Bucket Sort

Bucket Sort – sorting by buckets. The algorithm is similar to counting sort, with the difference that the numbers are collected in “buckets”-ranges, then the buckets are sorted using any other, sufficiently productive, sorting algorithm, and the final chord is the unfolding of the “buckets” one by one, resulting in a sorted list.

The algorithm’s time complexity is O(nk). The algorithm works in linear time for data that obeys a uniform distribution law. To put it simply, the elements must be in a certain range, without “spikes”, for example, numbers from 0.0 to 1.0. If among such numbers there are 4 or 999, then such a series is no longer considered “even” according to the yard laws.

Example of implementation in Julia:

    buckets = Vector{Vector{Int}}()
    
    for i in 0:bucketsCount - 1
        bucket = Vector{Int}()
        push!(buckets, bucket)
    end

    maxNumber = maximum(numbers)

    for i in 0:length(numbers) - 1
        bucketIndex = 1 + Int(floor(bucketsCount * numbers[1 + i] / (maxNumber + 1)))
        push!(buckets[bucketIndex], numbers[1 + i])
    end

    for i in 0:length(buckets) - 1
        bucketIndex = 1 + i
        buckets[bucketIndex] = sort(buckets[bucketIndex])
    end

    flat = [(buckets...)...]
    print(flat, "\n")

end

numbersCount = 10
maxNumber = 10
numbers = rand(1:maxNumber, numbersCount)
print(numbers,"\n")
bucketsCount = 10
bucketSort(numbers, bucketsCount)

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