commit 469b5b2b3da791ea1660eaf8e35fd3ab238580fb
Author: saundersp <pierre.saundersgb@gmail.com>
Date:   Sun Jun 25 00:25:50 2023 +0200

    Added files

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..539fcfd
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,4 @@
+*.hi
+*.o
+Main
+Problems
diff --git a/Main.hs b/Main.hs
new file mode 100644
index 0000000..19b45f7
--- /dev/null
+++ b/Main.hs
@@ -0,0 +1,150 @@
+import Problems ( myLast, lastTwo, kth, myLength, rev, isPalindrome, flatten, NestedList(..), compress, pack, encode )
+--import Primes ( aspGetNextPrime, aspIsPrime, aspPrimes )
+import Data.Numbers.Primes ( isPrime, primes, primeFactors )
+import Math ( mandlebrot )
+
+-- Unit testing
+main :: IO()
+main = do
+    testMisc
+    testProblems
+    testPrimes
+    mandlebrot
+
+testMisc :: IO()
+testMisc = do
+    putStrLn ("A ranged list from 1 to 1 is " ++ show (range 1 1))
+    putStrLn ("A ranged list from -2 to 7 is " ++ show (range (-2) 7))
+    putStrLn ("A ranged list from 7 to -2 is " ++ show (range 7 (-2)))
+
+    let tab = [2,1,10,6,3,8,1,1,6,3] :: [Int]
+    putStrLn ("The initial list is " ++ show tab)
+    putStrLn ("The unique list is " ++ show (nub tab))
+
+    putStrLn ("Is the initial list in ascending order ? " ++ show (isAsc tab))
+    putStrLn ("Is 1..10 in ascending order ? " ++ show (isAsc (range 1 10)))
+    putStrLn ("Is 10..1 in ascending order ? " ++ show (isAsc (range 10 1)))
+
+    putStrLn ("Is 3 is the list ? : " ++ show (isInList 3 tab))
+    putStrLn ("Is 4 is the list ? : " ++ show (isInList 4 tab))
+    putStrLn ("Is 5 is the list ? : " ++ show (isInList 5 tab))
+    putStrLn ("Is 10 is the list ? : " ++ show (isInList 10 tab))
+
+    putStrLn ("The sorted list is " ++ show (sortList tab))
+
+    putStrLn ("The reverse sorted list is " ++ show (revSortList tab))
+
+    putStrLn ("FizzBuzz 50 " ++ show (fizzBuzz [0..50]))
+
+    putStrLn ("Fionacci 10 " ++ show (fibonacci 10))
+    putStrLn ("FionacciList 10 " ++ show (fibonnaciSequence 10))
+
+testProblems:: IO()
+testProblems = do
+    let assert :: (Eq a) => (Show a) => String -> a -> a -> String
+        assert n r e = "Problem " ++ n ++ (if r == e then " Success" else " Failed, expected " ++ show e ++ " but got " ++ show r)
+
+    putStrLn (assert "1a" (myLast [1, 2, 3, 4]) (Just 4))
+    putStrLn (assert "1b" (myLast ([] :: [Bool])) Nothing)
+    putStrLn (assert "1c" (myLast ['x', 'y', 'z']) (Just 'z'))
+    putStrLn (assert "2a" (lastTwo ['a', 'b', 'c', 'd']) (Just ('c', 'd')))
+    putStrLn (assert "2b" (lastTwo ['a']) Nothing)
+    putStrLn (assert "3a" (kth ['a', 'b', 'c', 'd', 'e'] 2) (Just 'c'))
+    putStrLn (assert "3b" (kth ['a'] 2) Nothing)
+    putStrLn (assert "4a" (myLength ['a', 'b', 'c']) 3)
