Implementation of the nth-prime exercise (#422)

Implementation of the nth-prime exercise

Author: NobbZ

config.json

@@ -520,6 +520,17 @@
         "matrices"
       ]
     },
+    {
+      "slug": "nth-prime",
+      "uuid": "8600a843-ec71-4f1a-b9fe-2ed515035101",
+      "core": false,
+      "unlocked_by": "hamming",
+      "difficulty": 4,
+      "topics": [
+        "algorithms",
+        "math"
+      ]
+    },
     {
       "slug": "largest-series-product",
       "uuid": "b312ff0e-90e3-4dd8-99dc-df4a9deb1907",

exercises/nth-prime/README.md

@@ -0,0 +1,39 @@
+# Nth Prime
+
+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.
+
+## Running tests
+
+In order to run the tests, issue the following command from the exercise
+directory:
+
+For running the tests provided, `rebar3` is used as it is the official build and
+dependency management tool for erlang now. Please refer to [the tracks installation
+instructions](http://exercism.io/languages/erlang/installation) on how to do that.
+
+In order to run the tests, you can issue the following command from the exercise
+directory.
+
+```bash
+$ rebar3 eunit
+```
+
+## Questions?
+
+For detailed information about the Erlang track, please refer to the
+[help page](http://exercism.io/languages/erlang) on the Exercism site.
+This covers the basic information on setting up the development
+environment expected by the exercises.
+
+## Source
+
+A variation on Problem 7 at Project Euler [http://projecteuler.net/problem=7](http://projecteuler.net/problem=7)
+
+## Submitting Incomplete Solutions
+It's possible to submit an incomplete solution so you can see how others have completed the exercise.

exercises/nth-prime/rebar.config

@@ -0,0 +1,30 @@
+%% Erlang compiler options
+{erl_opts, [debug_info, warnings_as_errors]}.
+
+{deps, [{erl_exercism, "0.1.2"}]}.
+
+{dialyzer, [
+  {warnings, [underspecs, no_return]},
+  {get_warnings, true},
+  {plt_apps, top_level_deps}, % top_level_deps | all_deps
+  {plt_extra_apps, []},
+  {plt_location, local}, % local | "/my/file/name"
+  {plt_prefix, "rebar3"},
+  {base_plt_apps, [stdlib, kernel, crypto]},
+  {base_plt_location, global}, % global | "/my/file/name"
+  {base_plt_prefix, "rebar3"}
+]}.
+
+%% eunit:test(Tests)
+{eunit_tests, []}.
+%% Options for eunit:test(Tests, Opts)
+{eunit_opts, [verbose]}.
+
+%% == xref ==
+
+{xref_warnings, true}.
+
+%% xref checks to run
+{xref_checks, [undefined_function_calls, undefined_functions,
+  locals_not_used, exports_not_used,
+  deprecated_function_calls, deprecated_functions]}.

exercises/nth-prime/src/example.erl

@@ -0,0 +1,57 @@
+-module(example).
+
+-export([prime/1]).
+
+
+prime(N) when is_integer(N), N>0 ->
+	Generator=prime_generator(),
+	prime(Generator, N, []).
+
+prime(Generator, N, KnownPrimes0) when length(KnownPrimes0)<N ->
+	Next=next_candidate(Generator),
+	KnownPrimes1=case is_prime(Next, KnownPrimes0) of
+		true -> KnownPrimes0++[Next];
+		false -> KnownPrimes0
+	end,
+	prime(Generator, N, KnownPrimes1);
+prime(_, _, Primes) ->
+	lists:last(Primes).
+
+is_prime(Candidate, KnownPrimes) ->
+	SqrtCandidate=math:sqrt(Candidate),
+	is_prime(Candidate, SqrtCandidate, KnownPrimes).
+
+is_prime(_, _, []) ->
+	true;
+is_prime(_, SqrtCandidate, [KnownPrime|_]) when KnownPrime>SqrtCandidate ->
+	true;
+is_prime(Candidate, _, [KnownPrime|_]) when Candidate rem KnownPrime=:=0 ->
+	false;
+is_prime(Candidate, SqrtCandidate, [_|KnownPrimes]) ->
+	is_prime(Candidate, SqrtCandidate, KnownPrimes).
+
+next_candidate(Generator) ->
+	Candidate=receive {Generator, Candidate1} -> Candidate1 end,
+	Generator ! {self(), next},
+	Candidate.
+
+prime_generator() ->
+	Generator=spawn_link(
+		fun () -> prime_generator_loop() end
+	),
+	Generator ! {self(), next},
+	Generator.
+
+prime_generator_loop() ->
+	prime_generator_loop(2).
+
+prime_generator_loop(2) ->
+	receive {Reply, next} -> Reply ! {self(), 2} end,
+	prime_generator_loop(3);
+prime_generator_loop(3) ->
+	receive {Reply, next} -> Reply ! {self(), 3} end,
+	prime_generator_loop(6);
+prime_generator_loop(N) ->
+	receive {Reply1, next} -> Reply1 ! {self(), N-1} end,
+	receive {Reply2, next} -> Reply2 ! {self(), N+1} end,
+	prime_generator_loop(N+6).

exercises/nth-prime/src/nth_prime.app.src

@@ -0,0 +1,9 @@
+{application, nth_prime,
+  [{description, "exercism.io - nth-prime"},
+    {vsn, "0.0.1"},
+    {modules, []},
+    {registered, []},
+    {applications, [kernel,
+      stdlib]},
+    {env, []}
+]}.

exercises/nth-prime/src/nth_prime.erl

@@ -0,0 +1,6 @@
+-module(nth_prime).
+
+-export([prime/1]).
+
+
+prime(_N) -> undefined.

exercises/nth-prime/test/nth_prime_tests.erl

@@ -0,0 +1,29 @@
+%% Based on canonical data version 2.1.0.1
+%% Generated with 'testgen v0.1.0'
+%% https://github.com/exercism/problem-specifications/raw/4a3ba76cf247f83f2417b35df68404279942df07/exercises/nth-prime/canonical-data.json
+%% This file is automatically generated from the exercises canonical data.
+
+-module(nth_prime_tests).
+
+-include_lib("erl_exercism/include/exercism.hrl").
+-include_lib("eunit/include/eunit.hrl").
+
+
+
+
+'1_first_prime_test_'() ->
+    {"first prime", ?_assertEqual(2, nth_prime:prime(1))}.
+
+'2_second_prime_test_'() ->
+    {"second prime", ?_assertEqual(3, nth_prime:prime(2))}.
+
+'3_sixth_prime_test_'() ->
+    {"sixth prime", ?_assertEqual(13, nth_prime:prime(6))}.
+
+'4_big_prime_test_'() ->
+    {"big prime",
+     ?_assertEqual(104743, nth_prime:prime(10001))}.
+
+'5_there_is_no_zeroth_prime_test_'() ->
+    {"there is no zeroth prime",
+     ?_assertError(_, nth_prime:prime(0))}.