Category Archives: Painter

Euler problem 17.2

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import Data.Char ( digitToInt )

one :: [String]
one =
  [ "one",
    "two",
    "three",
    "four",
    "five",
    "six",
    "seven",
    "eight",
    "nine",
    "ten",
    "eleven",
    "twelve",
    "thirteen",
    "fourteen",
    "fifteen",
    "sixteen",
    "seventeen",
    "eighteen",
    "nineteen"
  ]

ty :: [String]
ty =
  [ "twenty",
    "thirty",
    "forty",
    "fifty",
    "sixty",
    "seventy",
    "eighty",
    "ninety"
  ]

english :: Int -> [Char]
english x
  | x == 0 = []
  | x < 20 = one !! (x - 1)
  | x >= 20 && x < 100 =
      ty !! (firstDigit x - 2)
        ++ " "
        ++ english (x - firstDigit x * 10)
        
  | x < 1000 && x `mod` 100 == 0 =
      one !! (firstDigit x - 1)
        ++ " hundred"
      
  | x > 100 && x <= 999 =
      one !! (firstDigit x - 1)
        ++ " hundred and "
        ++ english (x - firstDigit x * 100)
        
  | x == 1000 = "one thousand"
  | otherwise = "error"
  where
    firstDigit = digitToInt . head . show

removeSpace :: [Char] -> [Char]
removeSpace = filter (`notElem` " ")

engCat :: [Int] -> [Char]
engCat = concatMap english

e17 :: Int
e17 = length . removeSpace $ engCat [1..1000]

— based on Haskell official

λ> e17
21124

— colorized by palette fm

— Me@2023-11-07 11:24:03 PM

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2023.11.08 Wednesday (c) All rights reserved by ACHK

Euler problem 10.2

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Find the sum of all the primes below two million.

removeIf :: (a -> Bool) -> [a] -> [a]
removeIf p = filter (not . p)

sieveIter :: Integral a => [a] -> [a] -> [a]
sieveIter [] (x:xs) = x:xs
sieveIter (x:xs) acc
  | x^2 > last (x:xs) = reverse acc++(x:xs)
  | otherwise = sieveIter xss (x:acc)
  where
    xss = removeIf (\n -> n `mod` x == 0) xs

primeList :: Integral a => [a] -> [a]
primeList xs = sieveIter xs []

pL :: [Integer]
pL = primeList [2..2000000]

f :: Integer
f = sum (takeWhile (< 2000000) pL)

— colorized by palette fm

— Me@2023-02-25 12:35:57 PM

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2023.02.26 Sunday (c) All rights reserved by ACHK

cmu-infix

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is

a library for writing infix mathematical notation in Common Lisp.

To install it:

1. In the Bash terminal, get Quicklisp by the following command:

sudo apt-get install cl-quicklisp

The file quicklisp.lisp will be created at

/usr/share/common-lisp/source/quicklisp/quicklisp.lisp

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2. Run the command

sbcl --load /usr/share/common-lisp/source/quicklisp/quicklisp.lisp

3. Follow the install instructions:

(quicklisp-quickstart:install)

(ql:add-to-init-file)

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4. To enable the library, in the Common Lisp REPL, run the code:

(ql:quickload :cmu-infix)

5. And then run:

(named-readtables:in-readtable cmu-infix:syntax)

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6. To test the library, run:

(defmacro add (x y)
  `(let ((a ,x)
         (b ,y))
     #I(a+b)))

(add 2 3)

(macroexpand-1 '(add 2 3))

(macroexpand-1 '#I(1+2-3*5^^6))

(eval (macroexpand-1 '#I(1+2-3*5^^6)))

— Me@2022-12-25 10:13:04 AM

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2022.12.25 Sunday (c) All rights reserved by ACHK

Pier, 2.2

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Euler problem 9.1

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There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

(defun e9c ()
  (loop :for a :from 1 :to 1000 :do
    (loop :for b :from 1 :to a :do
      (let ((c (- 1000 (+ a b))))
        (if (= (+ (* a a) (* b b)) (* c c))
            (return-from e9c
                (list a b c (* a b c))))))))

— colorized by palette fm

— Me@2022-12-05 05:59:49 PM

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2022.12.05 Monday (c) All rights reserved by ACHK

Euler problem 8.3

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Directory[]

mString := Import["n.txt"]

nString := StringDelete[mString, "\n" | "\r"]

nList := Map[FromDigits, Characters[nString]]

take13[lst_] := Times @@ Take[lst,13]

Fmax13n[lst_, n_] := If[Length[lst] < 13,
                        n,
                        With[{t13 = take13[lst]},
                            If[n > t13,
                                Fmax13n[Rest[lst], n],
                                Fmax13n[Rest[lst], t13]]]]

Fmax13n[nList, 0]

Wmax13n[lst_, n_] := Which[
                        Length[lst] < 13, n,
                        t13 = take13[lst];
                            n > t13, Wmax13n[Rest[lst], n],
                            True, Wmax13n[Rest[lst], t13]]

Wmax13n[nList, 0]

Fmax13n[nList, 0] - Wmax13n[nList, 0]

— colorized by palette fm

— Me@2022-11-24 05:51:56 PM

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2022.11.24 Thursday (c) All rights reserved by ACHK

Pier, 1.2

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Euler problem 8.1

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73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

(defun file-get-contents (filename)
  (with-open-file (stream filename)
    (let ((contents (make-string
                     (file-length stream))))
      (read-sequence contents stream)
      contents)))

(defun file-get-lines (filename)
  (with-open-file (stream filename)
    (loop :for line = (read-line stream nil)
          :while line
          :collect line)))

(file-get-lines #P"n.txt")

(defun string-to-list (the-string)
  (loop :for char :across the-string
        :collect char))

(defun char-to-integer-list (char-list)
  (mapcar #'digit-char-p char-list))

(let ((the-digits (char-to-integer-list
           (string-to-list
            (remove #\newline
                    (file-get-contents #P"n.txt"))))))

  (loop :for i :from 0 :to (- (length the-digits) 13)
        :maximize (apply #'*
                    (subseq
                      the-digits i (+ i 13)))))

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— colorized by palette fm

— Me@2022-11-12 04:50:19 PM

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2022.11.12 Saturday (c) All rights reserved by ACHK

1994

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This was my Art result. I had a great art teacher Mr Lo in that year. He taught us a lot of design concepts.

— Me@2020-12-29 10:52:04 AM

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2020.12.29 Tuesday (c) All rights reserved by ACHK

Pier

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d_2020_03_24__22_44_50_PM_

It was a picture I drawn in 1997. It was the summer holiday after my HKCEE public exam. It was a drawing trip with my school’s Art Club. The location was Sai Kung Pier.

As far as I remember, I haven’t drawn since then. Perhaps I do not like to draw alone. Hope that one day I could find my girlfriend finally so that I have someone to draw with.

— Me@2020-03-24 10:37:58 PM

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2020.03.26 Thursday (c) All rights reserved by ACHK

Genius 3

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* If you knew how much work went into it, you would not call it genius.

o On the paintings in the Sistine Chapel

— Michelangelo Buonarroti

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2011.01.10 Monday ACHK

Pianist

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An expert pianist can play notes faster than the brain can send signals to his hand. Likewise an artist, after a while, can make visual perception flow in through his eye and out through his hand as automatically as someone tapping his foot to a beat.

— Paul Graham

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2010.06.12 Saturday ACHK