+    putStrLn (assert "4b" (myLength []) 0)
+    putStrLn (assert "4c" (myLength "Hello, world!") 13)
+    putStrLn (assert "5 " (rev ['a', 'b', 'c']) ['c', 'b', 'a'])
+    putStrLn (assert "6a" (isPalindrome ['x', 'a', 'm', 'a', 'x']) True)
+    putStrLn (assert "6b" (isPalindrome ['a', 'b']) False)
+    putStrLn (assert "7a" (flatten (Elem 5)) [5])
+    putStrLn (assert "7b" (flatten (List [Elem 1, List [Elem 2, List [Elem 3, Elem 4], Elem 5]])) [1, 2, 3, 4, 5])
+    putStrLn (assert "7c" (flatten (List [])) ([] :: [Int]))
+    putStrLn (assert "8 " (compress "aaabccaadeeee") "abcade")
+    putStrLn (assert "9 " (pack ['a', 'a', 'a', 'a', 'b', 'c', 'c', 'a', 'a', 'd', 'e', 'e', 'e', 'e']) ["aaaa", "b", "cc", "aa", "d", "eeee"])
+    --putStrLn (assert "10" (encode "aaabccaadeeee") [(4, 'a'),(1, 'b'),(2, 'c'),(2, 'a'),(1, 'd'),(4, 'e')])
+
+testPrimes:: IO()
+testPrimes = do
+    putStrLn ("Is 2 prime ? " ++ show (isPrime 2))
+    putStrLn ("Is 15 prime ? " ++ show (isPrime 15))
+    putStrLn ("Is 17 prime ? " ++ show (isPrime 17))
+
+    --putStrLn ("ASP : Is 2 prime ? " ++ show (aspIsPrime 2))
+    --putStrLn ("ASP : Is 15 prime ? " ++ show (aspIsPrime 15))
+    --putStrLn ("ASP : Is 17 prime ? " ++ show (aspIsPrime 17))
+
+    putStrLn ("primeFactors 15 " ++ show (primeFactors 15))
+    putStrLn ("primeFactors 45154 " ++ show (primeFactors 45154))
+
+    --putStrLn ("ASP : primeFactors 15 " ++ show (aspPrimeFactors 15))
+    --putStrLn ("ASP : primeFactors 45154 " ++ show (aspPrimeFactors 45154))
+
+    putStrLn ("primes : " ++ show (take 15 primes))
+    --putStrLn ("ASP : primes : " ++ show (take 15 aspPrimes))
+
+-- Sorting a given list
+sortList :: [Int] -> [Int]
+sortList [] = []
+sortList (x:xs) = sortList ys ++ [x] ++ sortList zs
+    where
+    ys = [a | a <- xs, a < x]
+    zs = [a | a <- xs, a >= x]
+
+-- Reverse sorting a given list
+revSortList :: [Int] -> [Int]
+revSortList [] = []
+revSortList (x:xs) = revSortList ys ++ [x] ++ revSortList zs
+    where
+    ys = [a | a <- xs, a >= x]
+    zs = [a | a <- xs, a < x]
+
+-- Is a certain element in a given list ?
+isInList :: (Eq a) => a -> [a] -> Bool
+isInList _ [] = False
+isInList e (x:xs) = (e == x) || isInList e xs
+
+-- Create a list between from a to b
+range :: Int -> Int -> [Int]
+range a b
+    | a == b    = [b]
+    | a > b     = rev (range b a)
+    | otherwise = [a..b]
+
+-- Remove all duplicates from a given list
+nub :: (Eq a) => [a] -> [a]
+nub [] = []
+-- Remove duplicates after (tail recursion)
+nub (x:xs) = x : nub [a | a <- xs, a /= x]
+-- Remove duplicates before (no tail recursion)
+--nub (x:xs) = if x `elem` xs then nub xs else x : nub xs
+
+-- Is a given list in an ascending order ?
