From: Julien Moutinho <julm@sourcephile.fr>
Date: Mon, 13 Jan 2025 18:45:33 +0000 (+0100)
Subject: init
X-Git-Url: https://git.sourcephile.fr/haskell/mpms.git/commitdiff_plain?ds=sidebyside

init
---

53946443a9270d87c6de11afc59e67f27e97652e
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..bb3d4b9
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,19 @@
+*.actual.*
+*.eventlog
+*.eventlog.html
+*.eventlog.json
+*.hi
+*.hp
+*.o
+*.orig
+*.prof
+*.root
+.direnv/
+.ghc.environment.*
+.stack-work/
+dist/
+dist-newstyle/
+dump-core/
+hlint.html
+result*
+.pre-commit-config.yaml
diff --git a/Main.hs b/Main.hs
new file mode 100755
index 0000000..eac855e
--- /dev/null
+++ b/Main.hs
@@ -0,0 +1,203 @@
+#!/usr/bin/env -S nix -L shell .#ghc --command runghc
+-- #!/usr/bin/env -S nix -L shell .#ghc .#ghcid --command ghcid --test :main
+-- SPDX-FileCopyrightText: 2022 Julien Mouyinho <julm+most-perfect-magic-squares@sourcephile.fr>
+-- SPDX-License-Identifier: CC0-1.0
+{-# OPTIONS_GHC -Wno-missing-signatures #-}
+{-# LANGUAGE BlockArguments #-}
+{-# LANGUAGE NoImplicitPrelude #-}
+{-# LANGUAGE OverloadedStrings #-}
+module Main where
+
+-- import Blaze.ByteString.Builder (Builder)
+import Data.ByteString qualified as BS
+import Relude
+import System.IO qualified as IO
+import Text.Blaze
+import qualified Text.Blaze.Html5 as H
+import qualified Text.Blaze.Html5.Attributes as HA
+import qualified Text.Blaze.Renderer.Utf8 as Blaze
+import Data.List ((\\))
+import Data.List qualified as List
+
+data I = D | M | C | Y
+  deriving (Eq, Ord, Show)
+data Cell = I I | H I
+  deriving (Eq, Ord, Show)
+
+mpms4 :: a -> a -> a -> a -> a -> a -> a -> a -> [[a]]
+mpms4 iD iM iC iY hD hM hC hY =
+  [ [iD, iM, iC, iY]
+  , [iC, iY, iD, iM]
+  , [hC, hY, hD, hM]
+  , [hD, hM, hC, hY]
+  ]
+
+isValid :: [Cell] -> Bool
+isValid [I D, I M, I C, I Y] = True
+isValid [H D, H M, H C, H Y] = True
+isValid [I a, I b, H aa, H bb] | a == aa && b == bb = True
+isValid _ = False
+
+squary :: [[((Integer, Integer), Cell)]]
+squary =
+  zipWith (\r -> zipWith (\c -> ((r,c),)) [0..]) [0..] $
+  mpms4 (I D) (I M) (I C) (I Y) (H D) (H M) (H C) (H Y)
+allPaths = combins 4 (concat squary)
+validPaths = filter (isValid . sort . (snd <$>)) $ allPaths
+validSortedPaths = sortBy (compare `on` (snd <$>)) validPaths
+validSortedCoords = sort $ (fst <$>) <$> validPaths
+
+mostPerfectMagicSquare4 :: Fractional a => a -> a -> a -> a -> [[a]]
+mostPerfectMagicSquare4 d m c y = mpms4 d m c y (h d) (h m) (h c) (h y)
+  where h x = ((d + m + c + y) / 2) - x
+
+square :: [[Int]]
