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@ -0,0 +1,162 @@
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open System
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let rec gcd a b =
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if b = 0 then abs a
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else gcd b (a % b)
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let areCoprime a b =
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gcd a b = 1
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let traverseCoprime (n: int) (operation: int -> int -> int) (initialValue: int) =
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[1..n]
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|> List.filter (fun i -> areCoprime n i)
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|> List.fold operation initialValue
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let eulerFunction (n: int) =
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let countOperation _ acc = acc + 1
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traverseCoprime n countOperation 0
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let eulerFunctionFormula (n: int) =
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let isPrime n =
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if n <= 1 then false
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elif n <= 3 then true
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elif n % 2 = 0 || n % 3 = 0 then false
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else
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let sqrt_n = int (sqrt (float n))
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let rec checkDivisors i =
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if i > sqrt_n then true
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elif n % i = 0 || n % (i + 2) = 0 then false
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else checkDivisors (i + 6)
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checkDivisors 5
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let rec getUniquePrimeFactors n divisor factors =
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if n <= 1 then factors
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elif n % divisor = 0 then
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let newFactors = if List.contains divisor factors then factors else divisor :: factors
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getUniquePrimeFactors (n / divisor) divisor newFactors
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else
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getUniquePrimeFactors n (divisor + 1) factors
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if n = 1 then 1
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else
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let primeFactors =
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if isPrime n then [n]
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else
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let factors = getUniquePrimeFactors n 2 []
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factors |> List.filter isPrime |> List.sort
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let result =
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primeFactors
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|> List.fold (fun acc p -> acc * (1.0 - 1.0 / float p)) (float n)
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int result
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let testTraverseCoprime () =
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printfn "Тестирование функции traverseCoprime:"
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let testCases = [2; 5; 10; 12; 15; 20; 30]
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for n in testCases do
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let coprimes = [1..n] |> List.filter (fun i -> areCoprime n i)
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let sum = traverseCoprime n (fun a b -> a + b) 0
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let expectedSum = List.sum coprimes
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let product = traverseCoprime n (fun a b -> a * b) 1
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let expectedProduct = List.fold (fun acc x -> acc * x) 1 coprimes
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let count = traverseCoprime n (fun _ acc -> acc + 1) 0
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let expectedCount = List.length coprimes
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printfn "n = %d, взаимно простые числа: %A" n coprimes
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printfn " Сумма: %d (ожидаемая: %d) - %s"
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sum expectedSum
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(if sum = expectedSum then "OK" else "ОШИБКА")
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printfn " Произведение: %d (ожидаемое: %d) - %s"
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product expectedProduct
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(if product = expectedProduct then "OK" else "ОШИБКА")
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printfn " Количество: %d (ожидаемое: %d) - %s"
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count expectedCount
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(if count = expectedCount then "OK" else "ОШИБКА")
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printfn ""
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let testEulerFunction () =
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printfn "Тестирование функции Эйлера (phi):"
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let expectedValues = [
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(1, 1); (2, 1); (3, 2); (4, 2); (5, 4); (6, 2); (7, 6); (8, 4); (9, 6);
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(10, 4); (12, 4); (15, 8); (20, 8); (30, 8); (36, 12); (48, 16); (60, 16); (100, 40)
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]
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for (n, expected) in expectedValues do
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let result = eulerFunction n
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printfn " φ(%2d) = %2d (ожидаемое: %2d) - %s"
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n result expected
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(if result = expected then "OK" else "ОШИБКА")
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printfn ""
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let compareEulerFunctions () =
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printfn "Сравнение двух способов вычисления функции Эйлера:"
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let testCases = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 15; 20; 30; 36; 48; 60; 100]
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for n in testCases do
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let result1 = eulerFunction n
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let result2 = eulerFunctionFormula n
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printfn " n = %3d: φ(n) = %3d (через обход), φ(n) = %3d (по формуле) - %s"
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n result1 result2
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(if result1 = result2 then "СОВПАДАЕТ" else "РАЗЛИЧАЕТСЯ")
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printfn ""
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[<EntryPoint>]
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let main argv =
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Console.OutputEncoding <- Text.Encoding.UTF8
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printfn "Задание 14. Тестирование функции обхода взаимно простых чисел и вычисление функции Эйлера."
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printfn ""
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testTraverseCoprime()
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testEulerFunction()
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compareEulerFunctions()
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printfn "Интерактивный режим:"
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let tryAgain = ref true
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while !tryAgain do
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printf "Введите число для вычисления функции Эйлера (или 'q' для выхода): "
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let input = Console.ReadLine()
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match input.ToLower() with
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| "q" | "quit" | "exit" ->
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tryAgain := false
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| _ ->
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match Int32.TryParse(input) with
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| true, n when n > 0 ->
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let startTime1 = DateTime.Now
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let phi1 = eulerFunction n
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let endTime1 = DateTime.Now
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let startTime2 = DateTime.Now
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let phi2 = eulerFunctionFormula n
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let endTime2 = DateTime.Now
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printfn " φ(%d) = %d" n phi1
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printfn " Через обход: %A" (endTime1 - startTime1)
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printfn " По формуле: %A" (endTime2 - startTime2)
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if n <= 30 then
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let coprimes = [1..n] |> List.filter (fun i -> areCoprime n i)
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printfn " Взаимно простые числа с %d: %A" n coprimes
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printfn ""
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| _ ->
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printfn " Некорректный ввод. Пожалуйста, введите положительное целое число.\n"
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0
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