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Add new practice exercise sieve
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# Instructions | ||
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Your task is to create a program that implements the Sieve of Eratosthenes algorithm to find prime numbers. | ||
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A prime number is a number that is only divisible by 1 and itself. | ||
For example, 2, 3, 5, 7, 11, and 13 are prime numbers. | ||
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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. | ||
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A number that is **not** prime is called a "composite number". | ||
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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: | ||
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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). | ||
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You keep repeating these steps until you've gone through every number in your list. | ||
At the end, all the unmarked numbers are prime. | ||
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~~~~exercism/note | ||
[Wikipedia's Sieve of Eratosthenes article][eratosthenes] has a useful graphic that explains the algorithm. | ||
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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. | ||
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[eratosthenes]: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes | ||
~~~~ |
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# Introduction | ||
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You bought a big box of random computer parts at a garage sale. | ||
You've started putting the parts together to build custom computers. | ||
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You want to test the performance of different combinations of parts, and decide to create your own benchmarking program to see how your computers compare. | ||
You choose the famous "Sieve of Eratosthenes" algorithm, an ancient algorithm, but one that should push your computers to the limits. |
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{ | ||
"authors": [ | ||
"jiegillet" | ||
], | ||
"files": { | ||
"solution": [ | ||
"src/Sieve.elm" | ||
], | ||
"test": [ | ||
"tests/Tests.elm" | ||
], | ||
"example": [ | ||
".meta/src/Sieve.example.elm" | ||
] | ||
}, | ||
"blurb": "Use the Sieve of Eratosthenes to find all the primes from 2 up to a given number.", | ||
"source": "Sieve of Eratosthenes at Wikipedia", | ||
"source_url": "https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes" | ||
} |
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module Sieve exposing (primes) | ||
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import Array exposing (Array) | ||
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primes : Int -> List Int | ||
primes limit = | ||
let | ||
-- an array, with indices from 0 until limit, each with a Bool value representing primeness | ||
initialSieve = | ||
Array.initialize (limit + 1) (\n -> n >= 2) | ||
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initialPrime = | ||
Just 2 | ||
in | ||
runSieve initialPrime initialSieve | ||
|> Array.toIndexedList | ||
|> List.filterMap | ||
(\( index, isPrime ) -> | ||
if isPrime then | ||
Just index | ||
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else | ||
Nothing | ||
) | ||
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runSieve : Maybe Int -> Array Bool -> Array Bool | ||
runSieve maybePrime sieve = | ||
case maybePrime of | ||
Nothing -> | ||
sieve | ||
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Just prime -> | ||
let | ||
removeMultiples : Int -> (Array Bool -> Array Bool) | ||
removeMultiples multiple = | ||
if multiple > Array.length sieve then | ||
identity | ||
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else | ||
Array.set multiple False | ||
>> removeMultiples (multiple + prime) | ||
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sieveWithPrimeMultipleRemoved : Array Bool | ||
sieveWithPrimeMultipleRemoved = | ||
removeMultiples (2 * prime) sieve | ||
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findNextPrime : Int -> Maybe Int | ||
findNextPrime index = | ||
case Array.get index sieveWithPrimeMultipleRemoved of | ||
Nothing -> | ||
Nothing | ||
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Just True -> | ||
Just index | ||
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Just False -> | ||
findNextPrime (index + 1) | ||
in | ||
runSieve (findNextPrime (prime + 1)) sieveWithPrimeMultipleRemoved |
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# This is an auto-generated file. | ||
# | ||
# Regenerating this file via `configlet sync` will: | ||
# - Recreate every `description` key/value pair | ||
# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications | ||
# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion) | ||
# - Preserve any other key/value pair | ||
# | ||
# As user-added comments (using the # character) will be removed when this file | ||
# is regenerated, comments can be added via a `comment` key. | ||
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[88529125-c4ce-43cc-bb36-1eb4ddd7b44f] | ||
description = "no primes under two" | ||
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[4afe9474-c705-4477-9923-840e1024cc2b] | ||
description = "find first prime" | ||
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[974945d8-8cd9-4f00-9463-7d813c7f17b7] | ||
description = "find primes up to 10" | ||
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[2e2417b7-3f3a-452a-8594-b9af08af6d82] | ||
description = "limit is prime" | ||
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[92102a05-4c7c-47de-9ed0-b7d5fcd00f21] | ||
description = "find primes up to 1000" |
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{ | ||
"type": "application", | ||
"source-directories": [ | ||
"src" | ||
], | ||
"elm-version": "0.19.1", | ||
"dependencies": { | ||
"direct": { | ||
"elm/core": "1.0.5", | ||
"elm/json": "1.1.3", | ||
"elm/parser": "1.1.0", | ||
"elm/random": "1.0.0", | ||
"elm/regex": "1.0.0", | ||
"elm/time": "1.0.0" | ||
}, | ||
"indirect": {} | ||
}, | ||
"test-dependencies": { | ||
"direct": { | ||
"elm-explorations/test": "2.1.0", | ||
"rtfeldman/elm-iso8601-date-strings": "1.1.4" | ||
}, | ||
"indirect": { | ||
"elm/bytes": "1.0.8", | ||
"elm/html": "1.0.0", | ||
"elm/virtual-dom": "1.0.3" | ||
} | ||
} | ||
} |
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module Sieve exposing (primes) | ||
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primes : Int -> List Int | ||
primes limit = | ||
Debug.todo "Please implement primes" |
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module Tests exposing (tests) | ||
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import Expect | ||
import Sieve | ||
import Test exposing (Test, describe, skip, test) | ||
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tests : Test | ||
tests = | ||
describe "Sieve" | ||
[ -- skip <| | ||
test "no primes under two" <| | ||
\() -> | ||
Sieve.primes 1 | ||
|> Expect.equal [] | ||
, skip <| | ||
test "find first prime" <| | ||
\() -> | ||
Sieve.primes 2 | ||
|> Expect.equal [ 2 ] | ||
, skip <| | ||
test "find primes up to 10" <| | ||
\() -> | ||
Sieve.primes 10 | ||
|> Expect.equal [ 2, 3, 5, 7 ] | ||
, skip <| | ||
test "limit is prime" <| | ||
\() -> | ||
Sieve.primes 13 | ||
|> Expect.equal [ 2, 3, 5, 7, 11, 13 ] | ||
, skip <| | ||
test "find primes up to 1000" <| | ||
\() -> | ||
Sieve.primes 1000 | ||
|> Expect.equal [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 ] | ||
] |
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Is this to avoid a casing type problem with the title of the exercise?
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Exactly, it's too easy to miss when the name is prefilled, it happened a lot that people didn't change it (me included). At least with a big TODO you can't miss it (hopefully).