+isAsc :: (Ord t) => [t] -> Bool
+isAsc [] = True
+isAsc [x] = True
+isAsc (x:y:xs) = (x <= y) && isAsc (y:xs)
+
+-- FizzBuzz
+fizzBuzz :: [Int] -> [[Char]]
+fizzBuzz [] = []
+fizzBuzz (x:xs) = isFizzBuzz x : fizzBuzz xs
+    where
+    isFizzBuzz :: Int -> [Char]
+    isFizzBuzz x
+        | mod x 15 == 0 = "FizzBuzz"
+        | mod x 5 == 0 = "Buzz"
+        | mod x 3 == 0 = "Fizz"
+        | otherwise = show x
+
+-- Fibonnaci number at indice n
+fibonacci :: Int -> Int
+fibonacci 0 = 0
+fibonacci 1 = 1
+fibonacci n = fibonacci (n - 1) + fibonacci (n - 2)
+
+-- Fibonnaci sequence until indice n
+fibonnaciSequence :: Int -> [Int]
+fibonnaciSequence 0 = [0]
+fibonnaciSequence 1 = [1]
+fibonnaciSequence n = fibonnaciSequence (n - 1) ++ [fibonacci n]
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..2210eda
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,15 @@
+.PHONY: all Main debug start clean
+
+all: Main
+
+Main: Main.hs
+	@ghc -Wno-tabs Main.hs
+
+start: Main
+	@./Main
+
+debug: Main.hs
+	@ghc -Wno-tabs -keep-hc-files -keep-tmp-files $^
+
+clean:
+	@rm *.hi Main *.o || true
diff --git a/Math.hs b/Math.hs
new file mode 100644
index 0000000..a74cf7f
--- /dev/null
+++ b/Math.hs
@@ -0,0 +1,60 @@
+module Math ( mandlebrot ) where
+
+import Graphics.UI.GLUT
+import Data.Complex
+
+iterations = 10
+
+x // y = fromIntegral x / fromIntegral y
+
+-- Divides [a] into [[a], [a], ...] with each sublist of length n,
+-- except the last sublist which has length <= n
+chunkify n [] = []
+chunkify n xs = let (xs', rest) = splitAt n xs
+                in xs' : chunkify n rest
+
+-- Converts a coordinate in screen space to a vertex.
+pix2vert (Size w h) (x, y) = Vertex2 ((3 // w * fromIntegral x) - 2.0)
+                             ((2 // h * fromIntegral y) - 1.0)
+
+-- List of all the vertices that represent screen pixels.
+vertices :: IO [Vertex2 GLfloat]
+vertices = get windowSize >>= \(Size w h) -> return $ [pix2vert (Size w h) (x, y) | x <- [0..w-1], y <- [0..h-1]]
+
+-- Gets the color for a number of iterations.
+getcolor :: Int -> Color3 Float
+getcolor iter | iter == iterations = Color3 0 0 0
+              | otherwise          = Color3 (amt * 0.5) amt (amt * 0.5)
+              where amt = iter // iterations
+
+-- Returns the number of iterations <= the maximum iterations of the Mandlebrot set at the given vertex
+mandel (Vertex2 r i) = length . takeWhile (\z -> magnitude z <= 2) .
+                       take iterations $ iterate (\z -> z^2 + (r :+ i)) 0
+
+-- plots one point.
+drawVert v = do color . getcolor $ mandel v
+                vertex v
+
+-- draws all th vertices in slices (to update the display while drawing).
+display' chunks = do mapM_ (\vs -> do renderPrimitive Points $ mapM_ drawVert vs
+                                      flush) chunks
+                     displayCallback $= display
+
+display = do clear [ ColorBuffer ]
+             displayCallback $= (vertices >>= display' . chunkify 256)
+             get currentWindow >>= postRedisplay
+
+mandlebrot = do
+        getArgsAndInitialize
+        initialDisplayMode $= [ SingleBuffered, RGBMode ]
+        --initialWindowSize $= Size 1200 1024
+        --initialWindowPosition $= Position 100 100
+        createWindow "Mandlebrot"
+        clearColor $= Color4 0 0 0 0
+        matrixMode $= Projection
+        loadIdentity
+        --ortho (-3) 1 (-1) 1 (-1) 1
+        --ortho (-2) 1 (-1) 1 (-1) 1
+        ortho (-3) 1 (-1) 1 (-1) 1
+        displayCallback $= display
+        mainLoop
diff --git a/Primes.hs b/Primes.hs
new file mode 100644
index 0000000..18968ec
--- /dev/null
+++ b/Primes.hs
@@ -0,0 +1,21 @@
+module Primes ( aspGetNextPrime, aspIsPrime, aspPrimes ) where
+import Problems ( kth )
+
+aspGetNextPrime :: Int -> Int
+aspGetNextPrime 1 = 2
+aspGetNextPrime 2 = 3
+aspGetNextPrime n
+    | otherwise = aspGetNextPrime (n + 2)
+
+aspIsPrime :: Int -> Bool
+aspIsPrime 1 = False
+aspIsPrime n = mod n (aspGetNextPrime 1) == 0
+--    where
+--    recMod
+
+--aspPrimeFactors :: Int -> [Int]
+--aspPrimeFactors 1 = [1]
+
+--aspPrimes :: (Integral Int) => [Int]
+aspPrimes = sieve [2..]
