Step by Step solution about How to resolve the algorithm Sub-unit squares step by step in the Haskell programming language

This Haskell code defines two functions: isSquareNumber and isSubunitSquare, and then uses them to generate a list of the first 7 subunit square numbers in solution.

Here's a breakdown of the code:

1. isSquareNumber checks if a given integer n is a perfect square. It does this by calculating the square root of n, rounding it down to the nearest integer using floor, and checking if the result squared is equal to n.

2. isSubunitSquare checks if a given integer n is a subunit square. A subunit square is a number that is both a perfect square and has the property that its digits, when decremented by 1 and then converted back to digits, form another perfect square.

3. The code first converts n to a string numstr using show.

4. It then creates a new number subunitnum by mapping a function over the digits of numstr. This function decrements each digit by 1 and then converts it back to a digit using intToDigit.

5. Finally, it checks if both n and subunitnum are perfect squares using isSquareNumber.

6. solution generates a list of the first 7 subunit square numbers by filtering the list of all positive integers starting from 1 using isSubunitSquare and then taking the first 7 elements using take.

import Data.Char ( digitToInt , intToDigit )

isSquareNumber :: Int -> Bool 
isSquareNumber n = root * root == n
 where
  root :: Int
  root = floor $ sqrt $ fromIntegral n

isSubunitSquare :: Int -> Bool
isSubunitSquare n 
   |elem '0' numstr = False
   |otherwise = isSquareNumber n && isSquareNumber subunitnum
   where
    numstr :: String
    numstr = show n
    subunitnum :: Int
    subunitnum = read $ map (intToDigit . pred . digitToInt ) numstr 

solution :: [Int]
solution = take 7 $ filter isSubunitSquare [1,2..]