transformed by the parameter function. For this to work the parameter function must take exactly one value in and return a value out. An example will clarify this concept:

[77]:

def double(x):
return 2*x
L=[12,4,-1]
print(map(double, L))

<map object at 0x7fb81413ef60>


The map function returns a map object for efficiency reasons. However, since we only want print the contents, we first convert it to a list and then print it:

[78]:

print(list(map(double,L)))

[24, 8, -2]


When one reads numeric data from a file or from the internet, the numbers are usually in string form. Before they can be used in computations, they must first be converted to ints or floats. A simple example will showcase this.

[79]:

s="12 43 64 6"
L=s.split()        # The split method of the string class, breaks the string at whitespaces
# to a list of strings.
print(L)
print(sum(map(int, L)))  # The int function converts a string to an integer

['12', '43', '64', '6']
125


Sometimes it feels unnecessary to write a function is you are only going to use it in one map function call. For example the function

[80]:

def add_double_and_square(x):
return 2*x+x**2


It is not likely that you will need it elsewhere in your program. The solution is to use an expression called lambda to define a function with no name. Because it is an expression, we can put it, for instance, in an argument list of a function call. The lambda expression has the form lambda param1,param2, ... : expression, where after the lambda keyword you list the parameters of the function, and after the colon is the expression that uses the parameters to compute the return value of the function. Let’s replace the above add_double_and_square function with a lambda function and apply it to a list using the map function.

[81]:

L=[2,3,5]
print(list(map(lambda x : 2*x+x**2, L)))

[8, 15, 35]


Write a function transform that gets two strings as parameters and returns a list of integers. The function should split the strings into words, and convert these words to integers. This should give two lists of integers. Then the function should return a list whose elements are multiplication of two integers in the respective positions in the lists. For example transform("1 5 3", "2 6 -1") should return the list of integers [2, 30, -3].

You have to use split, map, and zip functions/methods. You may assume that the two input strings are in correct format.

#### Filter function¶

The filter function takes a function and a list as parameters. But unlike with the map construct, now the parameter function must take exactly one parameter and return a truth value (True or False). The filter function then creates a new list with only those elements from the original list for which the parameter function returns True. The elements for which the parameter function returns False are filtered out. An example will demonstrate the filter function:

[1]:

def is_odd(x):
"""Returns True if x is odd and False if x is even"""
return x % 2 == 1         # The % operator returns the remainder of integer division
L=[1, 4, 5, 9, 10]
print(list(filter(is_odd, L)))

[1, 5, 9]


The even elements of the list were filtered out.

Note that the filter function is rarely used in modern python since list comprehensions can do the same thing while also doing whatever we want to do with the filtered values.

[3]:

[l**2 for l in L if is_odd(l)] # squares of odd values

[3]:

[1, 25, 81]


That said, filter is a useful function to know.

Write a function positive_list that gets a list of numbers as a parameter, and returns a list with the negative numbers and zero filtered out using the filter function.

The function call positive_list([2,-2,0,1,-7]) should return the list [2,1]. Test your function in the main function.

#### The reduce function¶

The sum function that returns the sum of a numeric list, can be though to reduce a list to a single element. It does this reduction by repeatedly applying the + operator until all the list elements are consumed. For instance, the list [1,2,3,4] is reduced by the expression (((0+1)+2)+3)+4 of repeated applications of the + operator. We could implement this with the following function:

[83]:

def sumreduce(L):
s=0
for x in L:
s = s+x
return s


Because this is a common pattern, the reduce function is a common inclusion in functional programming languages. In Python reduce is included in the functools modlue. You give the operator you want to use as a parameter to reduce (addition in the above example). You may also give a starting value of the computation (starting value 0 was used above).

If no starting value is used, the first element of the iterable is used as the starting value.

We can now get rid of the separate function sumreduce by using the reduce function:

[2]:

L=[1,2,3,4]
from functools import reduce   # import the reduce function from the functools module
reduce(lambda x,y:x+y, L, 0)

[2]:

10


If we wanted to get a product of all numbers in a sequence, we would use

[3]:

reduce(lambda x,y:x*y, L, 1)

[3]:

24


This corresponds to the sequence (((1*1)*2)*3)*4 of application of operator *.

