Python exercises

The factorial of a number is all the numbers less than the number (but greater than 0) multiplied together. In maths we use the notation n! to mean the factorial of the number n.

For example 3! = 3 x 2 x 1, and 5! = 5 x 4 x 3 x 2 x 1.

Your task is to write a function called factorial that accepts a number and it returns the factorial of the number.

Test it

To make sure it works check it returns the correct results to these (use print(factorial(n)) where n is the number):

• factorial(3) = 6
• factorial(5) = 120

Research

What happens if you pass in 0 to your program?

What should happen? Try doing some research to find out!

Caesar cipher is an ancient cipher first used in Roman days.

The way it worked was to shift each letter of the alphabet by a certain amount.

For example, if the shift was 1 abc xyz would become bcd yza (z wraps back around to a). If the shift was 2 then the message cat would become ecv.

Your task is to create a function called caesar_shift(msg, n) where msg is a string containing the message and n is number of positions the message should be shifted by.

Here are some things that might be useful:

import string
alphabet = string.ascii_lowercase
# Prints 'abcdefghijklmnopqrstuvwxyz'
print(alphabet)

# Prints '3' (a = 0, b = 1, ...)
print(alphabet.index('d'))

# Prints 4 (% returns the remainder of the division - look into modular arithmetic)
print(30 % len(alphabet))

Test it

Try running caesar_shift('cat', 2), it should equal ecv.

Extension

What happens if your message contains both upper and lowercase letters? How does you program handle that case? How should it handle that case?

What if the message contains a space? Make sure your program keeps the space as it is without changing it when the text is shifted.

This is a classic programming interview question.

The idea is that your program should print the numbers from 1 to 1000, but if the number is a multiple of 3 you print Fizz, if it's a multiple of 5 you print Buzz. If it's a multiple of 3 and 5 then you print FizzBuzz.

Examples

The first 20 lines of output from your program should be:

1
2
Fizz
4
Buzz
Fizz
7
8
Fizz
Buzz
11
Fizz
13
14
FizzBuzz
16
17
Fizz
19
Buzz

Fibonacci numbers are the famous sequence of numbers where each number is the sum of the two previous numbers, and the sequence starts with 1 1.

Your task is to create a function called fibonacci(n) which prints out the first n fibonacci numbers.

Test it

• fibonacci(6) should print 1 1 2 3 5 8.
• fibonacci(2) should print 1 1.

The factors of a number are the numbers which divide the number and return a whole number (called an integer) - another way of thinking about this are numbers which divide the original number with remainder 0.

Let's look at an example such as 6:

• 1 is a factor of 6 since 6 ÷ 1 = 6.
• So is 2 since 6 ÷ 2 = 3, and 3 and 6.
• 4 is not a factor of 6 since 6 ÷ 4 = 2.5 and 2.5 isn't a whole number.

Your task is to create a function that returns a list of factors of a number.

Call this function factorise(n) where n is the number you want to factorise.

Hint: It may help to use n % x == 0 to check if n ÷ x has remainder 0, and you can find all the values of x in a loop.

Test it

• print(factorise(6)) should print [1, 2, 3, 6]
• print(factorise(8) == [1, 2, 8]) should print True

Prime numbers are numbers whose only factors are 1 and itself.

For example 7 is a prime number since it's only factors are 1 and 7 whereas 6 isn't a prime number since it's factors are 1, 2, 3 and 6.

Your task is to create a function called is_prime(n) that returns True if the number is a prime and False otherwise.

Extra

Whats the greatest number that you need to check up to in order to see if it's a prime number?

Hint: Factors come in pairs. For example when working out the factors of 15 once you check 3, you've already checked 5 since 15 ÷ 3 == 5.

Test it

• print(is_prime(2)) should print True (this is a special case)
• print(is_prime(13)) should print True
• print(is_prime(14)) should print False