Python - Loops and Iteration¶

In this notebook, we will be introducing loops and iteration. They are commonly used tools in programming as they allow us to perform repetitive tasks.

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Table of Contents:¶

While loops
For Loops
Range Function
Range function applied to sequences
Break Statements
Incrementing and Decrementing
Infinite Loops
Loops With If/Else statements
Nested Loops
Conclusion

While Loops:¶

While loops are extremely useful in programming. The idea of while loops is to execute a block of code while a boolean expression is True. In general, the syntax for a while loop is:

while something_True:
    Do some work

Here is an example of a basic while loop. This loop will print n as long as n is greater than 0. The computer will check the n > 0 condition after it decrements n. If that condition still holds, then we will continue to print and decrement. If n = 0 then the condition is no longer True, so the computer will not enter the while loop.

n = 10
while (n > 0):
    print(n)
    n = n - 1

Another example. Since n < 0 to start, the while condition is not satisfied.

n = -10
while (n > 0):
    print(n)
    n = n - 1
    
print("n is less than", 0)

For Loops:¶

for loops differ from while loops in that for loops will iterate a fixed number of times, whereas a while loop will continue until the condition is no longer satisfied. We generally use for loops to iterate over sequences such as lists and strings. The two keywords used in for loops are for and in.

In general, the syntax for a for loop is:

for Some_Variable_of_Interest in Sequence:
    Do some work

Note that the sequence can be a string, list, or a dictionary.

Here is an example of iterating over a string. The sequence part of this for loop contains a string, The computer will take the string and assign the first value in that string to the variable letter. Then the statement inside the for loop is executed. Each element in the string will then be assigned to the variable letter until there are no more letters left in the string.

for letter in "Dog":
    print("Current Letter:", letter)

Another example of iterating over a string. The same idea as above, but now the elements assigned to the variable are from a list.

fruits = ["banana", "apple", "mango"]
for fruit in fruits:
    print("Current fruit:", fruit)

The Range Function:¶

The range function is a function which generates a list of numbers, starting from 0, and going to the number n - 1 by default. Its function definition is given by:

range(start, stop, step)

start specifies the first number, stop specifies the last number, and step is the number by which we increment. start is included in the list, but stop is not. Each parameter has to be an integer.

for i in range(5):
    print(i)

for i in range(3, 6):
    print(i)

for i in range(4, 10, 2):
    print(i)

for i in range(0, -10, -2):
    print(i)

Iterating over list indices and dictionary keys:¶

We can apply the range function to iterate over the index of a list. This can be useful if we want to iterate over the list in some order that is not the default. For dictionaries, a for loop will loop over the keys of the dictionary.

An example of iterating through a list using range. What happens here is the same as what happens above when we interated through a string.

fruits = ["banana", "apple", "mango"]
for index in range(len(fruits)):
    print("Current fruit:", fruits[index])

An example of iteration on a dictionary.

d = {"x": 1, "y": 2, "z": 3}
for key in d:
    print(key, "corresponds to", d[key])

Application: Randomly Generated List¶

Suppose we wish to generate a list of numbers of size n.

We can use a for loop, the range function, and the randint function from the random library to do this.

The randint function will generate a random integer from a specified interval.

The syntax is randint(a,b). The values a and b are the endpoints, and are included as possible values.

Change the value of the size_of_list variable to see what happens.

size_of_list = 7

import random as rand
random_list = []

for i in range(0, size_of_list):
    # Append a random value to the list using the randint function 
    random_list.append(rand.randint(1,1000))
print(random_list)

The Break Statement:¶

Suppose that we wish to end a loop early if a certain condition is met. We can use what is known as a break statement. The break statement will terminate while and for loops early. Usually it is used in conjunction with if and else statements.

For example, This loop will add 1 to the variable n. If n is greater than 10 then the if statements will be True, and the while loop will be exited. After that the next line of code will be executed.

n = 0
while True:
    n = n + 1
    if n > 10:
        break
    print(n)
    
print("Done!")

Another example, this time iterating through the letters in a string, and breaking out if the letter is equal to h. Notice the == to check for equality.

for letter in "Python":
    if letter == "h":
        break
    print("Current Letter:", letter)

print("Done!")

Practice:¶

Code the following:

Using a loop of your choice, output the squares of the numbers 1 to 10.
Find the value of \(2^{16}\) using a for loop.
Using a for loop, print the reciprocals of the numbers from 1 to 20.

# Code goes here

Incrementing and Decrementing:¶

We can increment or decrement variables in loops using two different notations. We used one in a previous example, where we set a variable equal to itself plus 1 to increment by one each time through the loop. We can decrement in a similar way.

n = 5
while n > 0:
    print(n)
    n = n - 1
print("Blastoff!")

To increment or decrement we can also use the short form n += 1 or n -= 1.

n = 0
while n < 10:
    n += 2 # equivalent to  n = n + 2
    print(n)

print("Done!")

n = 10
while n > 0:
    print(n)
    n -= 1

Off by one error:¶

An off by one error occurs when a while loop or for loop executes one too many or one too few times. A common cause is using < or > when <= or >= should have been used.

Note the difference between the outputs of the following loops.

list_of_words = ['zero', 'one', 'two', 'three', 'four', 'five']
print('Loop 1:')
i = 0
while i < 5:
    print(list_of_words[i])
    i += 1
print('')
print('Loop 2:')
j = 0
while j <= 5:
    print(list_of_words[j])
    j += 1

Infinite Loops:¶

Infinite loops occur when the condition required to enter a loop never becomes False. This can cause undesirable behaviour or cause the computer to crash. We highly recommend avoiding these. The main culprit for these is forgetting to update a variable, or by having a loop condition that will never be False.

Just to illustrate the following code would continue to increment x and then eventually crash the kernel. The error here is that the while condition is always satisfied, we would need to change the condition to get the while loop working.

x = 6
while x > 5:
    print(x)
    x += 1

Sometimes infinite loops are desirable. For example computers waiting for a user input will be in an infinite loop checking for some sort of activity. This loop will continue until there is input or the device is turned off.

Loops with if/else statements:¶

As we saw when we were using the break statement, we can have conditional expressions inside loops.

The following code use the % operator, which give the remainder after division.

For example, 9 % 4 returns 1 since 9 ÷ 4 = 2 with a remainder of 1.

for n in range(10, 16):
    if n % 2 == 0:
        print(n, "is even.")
    else:
        print(n, "is odd.")

Nested Loops:¶

It is often useful to create what are known as nested loops. Nested loops are simply loops contained in a main loop. Usually, we would have code that looks like:

while something_True:
    Do some work
        while something_else_True:
            Do some other work

The following code iterates over n from 3 to 8 (not including 8) with a for loop. Each time through the for loop it uses a while loop to iterate over numbers from 1 to n.

for n in range(3, 8):
    print('Counting up to', n)
    i = 0
    while i < n:
        i += 1
        if i%2 == 0:
            print(i, 'is even')
        else:
            print(i, 'is odd')