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Microsoft Azure Notebooks - Live code - F#, R, and Python

I was exploring Jupyter notebooks , that combines live code, markdown and data, through Microsoft's implementation, known as MS Azure Notebooks , putting together a small library of R and F# notebooks . As Microsoft's FAQ for the service describes it as : ...a multi-lingual REPL on steroids. This is a free service that provides Jupyter notebooks along with supporting packages for R, Python and F# as a service. This means you can just login and get going since no installation/setup is necessary. Typical usage includes schools/instruction, giving webinars, learning languages, sharing ideas, etc. Feel free to clone and comment... In R Azure Workbook for R - Memoisation and Vectorization Charting Correlation Matrices in R In F# Charnownes Constant in FSharp.ipynb Project Euler - Problems 18 and 67 - FSharp using Dynamic Programming
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Project Euler - Problem 11

Description

  • In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
  • ..grid repeated below in code
  • The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
  • What is the greatest product of four adjacent numbers in any direction
  •  (up, down, left, right, or diagonally) in the 20×20 grid?

Solution

Like everyone else's solution, this on is basically a brute force algorithm, but I tried to keep it idiomatic, so no immutable value, and uses the yield keyword

let matrix =
    [[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; 04]]


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


let gatherMatrixValues =
    let max = List.length matrix
    let acrossValues =
        [for row=0 to (max-4) do
            for col=0 to (max-4) do
                yield TupleProd (matrix.[row].[col], matrix.[row].[col+1], matrix.[row].[col+2], matrix.[row].[col+3])]
    let downValues =
        [for row=0 to (max-4) do
            for col=0 to (max-4) do
                yield TupleProd (matrix.[row].[col], matrix.[row+1].[col], matrix.[row+2].[col], matrix.[row+3].[col])]
    let diagonalDownRight =
        [for row=0 to (max-4) do
            for col=0 to (max-4) do
                yield TupleProd (matrix.[row].[col], matrix.[row+1].[col+1], matrix.[row+2].[col+2], matrix.[row+3].[col+3])]
    let diagonalDownLeft =
        [for row=0 to (max-4) do
            for col=3 to (max-1) do
                yield TupleProd (matrix.[row].[col], matrix.[row+1].[col-1], matrix.[row+2].[col-2], matrix.[row+3].[col-3])]
    [List.max acrossValues; List.max downValues; List.max diagonalDownRight; List.max diagonalDownLeft]
    |> List.max

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