How to resolve the algorithm Sorting algorithms/Bead sort step by step in the Go programming language

Published on 12 May 2024 09:40 PM
#Go

How to resolve the algorithm Sorting algorithms/Bead sort step by step in the Go programming language

Table of Contents

Problem Statement

Sort an array of positive integers using the Bead Sort Algorithm. A   bead sort   is also known as a   gravity sort.

Algorithm has   O(S),   where   S   is the sum of the integers in the input set:   Each bead is moved individually. This is the case when bead sort is implemented without a mechanism to assist in finding empty spaces below the beads, such as in software implementations.

Let's start with the solution:

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

The provided Go program implements a bead sort algorithm to sort an array of integers a. The Bead sort is a sorting algorithm that simulates the process of using an abacus to perform sorting.

Implementation Details:

  1. Setup:

    • aMax defines the maximum value for the abacus poles (default is 1000).
    • all slice represents the entire space of the abacus (aMax * len(a) bytes).
    • abacus is a slice of byte slices, each representing a pole on the abacus.
  2. Bead Placement:

    • Concurrently, beads (represented by the ASCII character 'o') are placed on the abacus poles for each number in a.
    • The number of beads placed on a pole represents the value of the number.
  3. Bead Falling:

    • Again concurrently, beads are allowed to fall on each pole to the bottom.
    • A sync.WaitGroup is used to wait for all beads to finish falling.
  4. Sorting:

    • Beads are read out row by row to determine the sorted values.
    • The number of beads on a row (starting from the bottom) represents the sorted value.
  5. Final Result:

    • The sorted array is stored back in a.

Explanation of the Algorithm:

  • Bead sort is a non-comparative sorting algorithm. Instead of comparing elements, it uses the concept of an abacus to sort.
  • Each element is represented by a stack of beads on an abacus pole.
  • The number of beads on a pole represents the value of the element.
  • By allowing the beads to fall down the poles, beads are sorted in ascending order based on their weight (number of beads).
  • The sorted values are then read out row by row to obtain the final sorted array.

Concurrency: The program uses concurrency (goroutines and sync.WaitGroup) to perform the bead placement and falling operations concurrently, improving performance.

Conclusion: The bead sort algorithm is an interesting and efficient non-comparative sorting approach. The provided Go program effectively demonstrates the implementation of this algorithm, leveraging concurrency for improved performance.

Source code in the go programming language

package main

import (
    "fmt"
    "sync"
)

var a = []int{170, 45, 75, 90, 802, 24, 2, 66}
var aMax = 1000

const bead = 'o'

func main() {
    fmt.Println("before:", a)
    beadSort()
    fmt.Println("after: ", a)
}

func beadSort() {
    // All space in the abacus = aMax poles x len(a) rows.
    all := make([]byte, aMax*len(a))
    // Slice up space by pole.  (The space could be sliced by row instead,
    // but slicing by pole seemed a more intuitive model of a physical abacus.)
    abacus := make([][]byte, aMax)
    for pole, space := 0, all; pole < aMax; pole++ {
        abacus[pole] = space[:len(a)]
        space = space[len(a):]
    }
    // Use a sync.Waitgroup as the checkpoint mechanism.
    var wg sync.WaitGroup
    // Place beads for each number concurrently. (Presumably beads can be
    // "snapped on" to the middle of a pole without disturbing neighboring
    // beads.)  Also note 'row' here is a row of the abacus.
    wg.Add(len(a))
    for row, n := range a {
        go func(row, n int) {
            for pole := 0; pole < n; pole++ {
                abacus[pole][row] = bead
            }
            wg.Done()
        }(row, n)
    }
    wg.Wait()
    // Now tip the abacus, letting beads fall on each pole concurrently.
    wg.Add(aMax)
    for _, pole := range abacus {
        go func(pole []byte) {
            // Track the top of the stack of beads that have already fallen.
            top := 0
            for row, space := range pole {
                if space == bead {
                    // Move each bead individually, but move it from its
                    // starting row to the top of stack in a single operation.
                    // (More physical simulation such as discovering the top
                    // of stack by inspection, or modeling gravity, are
                    // possible, but didn't seem called for by the task.
                    pole[row] = 0
                    pole[top] = bead
                    top++
                }
            }
            wg.Done()
        }(pole)
    }
    wg.Wait()
    // Read out sorted numbers by row.
    for row := range a {
        x := 0
        for pole := 0; pole < aMax && abacus[pole][row] == bead; pole++ {
            x++
        }
        a[len(a)-1-row] = x
    }
}


  

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