+    where sieve (x:xs) = [ x | x <- xs, x mod p == 0]
diff --git a/Problems.hs b/Problems.hs
new file mode 100644
index 0000000..e5ef983
--- /dev/null
+++ b/Problems.hs
@@ -0,0 +1,98 @@
+module Problems ( myLast, lastTwo, kth, myLength, rev, isPalindrome, flatten, NestedList(..), compress, pack, encode ) where
+-- H99: Ninety-Nine Haskell Problems
+-- https://wiki.haskell.org/H-99:_Ninety-Nine_Haskell_Problems
+
+-- Find the last element of a list.
+myLast :: [t] -> Maybe t
+myLast [] = Nothing
+myLast [x] = Just x
+myLast (x:xs) = myLast xs
+
+-- Find the last but one element of a list.
+lastTwo :: [t] -> Maybe (t, t)
+lastTwo [] = Nothing
+lastTwo [x] = Nothing
+lastTwo [x, y] = Just(x, y)
+lastTwo (x:y:xs) = lastTwo xs
+
+-- Find the K'th element of a list. The first element in the list is number 1.
+kth :: [t] -> Int -> Maybe t
+kth [] _ = Nothing
+kth (x:xs) n = if n == 0 then Just x else kth xs (n - 1)
+
+-- Find the number of elements of a list.
+myLength :: [t] -> Int
+myLength [] = 0
+--myLength (_:xs) = 1 + myLength xs
+myLength (_:xs) = subMyLength xs 0 + 1
+    where
+    subMyLength :: [t] -> Int -> Int
+    subMyLength [] n = n
+    subMyLength (_:ys) n = subMyLength ys (n + 1)
+
+-- Reverse a list
+rev :: [t] -> [t]
+rev [] = []
+rev (x:xs) = rev xs ++ [x]
+
+-- Palindrome
+isPalindrome :: (Eq t) => [t] -> Bool
+isPalindrome [] = True
+--isPalindrome (x:xs) = (x == y) && equal_list xs ys
+--    where
+--    equal_list :: [t] -> [t] -> Bool
+--    equal_list [] [] = True
+--    equal_list (x1:x1s) (y1:y1s) = (x1 == y1) && equal_list x1s y1s
+--    (y:ys) = rev (x:xs)
+isPalindrome (x:xs) = (x == y) && (xs == ys)
+    where (y:ys) = rev (x:xs)
+
+-- Flatten a list
+data NestedList a = Elem a | List [NestedList a]
+flatten :: NestedList a -> [a]
+flatten (List []) = []
+flatten (Elem a) = [a]
+flatten (List (x:xs)) = flatten x ++ flatten (List xs)
+
+-- Eliminate consecutive duplicates of list elements.
+-- compress :: (Eq t) => [t] -> [t]
+-- compress [] = []
+-- compress [x] = [x]
+-- compress (x:xs) = x : unique x xs
+--     where
+--     unique :: (Eq t) => t -> [t] -> [t]
+--     unique _ [] = []
+--     unique x (y:ys) = if x == y then unique y ys else y : unique y ys
+
+compress :: (Eq t) => [t] -> [t]
+compress (x:ys@(y:_)) = if x == y then compress ys else x : compress ys
+compress x = x
+
+-- Pack consecutive duplicates of list elements into sublists.
+-- If a list contains repeated elements they should be placed in separate sublists.
+--pack :: (Eq t) => [t] -> [[t]]
+--pack [] = [[]]
+--pack [x] = [[x]]
+--pack (x:y:xs)
+--    | x == y = [x,y] : pack xs
+--    | otherwise = [x] : [y] : pack xs
+
+pack :: (Eq t) => [t] -> [[t]]
+pack [] = []
+pack (x:xs) = (x:first) : pack rest
+    where
+    getReps [] = ([], [])
+    getReps (y:ys)
+        | y == x = let (f, r) = getReps ys in (y:f, r)
+        | otherwise = ([], y:ys)
+    (first, rest) = getReps xs
+
+-- Run-length encoding of a list.
+-- Use the result of problem P09 to implement the so-called run-length encoding data compression method.
+-- Consecutive duplicates of elements are encoded as lists (N E) where N is the number of duplicates of the element E.
+encode :: (Eq t) => [t] -> [(Int, t)]
+encode [] = []
+-- encode (x:xs) = [(n,e) | ]
+--     where
+--     y:ys = pack (x:xs)
+