3.1 — Order of Expression Evaluation, Comparing Values, Conditional Execution

Debugging in Thonny to understand expression evaluation

In Thonny, we can use debugging features to understand how expressions are evaluated:

To show variables and their values, go to menu “View -> Variables”
First, run program in debug mode by clicking the “Debug current script” button (located next to the “Run current script” button and looks like a bug)
Then, we have two options:
- Run the program line-by-line using “Step over” button next to the “Debug” button
- Run program going inside each expression using “Step into” button (located next to “Step over” button)

Try the following examples in Thonny and use debug:

1x = 7
2
3# Increment value of variable x by 1
4x = x + 1
5
6#
7y = x * x + 2 * (x + 1) + max(x + 1, 5)
8
9# Calling print() with 4 arguments
10print("x =", x, "y =", y)

1x1 = 1.5
2y1 = 2
3
4print("Given points:", "(", x1, ",", y1, ")")
5
6point1 = "(" + str(x1) + ", " + str(y1) + ")" 
7print("Given points:", point1)

Boolean Values

Python has two values True and False of type bool, which are useful for expressing and storing yes/no or true/false kind of data.

1>>> True
2True
3>>> False
4False
5>>> type(True)
6<class 'bool'>
7>>> type(False)
8<class 'bool'>

Comparison Operators

comparison operators, also known as relational operators, are used to compare two values, such as numbers or string.
The result of such comparison is always a bool value i.e. True or False.

1# are these numbers equal?
2>>> 10 == 10  
3True
4>>> 10 == 20
5False

1>>> x = 5
2>>> y = 10
3>>> x == y
4False
5>>> x < y
6True
7>>> x > y
8False

1# A variable can store the result of a boolean expression 
2# (just like we did for arithmetic expressions)
3>>> x = 3
4>>> is_positive = (x > 0)
5>>> is_positive
6True
7
8>>> x = 5
9>>> y = 5
10>>> is_equal = (x == y)
11>>> is_equal
12True

Boolean Expressions

A boolean expression is an expression that evaluates to either True or False. Examples above show how boolean expressions are created using comparison operators.

Common error is using = (single equals sign) instead of == (double equals sign)
= is the assignment operator, used to create variable and assign it a value
== is a comparison operator used to check for equality between two values

List of comparison operators

x == y — True if x is equal to y, otherwise False
x != y — True if x is not equal to y, otherwise False
x < y — True if x is less than y, otherwise False
x > y — True if x is greater than y, otherwise False
x <= y — True if x is less than or equal to y, otherwise False
x >= y — True if x is greater than or equal to y, otherwise False

Order of operations

All comparison operators (e.g. ==, !=, etc.) have same priority and are evaluated from left to right.

All arithmetic and string operators have higher priority than comparison operators.

1>>> x = 5
2# + operator will be evaluated before ==
3>>> x + 1 == 6
4True

Write a program that takes an integer as input from the user and displays on your screen whether it is true or false that such integer is even.

Output

Enter a number: 5
5 is an even number: False

Output

Enter a number: 8
8 is an even number: True

1num = int(input("Enter a number: "))
2# Write code below

1num = int(input("Enter a number: "))
2
3# a number is even if remainder is 0 when it is divided by 2
4is_even = (num % 2 == 0)
5
6print(num, "is an even number:", is_even)
7
8# without using extra variable:
9# print(num, "is an even number:", num % 2 == 0)

Comparing strings

Comparison operators work for strings as well.
The comparison is done alphabetically i.e. following a dictionary order

1>>> "cat" == "cat"
2True
3>>> "cat" == "dog"
4False
5>>> "cat" != "Cat"
6True

1# "c" appears before "d" alphabetically
2>>> "cat" < "dog"
3True
4
5# A-Z appear before a-z alphabetically
6>>> "cat" < "Dog"
7False

1# Objects of different types are always not equal
2>>> "cat" == 123
3False
4
5# inequality is not allowed 
6# between a number and str
7>>> "cat" < 123
8TypeError: '<' not supported between instances of 'str' and 'int'
9
10# All of the above examples work the same when using variables
11>>> s1 = "cat"
12>>> s2 = "dog"
13>>> s1 == s2
14False

Equality and floating point numbers

Consider following example:

1>>> x = 1.1 + 2.2
2>>> x == 3.3  # why is this False?
3False

As we saw earlier, a floating-point number is stored with 64-bit finite precision.
This means that a number may not be stored as precisely as we would like.

Correct way to check if two float values are equal

We should check if they are “close enough”.

1>>> epsilon = 0.000001  # define how close two numbers need to be
2
3>>> x = 1.1 + 2.2
4>>> x
53.3000000000000003
6
7# Check if x and 3.3 are within epsilon distance
8>>> abs(x - 3.3) < epsilon
9True

The epsilon value depends on the application and how much error we are willing tolerate.

Logical Operators

Logical operators are useful to combine multiple conditions.

