sieve (#52)

Author: glennj

config.json

@@ -398,6 +398,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 4
+      },
+      {
+        "slug": "sieve",
+        "name": "Sieve",
+        "uuid": "a78a4a9e-5187-4db4-a10a-e174dba78f4c",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
       }
     ]
   },

exercises/practice/sieve/.busted

@@ -0,0 +1,5 @@
+return {
+  default = {
+    ROOT = { '.' }
+  }
+}

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

@@ -0,0 +1,101 @@
+# Instructions
+
+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 larger than 1 that is only divisible by 1 and itself.
+For example, 2, 3, 5, 7, 11, and 13 are prime numbers.
+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, first, write out all the numbers from 2 up to and including your given number.
+Then, follow these steps:
+
+1. Find the next unmarked number (skipping over marked numbers).
+   This is a prime number.
+2. Mark all the multiples of that prime number as **not** prime.
+
+Repeat the steps until you've gone through every number.
+At the end, all the unmarked numbers are prime.
+
+~~~~exercism/note
+The Sieve of Eratosthenes marks off multiples of each prime using addition (repeatedly adding the prime) or multiplication (directly computing its multiples), rather than checking each number for divisibility.
+
+The tests don't check that you've implemented the algorithm, only that you've come up with the correct primes.
+~~~~
+
+## Example
+
+Let's say you're finding the primes less than or equal to 10.
+
+- Write out 2, 3, 4, 5, 6, 7, 8, 9, 10, leaving them all unmarked.
+
+  ```text
+  2 3 4 5 6 7 8 9 10
+  ```
+
+- 2 is unmarked and is therefore a prime.
+  Mark 4, 6, 8 and 10 as "not prime".
+
+  ```text
+  2 3 [4] 5 [6] 7 [8] 9 [10]
+  ↑
+  ```
+
+- 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)_.
+
+  ```text
+  2 3 [4] 5 [6] 7 [8] [9] [10]
+    ↑
+  ```
+
+- 4 is marked as "not prime", so we skip over it.
+
+  ```text
+  2 3 [4] 5 [6] 7 [8] [9] [10]
+       ↑
+  ```
+
+- 5 is unmarked and is therefore a prime.
+  Mark 10 as not prime _(optional - as it's already been marked)_.
+
+  ```text
+  2 3 [4] 5 [6] 7 [8] [9] [10]
+          ↑
+  ```
+
+- 6 is marked as "not prime", so we skip over it.
+
+  ```text
+  2 3 [4] 5 [6] 7 [8] [9] [10]
+             ↑
+  ```
+
+- 7 is unmarked and is therefore a prime.
+
+  ```text
+  2 3 [4] 5 [6] 7 [8] [9] [10]
+                ↑
+  ```
+
+- 8 is marked as "not prime", so we skip over it.
+
+  ```text
+  2 3 [4] 5 [6] 7 [8] [9] [10]
+                   ↑
+  ```
+
+- 9 is marked as "not prime", so we skip over it.
+
+  ```text
+  2 3 [4] 5 [6] 7 [8] [9] [10]
+                       ↑
+  ```
+
+- 10 is marked as "not prime", so we stop as there are no more numbers to check.
+
+  ```text
+  2 3 [4] 5 [6] 7 [8] [9] [10]
+                           ↑
+  ```
+
+You've examined all the numbers and found that 2, 3, 5, and 7 are still unmarked, meaning they're the primes less than or equal to 10.

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": [
+      "sieve.moon"
+    ],
+    "test": [
+      "sieve_spec.moon"
+    ],
+    "example": [
+      ".meta/example.moon"
+    ]
+  },
+  "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/example.moon

@@ -0,0 +1,12 @@
+{
+  primes: (limit) ->
+    flags = [true for _ = 1, limit]
+    flags[1] = false
+
+    for i = 2, math.floor(math.sqrt limit)
+      if flags[i]
+        for j = i * i, limit, i
+          flags[j] = false
+
+    [i for i = 2, limit when flags[i]]
+}

exercises/practice/sieve/.meta/spec_generator.moon

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+formatted = (list, level) ->
+  joined = table.concat list, ', '
+  cmd = "echo '#{joined}' | fold -s -w 76"
+  fh = io.popen cmd, 'r'
+  return "{#{joined}}" if not fh
+
+  lines = [indent(line\gsub('%s+$', ''), level + 1) for line in fh\lines!]
+
+  result = {fh\close!}
+  lines = {joined} if not result[1]
+
+  if #lines == 1
+    "{#{lines[1]\gsub('^%s+', '')}}"
+  else
+    table.insert lines, 1, "{"
+    table.insert lines, (indent "}", level)
+    table.concat lines, '\n'
+
+
+{
+  module_name: 'Sieve',
+
+  generate_test: (case, level) ->
+    lines = {
+      "result = Sieve.#{case.property} #{case.input.limit}",
+      "expected = #{formatted case.expected, level}",
+      "assert.are.same expected, result"
+    }
+    table.concat [indent line, level for line in *lines], '\n'
+}

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

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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.
+
+[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/sieve.moon

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+{
+  primes: (limit) ->
+    error 'Implement me'
+}

exercises/practice/sieve/sieve_spec.moon

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+Sieve = require 'sieve'
+
+describe 'sieve', ->
+  it 'no primes under two', ->
+    result = Sieve.primes 1
+    expected = {}
+    assert.are.same expected, result
+
+  pending 'find first prime', ->
+    result = Sieve.primes 2
+    expected = {2}
+    assert.are.same expected, result
+
+  pending 'find primes up to 10', ->
+    result = Sieve.primes 10
+    expected = {2, 3, 5, 7}
+    assert.are.same expected, result
+
+  pending 'limit is prime', ->
+    result = Sieve.primes 13
+    expected = {2, 3, 5, 7, 11, 13}
+    assert.are.same expected, result
+
+  pending 'find primes up to 1000', ->
+    result = Sieve.primes 1000
+    expected = {
+      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
+    }
+    assert.are.same expected, result