Step by Step solution about How to resolve the algorithm Sorting algorithms/Insertion sort step by step in the Julia programming language

This Julia code implements the insertion sort algorithm, which is an in-place sorting algorithm that builds the final sorted array one item at a time. It works by comparing each element of the array with the elements to its left, and moving it to the correct position.

The function insertionsort! takes an array A of type T as input, where T is a subtype of Number. The ! in the function name indicates that the function modifies the input array in-place. The function returns the sorted array.

The function first iterates over the elements of the array from the second element to the last element. For each element A[i+1], it compares the element with the elements to its left, and moves it to the correct position.

The variable j is used to track the position of the element being compared. The while loop continues until j is greater than 0 and the element at A[j] is greater than the element being compared. If the element at A[j] is greater, the element at A[j+1] is moved to A[j], and j is decremented by 1.

Once the correct position for the element being compared has been found, the element is placed at that position and the loop moves on to the next element in the array.

The following is an example of how to use the insertionsort! function:

julia> x = randn(5)
5-element Array{Float64,1}:
0.7812555397389255
-0.10585431761395037
0.6808233360452348
-0.531351308078714
-1.780242073794295

julia> insertionsort!(x)
5-element Array{Float64,1}:
-1.780242073794295
-0.531351308078714
-0.10585431761395037
0.6808233360452348
0.7812555397389255

In this example, the insertionsort! function is applied to an array of five random numbers. The sorted array is returned and displayed.

# v0.6

function insertionsort!(A::Array{T}) where T <: Number
    for i in 1:length(A)-1
        value = A[i+1]
        j = i
        while j > 0 && A[j] > value
            A[j+1] = A[j]
            j -= 1
        end
        A[j+1] = value
    end
    return A
end

x = randn(5)
@show x insertionsort!(x)