Logical operators take boolean expressions as operands and produce a result of type bool when evaluated.

Python has 3 boolean operators:

not — a unary operator
and — binary operator
or — binary operator

Suppose x is a variable of type bool:

x	not x
False	True
True	False

not x evaluates to the opposite value of x.

Suppose x and y are variables of type bool:

x	y	x and y
True	True	True
True	False	False
False	True	False
False	False	False

x	y	x or y
True	True	True
True	False	True
False	True	True
False	False	False

x and y evaluates to True if and only if both x and y are True.

x or y evaluates to False if and only if both x and y are False.

Order of operations

In order of higher to lower priority: not, and, or

As usual, we can use parentheses in order to change the priority.

What does b and not a or b evaluate to if a = False and b = True ?

b and not a or b
True and not False or True
True and True or True
True or True
True

What does a and not (a or b) evaluate to if a = True and b = False ?

a and not (a or b)
True and not (True or False)
True and not True
True and False
False

Updated operator precedence table

Operator	Associativity
() (parentheses)	-
**	Right
Unary -	-
*, /, //, %	Left
Binary +, -	Left
==, !=, <, >, <=, >=	Left
not	-
and	Left
or	Left
= (assignment)	Right

You don’t need to memorize all this, use parenthesis when in doubt!

Try these examples in Thonny

Change the value of x and see results of boolean expressions.

1x = 30
2# Is an even number greater than 20?
3print(x % 2 == 0 and x > 20)
4
5x = 10
6# Is an even number or a multiple of 5 greater than 20?
7print(x % 2 == 0 or x % 5 == 0 and x > 20)
8
9# Is a multiple of 2 or 5, greater than 20? 
10print((x % 2 == 0 or x % 5 == 0) and x > 20)

Try it!

Write a program that takes 3 integers $x, y, z$ as inputs and prints out True if $y$ is an even number between $x$ and $z$ , False otherwise. Assume all 3 numbers will be different.

1# Retrieve inputs from the user
2x = int(input("Enter the x: "))
3y = int(input("Enter the y: "))
4z = int(input("Enter the z: "))
5
6# Write code below

1# Retrieve inputs from the user
2x = int(input("Enter the x: "))
3y = int(input("Enter the y: "))
4z = int(input("Enter the z: "))
5
6# check if y is even
7is_even = y % 2 == 0
8
9# check if y is between x and z
10is_between = (x < y and y < z) or (z < y and y < x)
11
12print(is_even and is_between)

Flow of execution

Flow of execution refers to order in which statements (lines of code) in our program are executed.
So far in our programs, each line was executed unconditionally.
For most programs, it is not enough as we need to make choices or run code repeatedly.

We need to control the flow of execution in our programs.

Control flow

The control flow of a program determines:

Which parts of the code should always be executed
Which parts should be executed only under certain conditions
Which parts should be executed repeatedly

All of these can be achieved using control flow statements:

if statement for conditional execution
for and while loops for repeated execution

`if` statement — to execute or not to execute

if  condition  :
    code block

condition must be a boolean expression
code block is one of more Python statements
code block is executed only if the condition is True, otherwise it is skipped.

Notice space before code block. It is called indentation.

Indentation is required to tell Python that the code belongs inside if statement.

Typically, 4 spaces are used for indentation. We can use tab key to indent.

Try the following examples with different values for variables.

1x = 10  
2if x > 0:
3    print(x, "is positive")

1num = -5.2
2
3absolute_num = num
4
5if num < 0:
6    absolute_num = -num
7    
8print("Absolute value of", num, "is", absolute_num)

1x = 1000
2y = 123
3
4min_value = x
5
6if y < min_value:
7    min_value = y
8    
9print("Minimum of", x, "and", y, "is", min_value)

if statement with else part

if statements can have else part to make a choice between two code blocks.

if  condition  :
    code block1
else :
    code block2

When condition is True, code block₁ is executed
Otherwise (condition is False) and code block₂ is executed
The code blocks are also called branches of the if-statement.

1x = 10  # change this to -5 and run
2
3if x > 0:
4   print("x is positive.")
5else:
6    print("x is not positive.")

Write a program that takes an integer as input from the user and displays whether the number is even or odd.

Output

Please enter a number: 5
The number 5 is odd

Output

Please enter a number: 8
The number 8 is even

1num = int(input("Please enter a number: "))
2
3# a number is even if remainder is zero when divided by 2
4if num % 2 == 0:
5    print("The number", num, "is even")
6else:
7    print("The number", num, "is odd")

Debugging in Thonny to understand expression evaluation

Boolean Values

Comparison Operators

Boolean Expressions

List of comparison operators

Order of operations

Comparing strings

Equality and floating point numbers

Correct way to check if two float values are equal

Logical Operators

Order of operations

Updated operator precedence table

Try these examples in Thonny

Flow of execution

Control flow

if statement — to execute or not to execute

if statement with else part

`if` statement — to execute or not to execute