Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

sieve: sync #2428

Merged
merged 1 commit into from
Apr 5, 2024
Merged

sieve: sync #2428

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
44 changes: 29 additions & 15 deletions exercises/practice/sieve/.docs/instructions.md
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,28 +1,42 @@
# Instructions

Your task is to create a program that implements the Sieve of Eratosthenes algorithm to find prime numbers.
Your task is to create a program that implements the Sieve of Eratosthenes algorithm to find all prime numbers less than or equal to a given number.

A prime number is a number that is only divisible by 1 and itself.
A prime number is a number larger than 1 that is only divisible by 1 and itself.
For example, 2, 3, 5, 7, 11, and 13 are prime numbers.

The Sieve of Eratosthenes is an ancient algorithm that works by taking a list of numbers and crossing out all the numbers that aren't prime.

A number that is **not** prime is called a "composite number".
By contrast, 6 is _not_ a prime number as it not only divisible by 1 and itself, but also by 2 and 3.

To use the Sieve of Eratosthenes, you first create a list of all the numbers between 2 and your given number.
Then you repeat the following steps:

1. Find the next unmarked number in your list. This is a prime number.
2. Mark all the multiples of that prime number as composite (not prime).
1. Find the next unmarked number in your list (skipping over marked numbers).
This is a prime number.
2. Mark all the multiples of that prime number as **not** prime.

You keep repeating these steps until you've gone through every number in your list.
At the end, all the unmarked numbers are prime.

```exercism/note
[Wikipedia's Sieve of Eratosthenes article][eratosthenes] has a useful graphic that explains the algorithm.

~~~~exercism/note
The tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes.
A good first test is to check that you do not use division or remainder operations.

[eratosthenes]: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
```
To check you are implementing the Sieve correctly, a good first test is to check that you do not use division or remainder operations.
~~~~

## Example

Let's say you're finding the primes less than or equal to 10.

- List out 2, 3, 4, 5, 6, 7, 8, 9, 10, leaving them all unmarked.
- 2 is unmarked and is therefore a prime.
Mark 4, 6, 8 and 10 as "not prime".
- 3 is unmarked and is therefore a prime.
Mark 6 and 9 as not prime _(marking 6 is optional - as it's already been marked)_.
- 4 is marked as "not prime", so we skip over it.
- 5 is unmarked and is therefore a prime.
Mark 10 as not prime _(optional - as it's already been marked)_.
- 6 is marked as "not prime", so we skip over it.
- 7 is unmarked and is therefore a prime.
- 8 is marked as "not prime", so we skip over it.
- 9 is marked as "not prime", so we skip over it.
- 10 is marked as "not prime", so we stop as there are no more numbers to check.

You've examined all numbers and found 2, 3, 5, and 7 are still unmarked, which means they're the primes less than or equal to 10.
Loading