Python Fundamentals

Elements of Programming

A programming language gives us three things:

• expressions - the simplest things the language "understands"
• means of combination - through which we build complex elements from simpler ones
• means of abstraction - which allow us to name and manipulate these compound elements as units

Expressions

>>> 256
256

>>> 137 + 349
486

>>> 5 * 99
495

>>> 10 / 5
2

Expressions (2)

You can combine expressions

>>> 21 + 35 + 12 + 7
75
>>> 3 * (2 * 4 + (3 + 5)) + ((10 - 7) + 6)
57

Assignment

You give something a name by assigning it to that name.

>>> size = 2
>>> size
2
>>> size * 5
10

Assignment (2)

>>> size = size + 2
>>> size
4

>>> pi = 3.1415926535897931
>>> pi
3.1415926535897931

This is also called binding a name to a value.

Review

We've now seen some of the elements of programming languages

• Numbers and arithmetic are primitive expressions
• Expressions can be nested to form more complex expressions
• Names can be associated with values to provide a limited means of abstraction

Functions

>>> def square(x):
...     return x * x

• def binds the name square to the operation
• x is a parameter, which gives the thing to be squared a local name
• the indented block of lines perform the operation
• return passes the value of applying the procedure to it's parameters back to the caller.

Functions (2)

>>> square(2)
4
>>> square(2 + 4)
36

Now we can use square as a building block

>>> def sum_of_squares(x, y):
...     return square(x) + square(y)
...
>>> sum_of_squares(3, 4)
25

Conditionals

Allow us to choose

We can now define the absolute value function:

>>> def abs(x):
...     if x < 0:
...         return -x
...     else:
...         return x

Exercise

See handout

Evaluate the following expressions in the interpreter (in the given order)

1. 10

2. 5 + 3 + 4

3. 9 - 1

4. 6 / 2

5. (2 * 4) + (4 - 6)

6. a = 3

7. b = a + 1

8. a + b + a * b

9. a == b

10. if b > a and b < a * b:

    print b

    else:

    print a

11. 5 / 2

    Is that the value you expected?

12. 5.0 / 2

    You see this behavior because Python implements "floor division" for integers (the result is rounded down to the nearest integer). This is unsurprising for people familiar with the C programming language, but quite a shock for most others.

    Because of this unintuitive behavior, it's unusual to see the / operator applied to two integers (or two names bound to integer values). Normally, division is written:

    x * 1.0 / y
    

    And deliberate floor division is written:

    x // y
    

13. What is wrong with this (Python) expression? 1 + 1 = 2

14. Write a function that takes two arguments and returns their mean.

Booleans

Python supports a number of boolean operations, though the notation may not be what you are used to:

>>> 2 < 4
True
>>> 4 >= pi > 2
True
>>> not 2 == 1
True

>>> 2 == 2
True
>>> 2 != pi
True

Loops

Computers are very good at repetitive tasks. Python offers two main ways to repeat yourself.

• while loops execute a block of code until a condition is true
• for loops execute a block of code for each element in a sequence, stopping when the sequence is exhausted

While

What does this print?

def countdown(n):
    while n > 0:
        print n
        n = n-1
    print "Blastoff!"

countdown(10)

For

For loops process sequences.

range is a function that returns a list (more on these later).

>>> range(1, 10)
[1, 2, 3, 4, 5, 6, 7, 8, 9]

for i in range(0, 10):
    print i

Recursion

Loops express iteration (repetition of a process). This can also be done through recursion

def countdown(x):
    if x == 0:
        print "Blastoff"
    else:
        print x
        countdown(x-1)

Calling a procedure recursively and using a loop are two different ways to express the same thing.

Factorials

Often you can write the same loop in several ways.

We're going to write a function to calculate factorials using while loops, for loops and recursion.

n = 1 → n! = 1

n > 1 → n! = n(n-1)!

Factorials (while)

def fac_while(x):
    fac = 1
    count = 1
    while count <= x:
        fac = fac * count
        count = count + 1
    return fac

Factorials (for)

def fact_for(n):
    fac = 1
    for i in range(1, n+1):
        fac = fac * i
    return fac

Factorials (recursive)

def fac_r(n):
    if n == 1:
        return 1
    else:
        return n * fac_r(n-1)

Exercise

See handout