done 1 mobius

src/fib.erl

@@ -1,5 +1,5 @@
 -module(fib).
--export([fib_p/1]).
+-export([fib_p/1, fib_g/1, tail_fib/1, say/0, start_time_check/0]).
 
 % Сопоставление с образцом
 fib_p(0) -> 0;
@@ -9,4 +9,24 @@ fib_p(N) -> fib_p(N - 1) + fib_p(N - 2).
 % Сторожевая последовательность
 fib_g(N) when N < 1 -> 0;
 fib_g(N) when N < 2 -> 1;
-fib_g(N) -> fib_g(N-1) + fib_g(N-2).
+fib_g(N) -> fib_g(N - 1) + fib_g(N - 2).
+
+% Хвостовая рекурсия
+tail_fib(N) -> tfib(N, 0, 1).
+tfib(0, Result, Next) -> Result;
+tfib(N, Result, Next) -> tfib(N - 1, Next, Result + Next).
+
+say() -> io:format("The result is: ~p~n", [tail_fib(10)]).
+
+exec_time(Depth) ->
+  Start = os:timestamp(),
+  fib_p(Depth),
+  io:format("Depth = ~p, Time ~f sec~n", [Depth, (timer:now_diff(os:timestamp(), Start) / 1000)]).
+
+for(0, _, _) -> [];
+for(N, Term, Step) when N > 0 ->
+  exec_time(N),
+  [Term | for(N - Step, Term, Step)].
+
+start_time_check() ->
+  for(40, 20, 5).

src/mobius.erl

@@ -0,0 +1,94 @@
+%%%-------------------------------------------------------------------
+%%% @author ivan-igorevich
+%%% @copyright (C) 2023, self
+%%% @doc
+%%%
+%%% @end
+%%% Created : 13. Feb 2023 8:49 AM
+%%%-------------------------------------------------------------------
+-module(mobius).
+-author("ivan-igorevich").
+
+%% API
+-export([is_prime/1, prime_factors/1, is_square_multiple/1, find_square_multiples/2, say/1, start_time_check/0]).
+
+%% region is_prime
+is_prime(N) when N < 2 ->
+  false;
+is_prime(N) ->
+  is_prime(N, 2, trunc(math:sqrt(N)) + 1).
+
+is_prime(_, Max, Max) ->
+  true;
+is_prime(N, I, Max) ->
+  if
+    N rem I =:= 0 ->
+      false;
+    true ->
+      is_prime(N, I + 1, Max)
+  end.
+%% endregion is_prime
+
+%% region prime_factors
+prime_factors(N) ->
+  prime_factors(N, 2, []).
+
+prime_factors(X, N, Primes) when X rem N == 0 ->
+  prime_factors(trunc(X / N), 2, [N | Primes]);
+prime_factors(X, N, Primes) ->
+  case N < math:sqrt(X) + 1 of
+    true ->
+      prime_factors(X, N + 1, Primes);
+    false ->
+      [X | Primes]
+  end.
+%% endregion prime_factors
+
+%% region is_square_multiple
+is_square_multiple(N)->
+  is_square_multiple_fun(prime_factors(N)).
+
+is_square_multiple_fun([H | T]) ->
+  case lists:member(H, T) of
+    true -> true;
+    false -> is_square_multiple_fun(T)
+  end;
+
+is_square_multiple_fun([]) ->
+  false.
+%% endregion is_square_multiple
+
+%% region find_square_multiples
+find_square_multiples(Count, MaxN) ->
+  find_square_multiples_fun(Count, MaxN, []).
+
+find_square_multiples_fun(Count, CurrentNumber, FoundSquareMultipleNumber)
+  when length(FoundSquareMultipleNumber) == Count  ->
+  CurrentNumber + 1;
+
+find_square_multiples_fun(_, 2, _) ->
+  fail;
+
+find_square_multiples_fun(Count, TestNumber, FoundSquareMultipleNumber) ->
+  case is_square_multiple(TestNumber) of
+    true -> FoundsNumber = FoundSquareMultipleNumber ++ [TestNumber];
+    false -> FoundsNumber = []
+  end,
+  find_square_multiples_fun(Count, TestNumber - 1, FoundsNumber).
+%% endregion find_square_multiples
+
+for(0, _, _) -> [];
+for(N, Term, Step) when N > Term ->
+  exec_time(N),
+  [Term | for(N - Step, Term, Step)].
+
+start_time_check() ->
+  for(6, 4, 1).
+
+exec_time(Depth) ->
+  Start = os:timestamp(),
+  say(Depth),
+  io:format("Depth = ~p, Time ~f sec~n", [Depth, (timer:now_diff(os:timestamp(), Start) / 1000)]).
+
+say(Depth) -> io:format("The result is: ~p~n", [find_square_multiples(Depth, 30000)]).
+

test/fib_test.erl

@@ -11,7 +11,8 @@
 
 fib_test_() -> [
   {"Test fib_p", fun test_fib_p/0 },
-  {"Test fib_g", fun test_fib_g/0 }
+  {"Test fib_g", fun test_fib_g/0 },
+  {"Test tail_fib", fun test_tail_fib/0 }
 ].
 
 test_fib_p() ->
@@ -39,3 +40,16 @@ test_fib_g() ->
   ?assertEqual(21, fib:fib_g(8)),
   ?assertEqual(34, fib:fib_g(9)),
   ?assertEqual(55, fib:fib_g(10)).
+
+test_tail_fib() ->
+  ?assertEqual(0, fib:tail_fib(0)),
+  ?assertEqual(1, fib:tail_fib(1)),
+  ?assertEqual(1, fib:tail_fib(2)),
+  ?assertEqual(2, fib:tail_fib(3)),
+  ?assertEqual(3, fib:tail_fib(4)),
+  ?assertEqual(5, fib:tail_fib(5)),
+  ?assertEqual(8, fib:tail_fib(6)),
+  ?assertEqual(13, fib:tail_fib(7)),
+  ?assertEqual(21, fib:tail_fib(8)),
+  ?assertEqual(34, fib:tail_fib(9)),
+  ?assertEqual(55, fib:tail_fib(10)).

test/mobius_test.erl

@@ -0,0 +1,30 @@
+%%%-------------------------------------------------------------------
+%%% @author ivan-igorevich
+%%% @copyright (C) 2023, self
+%%% @doc
+%%%
+%%% @end
+%%% Created : 13. Feb 2023 9:03 AM
+%%%-------------------------------------------------------------------
+-module(mobius_test).
+-include_lib("eunit/include/eunit.hrl").
+
+mobius_test_() -> [
+  {"Test is_prime", fun test_is_prime/0},
+  {"Test prime_factors", fun test_find_square_multiples/0}
+].
+
+test_is_prime() ->
+  ?assertNot(mobius:is_prime(1)),
+  ?assert(mobius:is_prime(2)),
+  ?assert(mobius:is_prime(3)),
+  ?assertNot(mobius:is_prime(58)),
+  ?assert(mobius:is_prime(59)),
+  ?assertNot(mobius:is_prime(60)),
+  ?assertNot(mobius:is_prime(112)),
+  ?assert(mobius:is_prime(113)).
+
+
+test_find_square_multiples() ->
+  ?assertEqual(fail, mobius:find_square_multiples(3, 20)),
+  ?assertEqual(48, mobius:find_square_multiples(3, 50)).