
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. 


Quickselect[ds : DataStructure["DynamicArray", _], k_] := QuickselectWorker[ds, 1, ds["Length"], k];
QuickselectWorker[ds_, low0_, high0_, k_] := Module[{pivotIdx, low = low0, high = high0},
   While[True,
    If[low === high,
     Return[ds["Part", low]]
     ];
    pivotIdx = SelectPartition[ds, low, high];
    Which[k === pivotIdx,
     Return[ds["Part", k]],
     k < pivotIdx,
     high = pivotIdx - 1,
     True,
     low = pivotIdx + 1
     ]
    ]
   ];
SelectPartition[ds_, low_, high_] := Module[{pivot = ds["Part", high], i = low, j},
   Do[
    If[ds["Part", j] <= pivot,
     ds["SwapPart", i, j];
     i = i + 1
     ]
    ,
    {j, low, high - 1}
    ];
   ds["SwapPart", i, high];
   i
   ];
ds = CreateDataStructure["DynamicArray", {9, 8, 7, 6, 5, 0, 1, 2, 3, 4}];
Quickselect[ds, #] & /@ Range[10]