Add nth-prime exercise (#50)

Author: keiravillekode

config.json

@@ -342,6 +342,14 @@
         "prerequisites": [],
         "difficulty": 5
       },
+      {
+        "slug": "nth-prime",
+        "name": "Nth Prime",
+        "uuid": "fe8e3e7e-f239-40dc-8f3e-e07fa099da36",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
+      },
       {
         "slug": "variable-length-quantity",
         "name": "Variable Length Quantity",

exercises/practice/nth-prime/.docs/instructions.md

@@ -0,0 +1,7 @@
+# Instructions
+
+Given a number n, determine what the nth prime is.
+
+By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
+
+If your language provides methods in the standard library to deal with prime numbers, pretend they don't exist and implement them yourself.

exercises/practice/nth-prime/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "nth_prime.fut"
+    ],
+    "test": [
+      "test.fut"
+    ],
+    "example": [
+      ".meta/example.fut"
+    ]
+  },
+  "blurb": "Given a number n, determine what the nth prime is.",
+  "source": "A variation on Problem 7 at Project Euler",
+  "source_url": "https://projecteuler.net/problem=7"
+}

exercises/practice/nth-prime/.meta/example.fut

@@ -0,0 +1,14 @@
+def prime (number: i32): i32 =
+  if number < 3 then assert (number > 0) (number + 1) else
+  let capacity = i64.i32 (number * (32 - i32.clz number)) -- number * ceil(log2(number + 1))
+  let (_, _, p, _) = loop (a, remaining, p, step) = (replicate capacity false, number - 2, 1i64, 4i64) while (remaining > 0) do
+    let p2 = p + step
+    let step2 = 6 - step
+    in
+      if a[p2] then (a, remaining, p2, step2) else
+      let (a2, _) = loop (a2, multiple) = (a, p2 * p2) while multiple < capacity do
+        (a2 with [multiple] = true, multiple + 2 * p2)
+      in
+        (a2, remaining - 1, p2, step2)
+  in
+    i32.i64 p

exercises/practice/nth-prime/.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.
+
+[75c65189-8aef-471a-81de-0a90c728160c]
+description = "first prime"
+
+[2c38804c-295f-4701-b728-56dea34fd1a0]
+description = "second prime"
+
+[56692534-781e-4e8c-b1f9-3e82c1640259]
+description = "sixth prime"
+
+[fce1e979-0edb-412d-93aa-2c744e8f50ff]
+description = "big prime"
+
+[bd0a9eae-6df7-485b-a144-80e13c7d55b2]
+description = "there is no zeroth prime"

exercises/practice/nth-prime/nth_prime.fut

@@ -0,0 +1 @@
+def prime (number: i32): i32 = ???

exercises/practice/nth-prime/test.fut

@@ -0,0 +1,39 @@
+import "nth_prime"
+
+-- first prime
+-- ==
+-- input { 1 }
+-- output { 2 }
+
+-- second prime
+-- ==
+-- input { 2 }
+-- output { 3 }
+
+-- sixth prime
+-- ==
+-- input { 6 }
+-- output { 13 }
+
+-- seventh prime
+-- ==
+-- input { 7 }
+-- output { 17 }
+
+-- big prime
+-- ==
+-- input { 10001 }
+-- output { 104743 }
+
+-- very big prime
+-- ==
+-- input { 65537 }
+-- output { 821647 }
+
+-- there is no zeroth prime
+-- ==
+-- input { 0 }
+-- error: Error*
+
+let main (number: i32): i32 =
+  prime number