Note that use of the starting value is necessary, because we want to be able to reduce lists of length 0 as well. If no starting value is specified when run on an empty list, reduce will raise an exception.

## String handling¶

We have already seen how to index, slice, concatenate, and repeat strings. Let’s now look into what methods the str class offers. In Python strings are immutable. This means that for instance the following assignment is not legal:

[86]:

s="text"
# s[0] = "a"    # This is not legal in Python


Because of the immutability of the strings, the string methods work by returning a value; they don’t have any side-effects. In the rest of this section we briefly describe several of these methods. The methods are here divided into five groups.

### Classification of strings¶

All the following methods will take no parameters and return a truth value. An empty string will always result in False.

• s.isalnum() True if all characters are letters or digits
• s.isalpha() True if all characters are letters
• s.isdigit() True if all characters are digits
• s.islower() True if contains letters, and all are lowercase
• s.isupper() True if contains letters, and all are uppercase
• s.isspace() True if all characters are whitespace
• s.istitle() True if uppercase in the beginning of word, elsewhere lowercase

### String transformations¶

The following methods do conversions between lower and uppercase characters in the string. All these methods return a new string.

• s.lower() Change all letters to lowercase
• s.upper() Change all letters to uppercase
• s.capitalize() Change all letters to capitalcase
• s.title() Change to titlecase
• s.swapcase() Change all uppercase letters to lowercase, and vice versa

### Searching for substrings¶

All the following methods get the wanted substring as the parameter, except the replace method, which also gets the replacing string as a parameter

• s.count(substr) Counts the number of occurences of a substring
• s.find(substr) Finds index of the first occurence of a substring, or -1
• s.rfind(substr) Finds index of the last occurence of a substring, or -1
• s.index(substr) Like find, except ValueError is raised if not found
• s.rindex(substr) Like rfind, except ValueError is raised if not found
• s.startswith(substr) Returns True if string starts with a given substring
• s.endswith(substr) Returns True if string ends with a given substring
• s.replace(substr, replacement) Returns a string where occurences of one string are replaced by another

Keep also in mind that the expression "issi" in "mississippi" returns a truth value of whether the first string occurs in the second string.

• s.strip(x) Removes leading and trailing whitespace by default, or characters found in string x
• s.lstrip(x) Same as strip but only leading characters are removed
• s.rstrip(x) Same as strip but only trailing characters are removed
• s.ljust(n) Left justifies string inside a field of length n
• s.rjust(n) Right justifies string inside a field of length n
• s.center(n) Centers string inside a field of length n

An example of using the center method and string repetition:

[12]:

L=[1,3,5,7,9,1,1]
print("-"*11)
for i in L:
s="*"*i
print(f"|{s.center(9)}|")
print("-"*11)

-----------
|    *    |
|   ***   |
|  *****  |
| ******* |
|*********|
|    *    |
|    *    |
-----------


### Joining and splitting¶

The join(seq) method joins the strings of the sequence seq. The string itself is used as a delimitter. An example:

[88]:

"--".join(["abc", "def", "ghi"])

[88]:

'abc--def--ghi'

[5]:

L=[str(x) for x in range(100)]
s=""
for x in L:
s += " " + x    # Avoid doing this, it creates a new string at every iteration
print(s)            # Note the redundant initial space
print(" ".join(L))  # This is the correct way of building a string out of smaller strings

 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

If you want to build a string out of smaller strings, then first put the small strings into a list, and then use the join method to catenate the pieces together. It is much more efficient this way. Use the + catenation operator only if you have very few short strings that you want to catenate.

Below we can see that for our small (100 element) list, execution is an order of magnitude faster using the join method.

[6]:

%%timeit
s=""
for x in L:
s += " " + x

11.8 µs ± 114 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

[8]:

%%timeit
s = " ".join(L)

1.25 µs ± 6.42 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)


%%timeit is an IPython cell magic command, that is useful for timing execution in notebooks.

