neko-fi/lab 5/EulerFunction/Program.fs

open System

let rec gcd a b =
    if b = 0 then abs a
    else gcd b (a % b)

let areCoprime a b = 
    gcd a b = 1

let traverseCoprime (n: int) (operation: int -> int -> int) (initialValue: int) =
    [1..n] 
    |> List.filter (fun i -> areCoprime n i)
    |> List.fold operation initialValue

let eulerFunction (n: int) =
    let countOperation _ acc = acc + 1
    traverseCoprime n countOperation 0

let eulerFunctionFormula (n: int) =
    let isPrime n =
        if n <= 1 then false
        elif n <= 3 then true
        elif n % 2 = 0 || n % 3 = 0 then false
        else
            let sqrt_n = int (sqrt (float n))
            let rec checkDivisors i =
                if i > sqrt_n then true
                elif n % i = 0 || n % (i + 2) = 0 then false
                else checkDivisors (i + 6)
            checkDivisors 5

    let rec getUniquePrimeFactors n divisor factors =
        if n <= 1 then factors
        elif n % divisor = 0 then 
            let newFactors = if List.contains divisor factors then factors else divisor :: factors
            getUniquePrimeFactors (n / divisor) divisor newFactors
        else 
            getUniquePrimeFactors n (divisor + 1) factors

    if n = 1 then 1
    else
        let primeFactors = 
            if isPrime n then [n]
            else 
                let factors = getUniquePrimeFactors n 2 []
                factors |> List.filter isPrime |> List.sort

        let result = 
            primeFactors 
            |> List.fold (fun acc p -> acc * (1.0 - 1.0 / float p)) (float n)
            
        int result

let testTraverseCoprime () =
    printfn "Тестирование функции traverseCoprime:"
    
    let testCases = [2; 5; 10; 12; 15; 20; 30]
    
    for n in testCases do
        let coprimes = [1..n] |> List.filter (fun i -> areCoprime n i)
        let sum = traverseCoprime n (fun a b -> a + b) 0
        let expectedSum = List.sum coprimes
        
        let product = traverseCoprime n (fun a b -> a * b) 1
        let expectedProduct = List.fold (fun acc x -> acc * x) 1 coprimes
        
        let count = traverseCoprime n (fun _ acc -> acc + 1) 0
        let expectedCount = List.length coprimes
        
        printfn "n = %d, взаимно простые числа: %A" n coprimes
        
        printfn "  Сумма: %d (ожидаемая: %d) - %s" 
            sum expectedSum 
            (if sum = expectedSum then "OK" else "ОШИБКА")
            
        printfn "  Произведение: %d (ожидаемое: %d) - %s" 
            product expectedProduct 
            (if product = expectedProduct then "OK" else "ОШИБКА")
            
        printfn "  Количество: %d (ожидаемое: %d) - %s" 
            count expectedCount 
            (if count = expectedCount then "OK" else "ОШИБКА")
    
    printfn ""

let testEulerFunction () =
    printfn "Тестирование функции Эйлера (phi):"
    
    let expectedValues = [
        (1, 1); (2, 1); (3, 2); (4, 2); (5, 4); (6, 2); (7, 6); (8, 4); (9, 6); 
        (10, 4); (12, 4); (15, 8); (20, 8); (30, 8); (36, 12); (48, 16); (60, 16); (100, 40)
    ]
    
    for (n, expected) in expectedValues do
        let result = eulerFunction n
        printfn "  φ(%2d) = %2d (ожидаемое: %2d) - %s" 
            n result expected
            (if result = expected then "OK" else "ОШИБКА")
    
    printfn ""

let compareEulerFunctions () =
    printfn "Сравнение двух способов вычисления функции Эйлера:"
    
    let testCases = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 15; 20; 30; 36; 48; 60; 100]
    
    for n in testCases do
        let result1 = eulerFunction n
        let result2 = eulerFunctionFormula n
        
        printfn "  n = %3d: φ(n) = %3d (через обход), φ(n) = %3d (по формуле) - %s" 
            n result1 result2
            (if result1 = result2 then "СОВПАДАЕТ" else "РАЗЛИЧАЕТСЯ")
    
    printfn ""

[<EntryPoint>]
let main argv =
    Console.OutputEncoding <- Text.Encoding.UTF8
    
    printfn "Задание 14. Тестирование функции обхода взаимно простых чисел и вычисление функции Эйлера."
    printfn ""
    
    testTraverseCoprime()
    testEulerFunction()
    compareEulerFunctions()
    
    printfn "Интерактивный режим:"
    
    let tryAgain = ref true
    
    while !tryAgain do
        printf "Введите число для вычисления функции Эйлера (или 'q' для выхода): "
        let input = Console.ReadLine()
        
        match input.ToLower() with
        | "q" | "quit" | "exit" -> 
            tryAgain := false
        | _ ->
            match Int32.TryParse(input) with
            | true, n when n > 0 ->
                let startTime1 = DateTime.Now
                let phi1 = eulerFunction n
                let endTime1 = DateTime.Now
                
                let startTime2 = DateTime.Now
                let phi2 = eulerFunctionFormula n
                let endTime2 = DateTime.Now
                
                printfn "  φ(%d) = %d" n phi1
                printfn "  Через обход: %A" (endTime1 - startTime1)
                printfn "  По формуле: %A" (endTime2 - startTime2)
                
                if n <= 30 then
                    let coprimes = [1..n] |> List.filter (fun i -> areCoprime n i)
                    printfn "  Взаимно простые числа с %d: %A" n coprimes
                    
                printfn ""
            | _ ->
                printfn "  Некорректный ввод. Пожалуйста, введите положительное целое число.\n"
    
    0