
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


Use the quickselect algorithm on the vector

 [9, 8, 7, 6, 5, 0, 1, 2, 3, 4]
To show the first, second, third, ... up to the tenth largest member of the vector, in order, here on this page.

 Note: Quicksort has a separate task. 


F partition(&vector, left, right, pivotIndex)
   V pivotValue = vector[pivotIndex]
   swap(&vector[pivotIndex], &vector[right])
   V storeIndex = left
   L(i) left .< right
      I vector[i] < pivotValue
         swap(&vector[storeIndex], &vector[i])
         storeIndex++
   swap(&vector[right], &vector[storeIndex])
   R storeIndex
 
F _select(&vector, =left, =right, =k)
   ‘Returns the k-th smallest, (k >= 0), element of vector within vector[left:right+1] inclusive.’
   L
      V pivotIndex = (left + right) I/ 2
      V pivotNewIndex = partition(&vector, left, right, pivotIndex)
      V pivotDist = pivotNewIndex - left
      I pivotDist == k
         R vector[pivotNewIndex]
      E I k < pivotDist
         right = pivotNewIndex - 1
      E
         k -= pivotDist + 1
         left = pivotNewIndex + 1
 
F select(&vector, k)
   ‘
    Returns the k-th smallest, (k >= 0), element of vector within vector[left:right+1].
    left, right default to (0, len(vector) - 1) if omitted
   ’
   V left = 0
   V lv1 = vector.len - 1
   V right = lv1
   assert(!vector.empty & k >= 0, ‘Either null vector or k < 0 ’)
   assert(left C 0 .. lv1, ‘left is out of range’)
   assert(right C left .. lv1, ‘right is out of range’)
   R _select(&vector, left, right, k)
 
V v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4]
print((0.<10).map(i -> select(&:v, i)))