The method split(sep=None) divides a string into pieces that are separated by the string sep. The pieces are returned in a list. For instance, the call 'abc--def--ghi'.split("--") will result in

[90]:

'abc--def--ghi'.split("--")

[90]:

['abc', 'def', 'ghi']


If no parameters are given to the split method, then it splits at any sequence of white space.

Write function acronyms which takes a string as a parameter and returns a list of acronyms. A word is an acronym if it has length at least two, and all its characters are in uppercase. Before acronym detection, delete punctuation with the strip method.

Test this function in the main function with the following call:

print(acronyms("""For the purposes of the EU General Data Protection Regulation (GDPR), the controller of your personal information is International Business Machines Corporation (IBM Corp.), 1 New Orchard Road, Armonk, New York, United States, unless indicated otherwise. Where IBM Corp. or a subsidiary it controls (not established in the European Economic Area (EEA)) is required to appoint a legal representative in the EEA, the representative for all such cases is IBM United Kingdom Limited, PO Box 41, North Harbour, Portsmouth, Hampshire, United Kingdom PO6 3AU."""))


This should return ['EU', 'GDPR', 'IBM', 'IBM', 'EEA', 'EEA', 'IBM', 'PO', 'PO6', '3AU']

Write a function sum_equation which takes a list of positive integers as parameters and returns a string with an equation of the sum of the elements.

Example: sum_equation([1,5,7]) returns "1 + 5 + 7 = 13" Observe, the spaces should be exactly as shown above. For an empty list the function should return the string “0 = 0”.

## Modules¶

To ease management of large programs, software is divided into smaller pieces. In Python these pieces are called modules. A module should be a unit that is as independent from other modules as possible. Each file in Python corresponds to a module. Modules can contain classes, objects, functions, … For example, functions to handle regular expressions are in module re

The standard library of Python consists of hundreds of modules. Some of the most common standard modules include

• re
• math
• random
• os
• sys

Any file with extension .py that contains Python source code is a module. So, no special notation is needed to create a module.

### Using modules¶

Let’s say that we need to use the cosine function. This function, and many other mathematical functions are located in the math module. To tell Python that we want to access the features offered by this module, we can give the statement import math. Now the module is loaded into memory. We can now call the function like this:

math.cos(0)
1.0


Note that we need to include the module name where the cos function is found. This is because other modules may have a function (or other attribute of a module) with the same name. This usage of different namespace for each module prevents name clashes. For example, functions gzip.open, os.open are not to be confused with the builtin open function.

### Breaking the namespace¶

If the cosine is needed a lot, then it might be tedious to always specify the namespace, especially if the name of the namespace/module is long. For these cases there is another way of importing modules. Bring a name to the current scope with from math import cos statement. Now we can use it without the namespace specifier: cos(1).

Several names can be imported to the current scope with from math import name1, name2, ... Or even all names of the module with from math import * The last form is sensible only in few cases, normally it just confuses things since the user may have no idea what names will be imported.

### Module lookup¶

When we try to import a module mod with the import statement, the lookup proceeds in the following order:

• Check if it is a builtin module
• Check if the file mod.py is found in any of the folders in the list sys.path. The first item in this list is the current folder

When Python is started, the sys.path list is initialised with the contents of the PYTHONPATH environment variable

### Module hierarchy¶

The standard library contains hundreds of modules. Hence, it is hard to comprehend what the library includes. The modules therefore need to be organised somehow. In Python the modules can be organised into hierarchies using packages. A package is a module that can contain other packages and modules. For example, the numpy package contains subpackages core, distutils, f2py, fft, lib, linalg, ma, numarray, oldnumeric, random, and testing. And package numpy.linalg in turn contains modules linalg, lapack_lite and info.

### Importing from packages¶

The statement import numpy imports the top-level package numpy and its subpackages.

• import numpy.linalg imports the subpackage only, and
• import numpy.linalg.linalg imports the module only

If we want to skip the long namespace specification, we can use the form

from numpy.linalg import linalg


or

from numpy.linalg import linalg as lin


if we want to use a different name for the module. The following command imports the function det (computes the determinant of a matrix) from the module linalg, which is contained in a subpackage linalg, which belongs to package numpy:

from numpy.linalg.linalg import det


Had we only imported the top-level package numpy we would have to refer to the det function with the full name numpy.linalg.linalg.det.