+square = (round @Rational <$>) <$> mostPerfectMagicSquare4 24 03 19 74
+
+pathsByCombin :: [[[(Integer, Integer)]]]
+pathsByCombin =
+  [ [ [ (0,c) | c <- [0..3] ] ]
+  , [ [(0,c0), (0,c1), (0,c2), (1,c3)]
+      | [c0, c1, c2] <- combins 3 [0..3]
+      , let c3 = (List.head ([0..3] \\ [c0, c1, c2]) - 2) `mod` 4
+    ]
+  , [ [(0,c0), (0,c1), (1,c2), (1,c3)]
+      | [c0, c1] <- combins 2 [0..3]
+      , let [c2, c3] = ([0..3] \\ [c0, c1]) <&> (\c -> (c - 2) `mod` 4)
+    ]
+  , [ [(0,c0), (0,c1), (2,c2), (2,c3)]
+      | [c0, c1] <- combins 2 [0..3]
+      , let [c2, c3] = [c0, c1] <&> (\c -> (c - 2) `mod` 4)
+    ]
+  , [ [(0,c0), (0,c1), (3,c2), (3,c3)]
+      | [c0, c1] <- combins 2 [0..3]
+      , let [c2, c3] = [c0, c1]
+    ]
+  , [ [(0,c0), (1,c1), (1,c2), (1,c3)]
+      | [c0] <- combins 1 [0..3]
+      , let [c1, c2, c3] = ([0..3] \\ [c0]) <&> (\c -> (c - 2) `mod` 4)
+    ]
+  , [ [(0,c0), (1,c1), (2,c2), (2,c3)]
+      | [c0] <- combins 1 [0..3]
+      , [c1] <- combins 1 ([0..3] \\ [(c0 + 2) `mod` 4])
+      , let [c2, c3] = [(c0 + 2) `mod` 4, c1]
+    ]
+  , [ [(0,c0), (1,c1), (2,c2), (3,c3)]
+      | [c0] <- combins 1 [0..3]
+      , [c1] <- combins 1 ([0..3] \\ [(c0 + 2) `mod` 4])
+      , [c2, c3] <- [[(c0+2)`mod`4, (c1+2)`mod`4], [c1, c0]]
+    ]
+  , [ [(0,c0), (1,c1), (3,c2), (3,c3)]
+      | [c0] <- combins 1 [0..3]
+      , [c1] <- combins 1 ([0..3] \\ [(c0 + 2) `mod` 4])
+      , let [c2, c3] = [c0, (c1+2)`mod`4]
+    ]
+  , [ [(1,c0), (1,c1), (1,c2), (1,c3)]
+      | [c0, c1, c2, c3] <- combins 4 [0..3]
+    ]
+  , [ [(1,c0), (1,c1), (2,c2), (2,c3)]
+      | [c0, c1] <- combins 2 [0..3]
+      , let [c2, c3] = [c0, c1]
+    ]
+  , [ [(1,c0), (1,c1), (2,c2), (3,c3)]
+      | [c0, c1] <- combins 2 [0..3]
+      , let [c2, c3] = [c0, (c1 + 2) `mod` 4]
+    ]
+  , [ [(1,c0), (1,c1), (3,c2), (3,c3)]
+      | [c0, c1] <- combins 2 [0..3]
+      , let [c2, c3] = [(c0 + 2) `mod` 4, (c1 + 2) `mod` 4]
+    ]
+  , [ [(2,c0), (2,c1), (2,c2), (2,c3)]
+      | [c0, c1, c2, c3] <- combins 4 [0..3]
+    ]
+  , [ [(2,c0), (2,c1), (2,c2), (3,c3)]
+      | [c0, c1, c2] <- combins 3 [0..3]
+      , let [c3] = [0..3] \\ [c0, c1, c2]
+    ]
+  , [ [(2,c0), (2,c1), (3,c2), (3,c3)]
+      | [c0, c1] <- combins 2 [0..3]
+      , let [c2, c3] = [c0, c1]
+    ]
+  , [ [(2,c0), (3,c1), (3,c2), (3,c3)]
+      | [c0] <- combins 1 [0..3]
+      , let [c1, c2, c3] = ([0..3] \\ [(c0 + 2) `mod` 4])
+    ]
+  , [ [(3,c0), (3,c1), (3,c2), (3,c3)]
+      | [c0, c1, c2, c3] <- combins 4 [0..3]
+    ]
+  ]
+ol :: [b] -> [(Integer, b)]
+ol = zip [0..]
