From d56a8dc426854d85994042b68f8c6e245c46f535 Mon Sep 17 00:00:00 2001 From: Erik Schierboom Date: Sat, 30 Mar 2024 08:39:25 +0100 Subject: [PATCH] Sync the `sieve` exercise's docs with the latest data. --- .../practice/sieve/.docs/instructions.md | 40 +++++++++++++------ 1 file changed, 27 insertions(+), 13 deletions(-) diff --git a/exercises/practice/sieve/.docs/instructions.md b/exercises/practice/sieve/.docs/instructions.md index 3adf1d55..085c0a57 100644 --- a/exercises/practice/sieve/.docs/instructions.md +++ b/exercises/practice/sieve/.docs/instructions.md @@ -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. - 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.