SWiP Lab 2

type ulamek = int * int

exception DzieleniePrzezZero

//let ( ++ ) (a, b) (c, d) = (a*d + b*c, b*d)
//let ( -- ) (a, b) (c, d) = (a*d - b*c, b*d)
//let ( ** ) (a, b) (c, d) = (a*c, b*d)
//let ( /./ ) (a, b) (c, d) = (a,b) ** (d,c)
//let ( == ) (a, b)  (c, d) = (a*d = b*c)

let rec NWD = function
    | (0, n) -> n
    | (m, n) -> NWD(n % m, m)

let skroc (l,m) =
    let znak = if l*m<0 then -1 else 1
    let al = abs l
    let am = abs m
    let d  = NWD(al,am)
    in (znak * (al / d), am / d)

let naString (l, m) =
    let znak = if l*m<0 then "-" else "" (* deklaracje wewnetrzne *)
    let al = abs l (* wart.bezw. = liczba nat. *)
    let am = abs m
    let d = NWD(al, am)
    in znak + (System.Convert.ToString(al / d))
            + "/" + (System.Convert.ToString(am / d))

// ZADANIE 2

type samochod = {marka : string;  rocznik : int;  pojemnosc : float}

let siena = { marka = "FIAT"; rocznik = 1997; pojemnosc = 1586.0}
let maluch = { marka = "FIAT"; rocznik = 1987; pojemnosc = 648.0}

let malolitrazowy(x:samochod) = x.pojemnosc < 900.0;

type osoba = {imie : string; urodzony : int; adres : string}

let kier1 = {imie="Adam"; adres = "Rzeszów"; urodzony = 1960};
let kier2 = {imie="Olek"; adres = "Jasło"; urodzony = 1986};

let starszy(k1:osoba,k2:osoba) = k1.urodzony < k2.urodzony

type rej  = {pojazd : samochod; posiadacz: osoba}

let sam1:rej = {pojazd = siena; posiadacz = kier1};
let sam2:rej = {pojazd = maluch; posiadacz = kier2};

let wiekszapojemnosc (s1: rej, s2 :rej) =
    s1.pojazd.pojemnosc > s2.pojazd.pojemnosc;

// Zadania samodzielne

// 1

let checkIfZero (b, d) =
    if b = 0 || d = 0 then raise DzieleniePrzezZero

//let ( ++ ) (a, b) (c, d) =
//    checkIfZero (b, d)
//    (a*d + b*c, b*d)
//let ( -- ) (a, b) (c, d) =
//    checkIfZero (b, d)
//    (a*d - b*c, b*d)
//let ( ** ) (a, b) (c, d) =
//    checkIfZero (b, d)
//    (a*c, b*d)
//let ( /./ ) (a, b) (c, d) =
//    checkIfZero (b, d)
//    checkIfZero (b, c)
//    (a,b) ** (d,c)
//let ( == ) (a, b)  (c, d) =
//    checkIfZero (b, d)
//    (a*d = b*c)

// 2

type ulamekR = { l: int; m: int }

let ( ++++ ) a b =
    checkIfZero(a.m, b.m)
    { l = a.l * b.m; m = a.m * b.l }

let ( ---- ) a b =
    checkIfZero(a.m, b.m)
    { l = a.l * b.m - a.m * b.l; m = a.m * b.l }

let ( **** ) a b =
    checkIfZero(a.m, b.m)
    { l = a.l * b.l; m = a.m * b.m }

let ( /.../ ) a b =
    checkIfZero(a.m, b.m)
    checkIfZero(a.m, b.l)
    a **** { l = b.m; m = b.l }

let ( ==== ) a b =
    checkIfZero(a.m, b.m)
    a.l * b.m = a.m * b.l

let skrocR a =
    let znak = if a.l*a.m<0 then -1 else 1
    let al = abs a.l
    let am = abs a.m
    let d  = NWD(al,am)
    { l = znak * (al / d); m = am / d }

let naStringR a =
    let znak = if a.l*a.m<0 then "-" else "" (* deklaracje wewnetrzne *)
    let al = abs a.l (* wart.bezw. = liczba nat. *)
    let am = abs a.m
    let d = NWD(al, am)
    in znak + (System.Convert.ToString(al / d))
            + "/" + (System.Convert.ToString(am / d))
// 3

