Add sieve exercise

config.json

@@ -1234,6 +1234,20 @@
           "result"
         ],
         "difficulty": 5
+      },
+      {
+        "slug": "sieve",
+        "name": "sieve",
+        "uuid": "d95a08ac-fe7a-4cd5-8c87-d6ac4a9fc90f",
+        "practices": [
+          "lists"
+        ],
+        "prerequisites": [
+          "lists",
+          "pattern-matching",
+          "array"
+        ],
+        "difficulty": 5
       }
     ]
   },

exercises/practice/sieve/.docs/instructions.md

@@ -0,0 +1,28 @@
+# Instructions
+
+Your task is to create a program that implements the Sieve of Eratosthenes algorithm to find prime numbers.
+
+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.
+
+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".
+
+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).
+
+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
+~~~~

exercises/practice/sieve/.docs/introduction.md

@@ -0,0 +1,7 @@
+# Introduction
+
+You bought a big box of random computer parts at a garage sale.
+You've started putting the parts together to build custom computers.
+
+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.

exercises/practice/sieve/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "glennj"
+  ],
+  "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"
+}

exercises/practice/sieve/.meta/src/Sieve.example.elm

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+module Sieve exposing (primes)
+
+import Array exposing (Array)
+
+
+primes : Int -> List Int
+primes limit =
+    makeCandidates limit
+        |> markMultiples limit
+        |> extractPrimes
+
+
+makeCandidates : Int -> Array Bool
+makeCandidates limit =
+    Array.repeat (limit + 1) True
+        |> Array.set 0 False
+        |> Array.set 1 False
+
+
+extractPrimes : Array Bool -> List Int
+extractPrimes candidates =
+    Array.indexedMap (\idx val -> ( idx, val )) candidates
+        |> Array.filter (\( _, isPrime ) -> isPrime)
+        |> Array.map Tuple.first
+        |> Array.toList
+
+
+markMultiples : Int -> Array Bool -> Array Bool
+markMultiples limit candidates =
+    mark limit 2 candidates
+
+
+mark limit candidate candidates =
+    if candidate > isqrt limit then
+        candidates
+
+    else
+        case Array.get candidate candidates of
+            Nothing ->
+                -- should not happen
+                Array.empty
+
+            Just True ->
+                mark
+                    limit
+                    (candidate + 1)
+                    (markMultiplesOfPrime
+                        limit
+                        candidate
+                        (candidate * candidate)
+                        candidates
+                    )
+
+            Just False ->
+                mark
+                    limit
+                    (candidate + 1)
+                    candidates
+
+
+markMultiplesOfPrime limit prime current candidates =
+    if current > limit then
+        candidates
+
+    else
+        markMultiplesOfPrime
+            limit
+            prime
+            (current + prime)
+            (Array.set current False candidates)
+
+
+isqrt : Int -> Int
+isqrt =
+    toFloat >> sqrt >> floor

exercises/practice/sieve/.meta/tests.toml

@@ -0,0 +1,25 @@
+# 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.
+
+[88529125-c4ce-43cc-bb36-1eb4ddd7b44f]
+description = "no primes under two"
+
+[4afe9474-c705-4477-9923-840e1024cc2b]
+description = "find first prime"
+
+[974945d8-8cd9-4f00-9463-7d813c7f17b7]
+description = "find primes up to 10"
+
+[2e2417b7-3f3a-452a-8594-b9af08af6d82]
+description = "limit is prime"
+
+[92102a05-4c7c-47de-9ed0-b7d5fcd00f21]
+description = "find primes up to 1000"

exercises/practice/sieve/elm.json

@@ -0,0 +1,29 @@
+{
+    "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"
+        }
+    }
+}

exercises/practice/sieve/src/Sieve.elm

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+module Sieve exposing (primes)
+
+
+primes : Int -> List Int
+primes limit =
+    Debug.todo "Please implement this function"

exercises/practice/sieve/tests/Tests.elm

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+module Tests exposing (tests)
+
+import Expect
+import Sieve
+import Test exposing (Test, describe, skip, test)
+
+
+tests : Test
+tests =
+    describe "Sieve"
+        [ 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 ]
+        ]