
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. 


# Emit the k-th smallest item in the input array,
# or nothing if k is too small or too large.
# The smallest corresponds to k==1.
# The input array may hold arbitrary JSON entities, including null.
def quickselect(k):
 
  def partition(pivot):
    reduce .[] as $x
      # state: [less, other]
      ( [ [], [] ];                       # two empty arrays:
        if    $x  < pivot
        then .[0] += [$x]                 # add x to less
        else .[1] += [$x]                 # add x to other
        end
      );
 
  # recursive inner function has arity 0 for efficiency
  def qs:  # state: [kn, array] where kn counts from 0
    .[0] as $kn
     | .[1] as $a
    | $a[0] as $pivot
    | ($a[1:] | partition($pivot)) as $p
    | $p[0] as $left 
    | ($left|length) as $ll
    | if   $kn == $ll then $pivot
      elif $kn <  $ll then [$kn, $left] | qs
      else [$kn - $ll - 1, $p[1] ] | qs
      end;
 
  if length < k or k <= 0 then empty else [k-1, .] | qs end;