How to resolve the algorithm Greatest element of a list step by step in the Haskell programming language

Published on 7 June 2024 03:52 AM

How to resolve the algorithm Greatest element of a list step by step in the Haskell programming language

Table of Contents

Problem Statement

Create a function that returns the maximum value in a provided set of values, where the number of values may not be known until run-time.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Greatest element of a list step by step in the Haskell programming language

The provided Haskell code defines a function my_max twice, using two different approaches to calculate the maximum value from a list. Let's break down the code:

  1. First Definition of my_max:

    my_max = maximum

    This definition simply reassigns the my_max function to the built-in maximum function provided by the standard library. maximum takes a list as input and returns the maximum element in the list.

  2. Second Definition of my_max:

    my_max = foldl1 max

    This definition uses the foldl1 function to calculate the maximum value. foldl1 is a higher-order function that applies a binary function (in this case, max) to a list, starting from the leftmost element and recursively combining them. The max function returns the larger of its two arguments.

  3. Using maximumBy:

    import Data.List (maximumBy)
    import Data.Ord (comparing)
    
    wds :: [String]
    wds = ["alpha", "beta", "gamma", "delta", "epsilon", "zeta"]
    
    main :: IO ()
    main = print $ maximumBy (comparing length) wds

    In this section of code:

    • The maximumBy function is imported from the Data.List module. maximumBy takes two arguments: a comparison function and a list. It returns the element from the list that satisfies the comparison function.

    • A string list wds is defined with several Greek alphabet letters.

    • The main function prints the result of applying maximumBy to the list wds. The comparison function used is comparing length, which compares the lengths of the strings in the list.

  4. Definition of maximumBy:

    maximumBy
     :: Foldable t
     => (a -> a -> Ordering) -> t a -> a
    maximumBy cmp =
     let max_ x y =
           case cmp x y of
             GT -> x
             _ -> y
     in foldr1 max_

    This is the full definition of the maximumBy function that was imported earlier. It takes two type parameters: t (the foldable data type) and a (the element type). It also takes a comparison function cmp that takes two elements of type a and returns an Ordering value.

    The maximumBy function uses a helper function max_ to compare two elements. max_ returns the first element if the comparison function returns GT (greater than), and the second element otherwise.

    The foldr1 function is used to fold the list of elements using the max_ function. foldr1 applies the binary function (in this case, max_) to each element in the list, starting from the rightmost element and recursively combining them.

Source code in the haskell programming language

my_max = maximum


my_max = foldl1 max


import Data.List (maximumBy)
import Data.Ord (comparing)

wds :: [String]
wds = ["alpha", "beta", "gamma", "delta", "epsilon", "zeta"]

main :: IO ()
main = print $ maximumBy (comparing length) wds


maximumBy
  :: Foldable t
  => (a -> a -> Ordering) -> t a -> a
maximumBy cmp =
  let max_ x y =
        case cmp x y of
          GT -> x
          _ -> y
  in foldr1 max_


  

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