+
+main :: IO ()
+main = do
+  IO.withFile "mpms.html" IO.WriteMode $ \h ->
+    Blaze.renderMarkupToByteStringIO (BS.hPutStr h) do
+      H.docTypeHtml do
+        H.head do
+          H.title "Most-Perfect Magic Square"
+          H.link ! HA.rel "stylesheet"
+                 ! HA.type_ "text/css"
+                 ! HA.href "mpms.css"
+        H.body do
+          H.ul do
+            H.li $ "#squares = " <> show (length validSortedCoords)
+            H.li $ "sum = " <> show (sum (List.head square))
+          H.div ! HA.class_ "squares" $ do
+            forM_ validSortedCoords $ \path ->
+              H.div ! HA.class_ "square" $ do
+                forM_ (ol square) $ \(rowCoord, row) ->
+                    forM_ (ol row) $ \(colCoord, num) ->
+                      H.span ! HA.class_ ("square-num"<>""<>(if (rowCoord,colCoord) `elem` path then " num-path" else "")) $
+                        fromString $ show num
+
+-- | @'nCk' n k@ retourne le nombre de combinaisons
+-- de longueur 'k' d’un ensemble de longueur 'n'.
+--
+-- Computed using the formula:
+-- @'nCk' n (k+1) == 'nCk' n (k-1) * (n-k+1) / k@
+nCk :: Integral i => i -> i -> i
+n`nCk`k | n<0||k<0||n<k = error "nCk"
+        | otherwise     = go 1 1
+        where
+        go i acc = if k' < i then acc else go (i+1) (acc * (n-i+1) `div` i)
+        -- Use a symmetry to compute over smaller numbers,
+        -- which is more efficient and safer
+        k' = if n`div`2 < k then n-k else k
+
+-- | @combinOfRank n k r@ retourne les indices de permutation
+-- de la combinaison de 'k' entiers parmi @[1..n]@
+-- au rang lexicographique 'r' dans @[0..'nCk' n k - 1]@.
+--
+-- Construit chaque choix de la combinaison en prenant le prochain plus grand
+-- dont le successeur engendre un nombre de combinaisons
+-- qui dépasse le rang restant à atteindre.
+--
+-- DOC: <http://www.site.uottawa.ca/~lucia/courses/5165-09/GenCombObj.pdf>, p.26
+combinOfRank :: Integral i => i -> i -> i -> [i] 
+combinOfRank n k rk | rk<0||n`nCk`k<rk = error "combinOfRank"
+                    | otherwise = for1K 1 1 rk
+ where
+ for1K i j r | i <  k    = uptoRank i j r 
+             | i == k    = [j+r] -- because when i == k, nbCombs is always 1
+             | otherwise = []
+ uptoRank i j r | nbCombs <- (n-j)`nCk`(k-i)
+                , nbCombs <= r = uptoRank i (j+1) (r-nbCombs)
+                | otherwise    = j : for1K (i+1) (j+1) r
+
+-- | @combins k xs@ retourne les combinaisons
+-- de longueur 'k' des éléments de la liste 'xs'.
+combins :: Int -> [a] -> [[a]]
+combins k xs = combinsK xs List.!! (length xs - k)
+
+-- | @combinsK xs@ retourne toutes les combinaisons
+-- de longueur allant de @length xs@ à 0 de la liste 'xs',
+-- 
+-- Algorithme dynamique permettant un calcul de 'combins'
+-- relativement rapide du fait du partage de 'combinsKmoins1'.
