Step by Step solution about How to resolve the algorithm Dinesman's multiple-dwelling problem step by step in the Haskell programming language

This Haskell code solves a logic puzzle known as the Dinesman Puzzle. The puzzle involves five people living on different floors of a five-story apartment building. The goal is to determine which floor each person lives on, given a set of constraints.

The first version of the code uses list comprehensions and guards in the Control.Monad module to generate all possible solutions and filter out those that do not meet the constraints. The permutations function from the Data.List module is used to generate all possible combinations of the five people's floor numbers. The guard function is used to check if the solution meets each of the constraints. If a solution does not meet a constraint, the guard function fails, and the solution is discarded.

The second version of the code is more concise and uses pattern matching to generate and filter the solutions. The permutations function is again used to generate all possible combinations of the five people's floor numbers. The pattern matching is used to check if the solution meets each of the constraints. If a solution does not meet a constraint, the pattern match fails, and the solution is discarded.

The output of the code is a list of tuples, where each tuple represents a solution to the puzzle. Each tuple contains five integers, representing the floor numbers of Baker, Cooper, Fletcher, Miller, and Smith, respectively.

Here is a sample output of the code:

[(3,2,4,5,1)]

This output indicates that Baker lives on floor 3, Cooper lives on floor 2, Fletcher lives on floor 4, Miller lives on floor 5, and Smith lives on floor 1.

import Data.List (permutations)
import Control.Monad (guard)

dinesman :: [(Int,Int,Int,Int,Int)]
dinesman = do
  -- baker, cooper, fletcher, miller, smith are integers representing
  -- the floor that each person lives on, from 1 to 5
  
  -- Baker, Cooper, Fletcher, Miller, and Smith live on different floors 
  -- of an apartment house that contains only five floors.
  [baker, cooper, fletcher, miller, smith] <- permutations [1..5]
  
  -- Baker does not live on the top floor.
  guard $ baker /= 5
  
  -- Cooper does not live on the bottom floor.
  guard $ cooper /= 1
  
  -- Fletcher does not live on either the top or the bottom floor.
  guard $ fletcher /= 5 && fletcher /= 1
  
  -- Miller lives on a higher floor than does Cooper.
  guard $ miller > cooper
  
  -- Smith does not live on a floor adjacent to Fletcher's.
  guard $ abs (smith - fletcher) /= 1
  
  -- Fletcher does not live on a floor adjacent to Cooper's.
  guard $ abs (fletcher - cooper) /= 1
  
  -- Where does everyone live?
  return (baker, cooper, fletcher, miller, smith)

main :: IO ()
main = do
  print $ head dinesman -- print first solution: (3,2,4,5,1)
  print dinesman -- print all solutions (only one): [(3,2,4,5,1)]


import Data.List (permutations)

main :: IO ()
main =
  print
    [ ( "Baker lives on " <> show b,
        "Cooper lives on " <> show c,
        "Fletcher lives on " <> show f,
        "Miller lives on " <> show m,
        "Smith lives on " <> show s
      )
      | [b, c, f, m, s] <- permutations [1 .. 5],
        b /= 5,
        c /= 1,
        f /= 1,
        f /= 5,
        m > c,
        abs (s - f) > 1,
        abs (c - f) > 1
    ]