Here’s a recap of the module hierarchy:

numpy    package
.
linalg   subpackage
.
linalg   module
.
det     function


### Correspondence between folder and module hierarchies¶

The packages are represented by folders in the filesystem. The folder should contain a file named __init__.py that makes up the package body. This handles the initialisation of the package. The folder may contain also further folders (subpackages) or Python files (normal modules).

a/
__init__.py
b.py
c/
__init__.py
d.py
e.py


### Contents of a module¶

Suppose we have a module named mod.py. All the assignments, class definitions with the class statement, and function definitions with def statement will create new attributes to this module. Let’s import this module from another Python file using the import mod statement. After the import we can access the attributes of the module object using the normal dot notation: mod.f(), mod.myclass(), mod.a, etc. Note that Python doesn’t really have global variables that are visible to all modules. All variables belong to some module namespace.

One can query the attributes of an object using the dir function. With no parameters, it shows the attributes of the current module. Try executing dir() in an IPython shell or in a Jupyter notebook! After that, define the following attributes, and try running dir() again:

a=5
def f(i):
return i + 1


The above definitions created a data attribute called a and a function attribute called f. We will talk more about attributes next week when we will talk about objects.

Just like other objects, the module object contains its attributes in the dictionary modulename.__dict__ Usually a module contains at least the attributes __name__ and __file__. Other common attributes are __version__, __author__ and __doc__ , which contains the docstring of the module. If the first statement of a file is a string, this is taken as the docstring for that module. Note that the docstring of the module really must be the first non-empty non-comment line. The attribute __file__ is always the filename of the module.

The module attribute __name__ has value “__main__” if we in are the main program, otherwise some other module has imported us and name equals __file__.

In Python it is possible to put statements on the top-level of our module mod so that they don’t belong to any function. For instance like this:

for _ in range(3):
print("Hello")


But if somebody imports our module with import mod, then all the statements at the top-level will be executed. This may be surprising to the user who imported the module. The user will usually say, explicitly when he/she wants to execute some code from the imported module.

It is better style to put these statements inside some function. If they don’t fit in any other function, then you can use, for example, the function named main, like this:

def main():
for _ in range(3):
print("Hello")

if __name__ == "__main__":    # We call main only when this module is not being imported, but directly executed
main()                    # for example with 'python3 mod.py'


You probably have seen this mechanism used in the exercise stubs. Note that in Python the main has no special meaning, it is just our convention to use it here. Now if somebody imports mod, the for loop won’t be automatically executed. If we want, we can call it explicitly with mod.main().

for _ in range(3):
print("Hello")


Create your own module as file triangle.py in the src folder. The module should contain two functions:

• hypothenuse which returns the length of the hypothenuse when given the lengths of two other sides of a right-angled triangle
• area which returns the area of the right-angled triangle, when two sides, perpendicular to each other, are given as parameters.

Make sure both the functions and the module have descriptive docstrings. Add also the __version__ and __author__ attributes to the module. Call both your functions from the main function (which is in file usemodule.py).

## Summary¶

• We have learned that Python’s code blocks are denoted by consistent indenting, with spaces or tabs, unlike in many other languages
• Python’s for loops goes through all the elements of a container without the need of worrying about the positions (indices) of the elements in the container
• More generally, an iterable is an object whose elements can be gone through one by one using a for loop. Such as range(1,7)
• Python has dynamic typing: the type of a name is known only when we run the program. The type might not be fixed, that is, if a name is created, for example, in a loop, then its type might change at each iteration.
• Visibility of a name: a name that refers to a variable can disappear in the middle of a code block, if a del statement is issued!
• Python is good at string handling, but remember that if you want to concatenate large number of strings, use the join method. Concatenating by the + operator multiple times is very inefficient
• Several useful tools exist to process sequences: map, reduce, filter, zip, enumerate, and range. The unnamed lambda function can be helpful with these tools. Note that these tools (except the reduce) don’t return lists, but iterables, for efficiency reasons: Most often we don’t want to store the result from these tools to a container (such as a list), we may only want to iterate through the result!