+combinsK :: [a] -> [[[a]]]
+combinsK [] = [[[]]]
+combinsK (x : xs) =
+       zipWith (++) ([] : combinsKmoins1)
+                    (map (map (x :)) combinsKmoins1 ++ [[]])
+       where combinsKmoins1 = combinsK xs
diff --git a/flake.lock b/flake.lock
new file mode 100644
index 0000000..0871428
--- /dev/null
+++ b/flake.lock
@@ -0,0 +1,25 @@
+{
+  "nodes": {
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1734323986,
+        "narHash": "sha256-m/lh6hYMIWDYHCAsn81CDAiXoT3gmxXI9J987W5tZrE=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "394571358ce82dff7411395829aa6a3aad45b907",
+        "type": "github"
+      },
+      "original": {
+        "id": "nixpkgs",
+        "type": "indirect"
+      }
+    },
+    "root": {
+      "inputs": {
+        "nixpkgs": "nixpkgs"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}
diff --git a/flake.nix b/flake.nix
new file mode 100644
index 0000000..24aba64
--- /dev/null
+++ b/flake.nix
@@ -0,0 +1,95 @@
+# SPDX-FileCopyrightText: 2022 Julien Mouyinho <julm+most-perfect-magic-squares@sourcephile.fr>
+# SPDX-License-Identifier: CC0-1.0
+{
+  description = "Most-Perfect Magic Square";
+  inputs = {
+    nixpkgs.url = "flake:nixpkgs";
+  };
+  outputs =
+    inputs:
+    let
+      lib = inputs.nixpkgs.lib;
+      # Helper to build for each system in `lib.systems.flakeExposed`.
+      perSystem =
+        f:
+        lib.genAttrs lib.systems.flakeExposed (
+          system:
+          f rec {
+            inherit system;
+            pkgs = import inputs.nixpkgs { inherit system; };
+            haskellPackages = pkgs.haskellPackages;
+          }
+        );
+    in
+    {
+      # `nix -L build`
+      packages = perSystem (
+        { pkgs, system, haskellPackages, ... }:
+        {
+          # The Glasgow Haskell Compiler (GHC)
+          # Here made available as `.#ghc` for Main.hs's shebang
+          ghc = haskellPackages.ghcWithPackages (
+            haskellPackages: [
+              # Extra Haskell packages available
+              haskellPackages.blaze-builder
+              haskellPackages.blaze-html
+              haskellPackages.blaze-markup
+              haskellPackages.relude
+              haskellPackages.text
+              haskellPackages.transformers
+            ]
+          );
+          ghcid = pkgs.ghcid;
+          # A compiled version of `Main.hs`
+          # (instead of an interpreted one when run as `./Main.hs`)
+          # To avoid writing a `.cabal` file, `ghc --make` is called directly here,
+          # but should the script become a full fledge executable,
+          # a `.cabal` file should be written instead.
