Step by Step solution about How to resolve the algorithm Sorting algorithms/Cocktail sort with shifting bounds step by step in the Julia programming language

The code snippet you provided implements the Cocktail Shaker Sort in Julia, a programming language for scientific computing. The Cocktail Shaker Sort is a sorting algorithm that is similar to the Bubble Sort, but it scans the array in both directions, from left to right and right to left. The code is divided into two modules, CocktailShakerSorts and BenchmarkTools. The CocktailShakerSorts module implements the sorting algorithm and exports the CocktailShakerSort struct as the algorithm. The BenchmarkTools module is used to benchmark the sorting algorithm.

The sort! function is the main function of the sorting algorithm. It takes an AbstractVector A, two indices lo and hi, an algorithm a, and an Ordering ord. The lo and hi indices specify the range of the array to be sorted, and the a algorithm specifies the sorting algorithm to use. The ord Ordering specifies the ordering of the array, either ForwardOrdering or ReverseOrdering.

The sort! function first checks if the range of the array to be sorted is valid. If the range is not valid, it returns the array. If the range is valid, it sorts the array using the Cocktail Shaker Sort algorithm.

The Cocktail Shaker Sort algorithm works by scanning the array in both directions, from left to right and right to left. In each pass, the algorithm compares adjacent elements in the array and swaps them if they are out of order. The algorithm continues to scan the array in both directions until the array is sorted.

The BenchmarkTools module is used to benchmark the sorting algorithm. The @btime macro is used to measure the time it takes to sort an array. The sort! function is called twice, once with the default sorting algorithm and once with the Cocktail Shaker Sort algorithm. The time it takes to sort the array with each algorithm is printed to the console.

The output of the code snippet is as follows:

[5, 8, 2, 0, 6, 1, 9, 3, 4] => [0, 1, 2, 3, 4, 5, 6, 8, 9] => [9, 8, 6, 5, 4, 3, 2, 1, 0]

Using default sort, which is Quicksort with integers:
 9.719 ns (99 allocations: 2.20 KiB)

Using CocktailShakerSort:
 12.321 ns (13 allocations: 2.20 KiB)

As you can see, the Cocktail Shaker Sort algorithm is slightly slower than the default sorting algorithm, which is Quicksort. However, the Cocktail Shaker Sort algorithm is still a relatively efficient sorting algorithm, and it is easy to implement.

module CocktailShakerSorts

using Base.Order, Base.Sort
import Base.Sort: sort!
export CocktailShakerSort

struct CocktailSortAlg <: Algorithm end
const CocktailShakerSort = CocktailSortAlg()

function sort!(A::AbstractVector, lo::Int, hi::Int, a::CocktailSortAlg, ord::Ordering)
    if lo > 1 || hi < length(A)
        return sort!(view(A, lo:hi), 1, length(A), a, ord)
    end
    forward, beginindex, endindex = ord isa ForwardOrdering, 1, length(A) - 1

    while beginindex <= endindex
		newbegin, newend = endindex, beginindex
        for idx in beginindex:endindex
            if (forward && A[idx] > A[idx + 1]) || (!forward && A[idx] < A[idx + 1])
                A[idx + 1], A[idx] = A[idx], A[idx + 1]
                newend = idx
            end
        end
        # end has another in correct place, so narrow end by 1
        endindex = newend - 1

        for idx in endindex:-1:beginindex
            if (forward && A[idx] > A[idx + 1]) || (!forward && A[idx] < A[idx + 1])
                A[idx + 1], A[idx] = A[idx], A[idx + 1]
                newbegin = idx
            end
        end
        # beginning has another in correct place, so narrow beginning by 1
        beginindex = newbegin + 1
    end
    A
end

end # module

using .CocktailShakerSorts
using BenchmarkTools

cocktailshakersort!(v) = sort!(v; alg=CocktailShakerSort)

arr = [5, 8, 2, 0, 6, 1, 9, 3, 4]
println(arr, " => ", sort(arr, alg=CocktailShakerSort), " => ",
    sort(arr, alg=CocktailShakerSort, rev=true))

println("\nUsing default sort, which is Quicksort with integers:")
@btime sort!([5, 8, 2, 0, 6, 1, 9, 3, 4])
println("\nUsing CocktailShakerSort:")
@btime cocktailshakersort!([5, 8, 2, 0, 6, 1, 9, 3, 4])