Step by Step solution about How to resolve the algorithm Brazilian numbers step by step in the Haskell programming language

This Haskell code is designed to identify and display the first 20 "Brazilian numbers" in various categories. A Brazilian number is defined as an integer greater than or equal to 7 that either is even or has all of its digits equal to each other except for its last digit (which can be different).

Here's a breakdown of the code:

1. Importing Necessary Libraries:

   import Data.Numbers.Primes (primes)

   This line imports the primes function from the Data.Numbers.Primes library, which is used to generate a list of prime numbers.

2. Defining the isBrazil Function:

   isBrazil :: Int -> Bool
   isBrazil n = 7 <= n && (even n || any (monoDigit n) [2 .. n - 2])

   This function takes an integer n as input and returns True if n is a Brazilian number; otherwise, it returns False. A number is considered Brazilian if it meets two criteria:

   • It must be greater than or equal to 7 (7 <= n).
   • It must either be even (even n) or satisfy the monoDigit condition for digits between 2 and n - 2 (any (monoDigit n) [2 .. n - 2]).

3. Defining the monoDigit Function:

   monoDigit :: Int -> Int -> Bool
   monoDigit n b =
    let (q, d) = quotRem n b
    in d ==
       snd
         (until
            (uncurry (flip ((||) . (d /=)) . (0 ==)))
            ((`quotRem` b) . fst)
            (q, d))

   This function takes two integers, n and b, as input and returns True if n has all its digits (except for the last digit) equal to b; otherwise, it returns False. It uses the quotRem function to iteratively divide n by b and check whether the remainder (d) is equal to b.

4. Main Function:

   main :: IO ()

   This is the entry point of the program.

5. Using mapM_ to Process Lists of Data:

   main =
    mapM_
      (\(s, xs) ->
          (putStrLn . concat)
            [ "First 20 "
            , s
            , " Brazilians:\n"
            , show . take 20 $ filter isBrazil xs
            , "\n"
            ])
      [([], [1 ..]), ("odd", [1,3 ..]), ("prime", primes)]

   • mapM_ applies a function to each element of a list, returning a list of the results.
   • In this case, it takes a tuple (s, xs) as input, where s is a string label and xs is a list of integers.
   • Inside the function, it prints the label, the first 20 Brazilian numbers from the given list, and a newline character.
   • The list of tuples represents three different categories of numbers: all integers, odd integers, and prime integers.

In summary, this program generates lists of integers for each of the three categories (all, odd, and prime) and then uses the isBrazil function to identify the first 20 Brazilian numbers in each list. It finally prints the results in a readable format.

import Data.Numbers.Primes (primes)

isBrazil :: Int -> Bool
isBrazil n = 7 <= n && (even n || any (monoDigit n) [2 .. n - 2])

monoDigit :: Int -> Int -> Bool
monoDigit n b =
  let (q, d) = quotRem n b
  in d ==
     snd
       (until
          (uncurry (flip ((||) . (d /=)) . (0 ==)))
          ((`quotRem` b) . fst)
          (q, d))

main :: IO ()
main =
  mapM_
    (\(s, xs) ->
        (putStrLn . concat)
          [ "First 20 "
          , s
          , " Brazilians:\n"
          , show . take 20 $ filter isBrazil xs
          , "\n"
          ])
    [([], [1 ..]), ("odd", [1,3 ..]), ("prime", primes)]