+          default = pkgs.stdenv.mkDerivation {
+            name = "Main";
+            src = ./.;
+            buildInputs = [
+              inputs.self.packages.${system}.ghc
+            ];
+            buildPhase = ''
+              mkdir -p $out/bin
+              ghc -o "$out/bin/Main" -O2 --make ./Main.hs
+            '';
+          };
+        }
+      );
+      # `nix develop` or `direnv allow`
+      devShells = perSystem (
+        { pkgs, system, ... }:
+        {
+          default = pkgs.mkShell {
+            nativeBuildInputs = [
+              inputs.self.packages.${system}.ghc
+              pkgs.haskellPackages.haskell-language-server
+              pkgs.haskellPackages.hlint
+              pkgs.reuse
+            ];
+          };
+        }
+      );
+      # `nix flake check`
+      checks = perSystem (args: with args; {
+        git-hooks-check = inputs.git-hooks.lib.${system}.run {
+          src = ./.;
+          hooks = {
+            ormolu.settings.cabalDefaultExtensions = true;
+            cabal-fmt.enable = true;
+            fourmolu.enable = true;
+            hlint.enable = true;
+            nixfmt-rfc-style.enable = true;
+            reuse = {
+              enable = true;
+              entry = "${pkgs.reuse}/bin/reuse lint";
+              pass_filenames = false;
+            };
+          };
+        };
+      });
+    };
+}
+
diff --git a/magic-squares.html b/magic-squares.html
new file mode 100644
index 0000000..5efb7eb
--- /dev/null
+++ b/magic-squares.html
@@ -0,0 +1,2 @@
+<!DOCTYPE HTML>
+<html><head><title>Most-Perfect Magic Square</title><link rel="stylesheet" type="text/css" href="magic-squares.css"></head><body><ul><li>#squares = 132</li><li>sum = 120</li></ul><div class="squares"><div class="square"><span class="square-num num-path">24</span><span class="square-num num-path">3</span><span class="square-num num-path">19</span><span class="square-num num-path">74</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num num-path">3</span><span class="square-num num-path">19</span><span class="square-num">74</span><span class="square-num">19</span><span class="square-num num-path">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num num-path">3</span><span class="square-num">19</span><span class="square-num num-path">74</span><span class="square-num num-path">19</span><span class="square-num">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num num-path">3</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num num-path">19</span><span class="square-num num-path">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num num-path">3</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num num-path">36</span><span class="square-num num-path">57</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num num-path">3</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num num-path">36</span><span class="square-num">57</span><span class="square-num">36</span><span class="square-num num-path">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num num-path">3</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num">36</span><span class="square-num num-path">57</span><span class="square-num num-path">36</span><span class="square-num">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num num-path">3</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num num-path">36</span><span class="square-num num-path">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num">3</span><span class="square-num num-path">19</span><span class="square-num num-path">74</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">24</span><span class="square-num num-path">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num">3</span><span class="square-num num-path">19</span><span class="square-num">74</span><span class="square-num">19</span><span class="square-num num-path">74</span><span class="square-num">24</span><span class="square-num num-path">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num">3</span><span class="square-num num-path">19</span><span class="square-num">74</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num num-path">41</span><span class="square-num">-14</span><span class="square-num num-path">36</span><span class="square-num">57</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num">3</span><span class="square-num num-path">19</span><span class="square-num">74</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num num-path">41</span><span class="square-num">-14</span><span class="square-num">36</span><span class="square-num">57</span><span class="square-num num-path">36</span><span class="square-num">57</span><span class="square-num">41</span><span class="square-num">-14</span></div><div class="square"><span class="square-num num-path">24</span><span class="square-num">3</span><span class="square-num num-path">19</span><span class="square-num">74</span><span class="square-num">19</span><span class="square-num">74</span><span class="square-num">24</span><span class="square-num">3</span><span class="square-num">41</span><span class="square-num">-14</span><span class="square-num num-path">36</span><span 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\ No newline at end of file
diff --git a/mpms.css b/mpms.css
new file mode 100644
index 0000000..a56d492
--- /dev/null
+++ b/mpms.css
@@ -0,0 +1,37 @@
+.squares-by-combin {
+  display: flex;
+  flex-flow: row;
+  flex-wrap: wrap;
+}
+.squares {
+  display: flex;
+  flex-flow: row;
+  flex-wrap: wrap;
+  justify-content: space-between;
+}
+.square {
+  margin-left: 1ex;
+  margin-right: 1ex;
+  margin-bottom: 1ex;
+  margin-top: 1ex;
+  font-family: monospace;
+  display: grid;
+  gap: 3px;
+  grid-template-columns: repeat(4, 1fr);
+  //justify-items: center;
+  justify-self: center;
+  font-size: 18pt;
+  //border: 3px solid black;
+}
+.square-row {
+  /*grid-template-columns: repeat(4, 1em);*/
+}
+.square-num {
+  display:flex;
+  justify-content: center;
+  outline: 3px solid #666;
+  padding:1ex 1ex;
+}
+.num-path {
+  background-color:red;
+}