MeTryingToDoItWithoutForLoops.fs

#light
 
open System
 
let text = @"
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"
 
// figure out how big the matrix is
let rows = text.Split([| '\r'; '\n' |], StringSplitOptions.RemoveEmptyEntries).Length
 
let columns = text.Split([| '\r'; '\n' |], StringSplitOptions.RemoveEmptyEntries).[0]
                .Split([|' '|], StringSplitOptions.RemoveEmptyEntries).Length

// build it                
let cells = text.Split([| ' '; '\n'; '\r' |], StringSplitOptions.RemoveEmptyEntries)
 
let grid = Array2.init rows columns <| fun x y -> int cells.[(columns * x) + y]
 
// define our moves
let moveDown x y = x, y + 1
 
let moveRight x y = x + 1, y
 
let moveDiagnalDown x y = x + 1, y + 1
 
let moveDiagnalUp x y = x + 1, y - 1

let rec repeatMove f n x y =
    match n with
    | 0 -> x, y
    | _ -> let x', y' = f x y
           repeatMove f (n - 1) x' y'
    
let canMakeMoves f n w h x y =
    let x', y' = repeatMove f n x y
    x' >= 0 && x' <= w && y' >= 0 && y' <= h
    
let rec makeMoves f n x y (ms:'a[,]) =
    match n with
    | 0 -> []
    | _ -> let m = ms.[y, x]
           let x', y' = f x y
           m :: makeMoves f (n - 1) x' y' ms

// generate n-length sequences with a move, f           
let rec processLine f n x y ms =
    let h = Array2.length1 ms
    let w = Array2.length2 ms
    
    // TODO: I should combine canMakeMoves with makeMoves
    match canMakeMoves f n w h x y with
    | false -> []
    | true -> let m = makeMoves f n x y ms
              let x', y' = repeatMove f 1 x y
              m :: processLine f n x' y' ms

// generate n-length sequences with a move g, starting at a starting point 
// moving with f
let rec processLines f g n x y ms =
    let h = Array2.length1 ms
    let w = Array2.length2 ms
    
    match canMakeMoves f 1 w h x y with
    | false -> []
    | true -> let m = processLine g n x y ms
              let x', y' = repeatMove f 1 x y
              m @ processLines f g n x' y' ms

// These are all of our n-length sequences
let sequences n ms =
    processLines moveDown moveRight n 0 0 ms
    @ processLines moveRight moveDown n 0 0 ms
    @ processLines moveDown moveDiagnalDown n 0 0 ms
    @ processLines moveDown moveDiagnalUp n 0 0 ms
    @ processLines moveRight moveDiagnalDown n 0 0 ms
    @ processLines moveRight moveDiagnalUp n 0 ((Array2.length2 ms) - 1) ms
    
let products xs =
    xs |> List.map (fun x -> x |> List.reduce_left (*))

let answer =
    grid |> sequences 4 |> products |> Seq.max

do
    printfn "The answer is: %d" answer

Problem11-Take2.fs

#light

open System

(*
let text = @"
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"
*)

let text = @"
08 02 22 97
49 49 99 40
81 49 31 73
52 70 95 23
"
let rows = text.Split([| '\r'; '\n' |], StringSplitOptions.RemoveEmptyEntries).Length
let columns = text.Split([| '\r'; '\n' |], StringSplitOptions.RemoveEmptyEntries).[0]
                .Split([|' '|], StringSplitOptions.RemoveEmptyEntries).Length
                
let cells = text.Split([| ' '; '\n'; '\r' |], StringSplitOptions.RemoveEmptyEntries)
let grid = Array2.init rows columns <| fun x y -> int cells.[(columns * x) + y]

let sequences grid n = 
    seq { 
    
        let lx = Array2.length1 grid
        let ly = Array2.length2 grid
        
        (*
        // down
        for i = 0 to lx - 1 do 
            for j = 0 to ly - n do yield seq {
                for k = 0 to n - 1 do 
                    printfn "%d, %d" i (j + k)
                    yield grid.[i,j+k] }
        
        // across
        for j = 0 to ly - 1 do 
            for i = 0 to lx - n do yield seq {
                for k = 0 to n - 1 do 
                    printfn "%d, %d" (i + k) j
                    yield grid.[i+k,j] }
        
        // diagnal down from top side
        // from 0 to the last column that can yield at least one n-length sequence
        for i = 0 to lx - n do
            for j = 0 to ly - n do yield seq {
                for k = 0  to n - 1 do 
                    yield grid.[i+k,j+k] }
        
        // diagnal down from left side
        // from 1 to the last row that can yield at least one n-length sequence
        for j = 1 to ly - n do
            for i = 0 to lx - n do yield seq {
                for k = 0 to n - 1 do
                    yield grid.[i+k, j+k] }
        
        // diagnal up from left side
        for j = ly - 1 to n - 1 do
            for i = 0 to lx - n do yield seq {
                for k = 0 to n - 1 do
                    printfn "%d, %d" (i+k) (j-k)
                    yield grid.[i+k, j-k] }
        *)
        
        let is = seq { 0 .. lx - n }
        let js = seq { ly - 1 .. -1 .. lx - n }
        let ks = seq { 0 .. n - 1 }
        is |> Seq.map (fun i -> 
            js |> Seq.map (fun j ->
                ks |> Seq.map (fun k -> grid.[i + k, j - k])))
                    
            
        // diagnal up from bottom
        for i = 0 to lx - n do 
            printfn "diagnal up from bottom from %d, %d to %d, %d" i (ly - 1) (i + n - 1) (lx - n)
            for j = ly - 1 to lx - n do yield seq {
                printfn "from %d, %d to %d, %d" i j (i + n - 1) (j - n + 1)
                for k = 0 to n - 1 do 
                    printfn "%d, %d" (i + k) (j - k)
                    yield grid.[i + k, j - k] }
    }                               

let products (xs:int seq seq) = 
    xs |> Seq.map (fun x -> x |> Seq.reduce (*))
    
let answer = 
    sequences grid 4 |> products |> Seq.max