Sorting algorithms/Bead sort

Sorting algorithms/Bead sort
You are encouraged to solve this task according to the task description, using any language you may know.

Sorting Algorithm
This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or:

O(n logn) sorts

Heap sort | Merge sort | Patience sort | Quick sort

O(n log²n) sorts
Shell Sort

O(n²) sorts
Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort

other sorts
Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort

In this task, the goal is to sort an array of positive integers using the Bead Sort Algorithm.

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.

C++

<lang cpp>//this algorithm only works with positive, whole numbers. //O(2n) time complexity where n is the summation of the whole list to be sorted. //O(3n) space complexity.

1. include<iostream>
2. include<vector>

using namespace std;

void distribute( int dist, vector<int> &List)//*beads* go down into different buckets using gravity (addition). {

   if (dist > List.size() )
       List.resize(dist,0); //resize if too big for current vector

   for (int i=0; i < dist; i++)
       List[i] = List[i]+1;

}

int main() {

   vector<int> list;
   vector<int> list2;
   int myints[] = {5,3,1,7,4,1,1};
   vector<int> fifth (myints, myints + sizeof(myints) / sizeof(int) );

   cout << "#1 Beads falling down: ";
   for (int i=0; i < fifth.size(); i++)
       distribute (fifth[i], list);
   cout << endl;

   cout <<endl<< "Beads on their sides: ";
   for (int i=0; i < list.size(); i++)
       cout << " " << list[i];
   cout << endl;	

   //second part

   cout << "#2 Beads right side up: ";
   for (int i=0; i < list.size(); i++)
       distribute (list[i], list2);
   cout << endl;

   cout <<endl<< "Sorted list/array";
   for (int i=0; i < list2.size(); i++)
       cout << " " << list2[i];
   cout << endl;
   return 0;

}</lang>

Output:

Beads falling down:

Beads on their sides: 7 4 4 3 2 1 1 Beads right side up:

Sorted list/array 7 5 4 3 1 1 1

Tcl

<lang tcl>package require Tcl 8.5 proc beadsort numList {

   # Special case: empty list is empty when sorted.
   if {![llength $numList]} return
   # Set up the abacus...
   foreach n $numList {

for {set i 0} {$i<$n} {incr i} { dict incr vals $i }

   }
   # Make the beads fall...
   foreach n [dict values $vals] {

for {set i 0} {$i<$n} {incr i} { dict incr result $i }

   }
   # And the result is...
   dict values $result

}

1. Demonstration code

puts [beadsort {5 3 1 7 4 1 1}]</lang> Output:

7 5 4 3 1 1 1