let ( ++ ) (a, b) (c, d) =
    checkIfZero (b, d)
    skroc (a*d + b*c, b*d)
let ( -- ) (a, b) (c, d) =
    checkIfZero (b, d)
    skroc (a*d - b*c, b*d)
let ( ** ) (a, b) (c, d) =
    checkIfZero (b, d)
    skroc (a*c, b*d)
let ( /./ ) (a, b) (c, d) =
    checkIfZero (b, d)
    checkIfZero (b, c)
    skroc (a,b) ** (d,c)
let ( == ) (a, b)  (c, d) =
    checkIfZero (b, d)
    (a*d = b*c)

// 4

let naString4 (l, m) =
    let znak = if l*m<0 then "-" else "" (* deklaracje wewnetrzne *)
    let al = abs l (* wart.bezw. = liczba nat. *)
    let am = abs m
    let d = NWD(al, am)
    let almin = al / d
    let ammin = am / d
    let calk = almin / ammin
    let rest = almin % ammin
    in znak + (System.Convert.ToString(calk))
            + " "
            + (System.Convert.ToString(rest))
            + "/"
            + (System.Convert.ToString(ammin))

// 5

let ( +++ ) (a, b) (c, d) =
    (a + c, b + d)

let ( --- ) (a, b) (c, d) =
    (a - c, b - d)

let ( *** ) (a, b) (c, d) =
    (a * c - b * d, a * d - b * c)

let odwrotnosc (a, b) =
    let c = a*a + b*b
    if c = 0 then raise DzieleniePrzezZero
    else (a / c, -b / c)

let ( /../ ) (a, b) (c, d) =
    (a, b) ** odwrotnosc (c, d)

let sqrtComplex (a, b) =
    0

// 6

let rec powerToUlamek (a, b) n =
    if n = 0 then (1, 1)
    elif n < 0 then skroc (a, b)
    elif n = 1 then skroc (a * a, b * b)
    else powerToUlamek (a * a, b * b) (n - 1)

// 7

let rec pierwsza' (n, o) =
    if o < 1 then false
    elif o = 1 then true
    elif n % o = 0 then false
    else pierwsza' (n, o - 1)

let pierwsza n = pierwsza' (n, n - 1)

// 8

let rec podzielnaOdDo (o, d, dzielnik) =
    if o > d then -1
    elif o % dzielnik = 0 then o
    else podzielnaOdDo (o + 1, d, dzielnik)

// 9

let multiplyUlamekLiczba (a, b) c =
    checkIfZero(b, b)
    skroc (a * c, b)

let divideUlamekLiczba (a, b) c =
    checkIfZero(b, c)
    skroc ((a, b) /./ (c, 1))

let sqrtUlamek (a, b) =
    (System.Math.Sqrt(a), System.Math.Sqrt(b))

let odwrUlamek (a, b) =
    checkIfZero(a, b)
    (b, a)

// 10

type osobaX = {imie : string; nazwisko : string; telefon : string}

let osoba1 = { imie = "Jan"; nazwisko = "Kowalski"; telefon = "111000222" }
let osoba2 = { imie = "Roman"; nazwisko = "Nowak"; telefon = "222000111" }

let checkIfSameSurname a b =
    a.nazwisko = b.nazwisko

// 11

type ksiazka = { title: string; author: string; year: int; price: float }

let ksiazka1 = { title = "Tytuł"; author = "me"}

// main

[<EntryPoint>]
let main _ =
    //let q1 = (-2, 0)
    //let q2 = (5, -10)
    //let q3 = skroc (q1 ++ q2)
    //let q4 = skroc (q2 ** q3)
    //let q5 = skroc (q4 /./ q3)

    printf "%d" (podzielnaOdDo (11, 17, 5))

    //printf "%A\n" (skroc q3)
    //printf "%A\n" (q1 -- q2)
    //printf "%A\n" (q4)
    //printf "%A\n" (q5)
    //printf "%A\n" (q1 == q2)
    //printf "%s\n" (naString q4)
    //printf "%s\n" (naString q5)
    //printf "%d\n" (NWD (22, 24))
    //printf "%d\n" (NWD (0, 12))
    0