//Lab 2

open System.Numerics

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//Problem 1 - create fubes function using lambda expression

let cubes list = 

    List.map (fun n -> n * n * n) list

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printfn "Cubes of [2; 4; 6]: %A\n" 

    (cubes [ 2; 4; 6 ])

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//Problem 2 - Implement C(n ,k) & factorial function using bigint

let rec Factorial n : bigint = 

    match n with

    | n when n = bigint (1) -> 

        bigint (1)

    | _ -> n * Factorial(n - bigint (1))

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let C n k = 

    Factorial(n) 

    / (Factorial(k) * Factorial(n - k))

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printfn "C 20 5: %A\n" 

    (C (bigint (20)) (bigint (5)))

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//Problem 3 - Add two lists together w/ vecadd

let vecadd l1 l2 = List.map2 (+) l1 l2

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printfn 

    "vecadd [1;2;3] [4;5;6]: %A\nvecadd [1;2;-3;4][4;-5;6;7]: %A\n" 

    (vecadd [ 1; 2; 3 ] [ 4; 5; 6 ]) 

    (vecadd [ 1; 2; -3; 4 ] 

         [ 4; -5; 6; 7 ])

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//Problem 4 - vecadd w/ matrix additionj

let rec matadd m1 m2 = 

    match m1, m2 with

    | [], [] -> []

    | m1 :: m1tail, m2 :: m2tail -> 

        (vecadd m1 m2) 

        :: (matadd m1tail m2tail)

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printfn 

    "matadd [[1;4]; [2;5;] [3;6]], \n\t\t[[7;1]; [8;2]; [9;3]]:\n\t\t\t%A" 

    (matadd [ [ 1; 4 ]

              [ 2; 5 ]

              [ 3; 6 ] ] [ [ 7; 1 ]

                           [ 8; 2 ]

                           [ 9; 3 ] ])

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