Quickselect algorithm
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:
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.
11l
<lang 11l>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)))</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Action!
<lang Action!>PROC Swap(BYTE ARRAY tab INT i,j)
BYTE tmp
tmp=tab(i) tab(i)=tab(j) tab(j)=tmp
RETURN
BYTE FUNC QuickSelect(BYTE ARRAY tab INT count,index)
INT px,i,j,k BYTE pv
DO px=count/2 pv=tab(px) Swap(tab,px,count-1) i=0 FOR j=0 TO count-2 DO IF tab(j)<pv THEN Swap(tab,i,j) i==+1 FI OD
IF i=index THEN RETURN (pv) ELSEIF i>index THEN ;left part of tab from 0 to i-1 count=i ELSE Swap(tab,i,count-1) ;right part of tab from i+1 to count-1 tab==+(i+1) count==-(i+1) index==-(i+1) FI OD
RETURN (0)
PROC Main()
DEFINE COUNT="10" BYTE ARRAY data=[9 8 7 6 5 0 1 2 3 4],tab(COUNT) BYTE i,res
FOR i=0 TO COUNT-1 DO MoveBlock(tab,data,COUNT) res=QuickSelect(tab,COUNT,i) PrintB(res) Put(32) OD
RETURN</lang>
- Output:
Screenshot from Atari 8-bit computer
0 1 2 3 4 5 6 7 8 9
ALGOL 68
<lang algol68>BEGIN
# returns the kth lowest element of list using the quick select algorithm # PRIO QSELECT = 1; OP QSELECT = ( INT k, REF[]INT list )INT: IF LWB list > UPB list THEN # empty list # 0 ELSE # non-empty list # # partitions the subset of list from left to right # PROC partition = ( REF[]INT list, INT left, right, pivot index )INT: BEGIN # swaps elements a and b in list # PROC swap = ( REF[]INT list, INT a, b )VOID: BEGIN INT t = list[ a ]; list[ a ] := list[ b ]; list[ b ] := t END # swap # ; INT pivot value = list[ pivot index ]; swap( list, pivot index, right ); INT store index := left; FOR i FROM left TO right - 1 DO IF list[ i ] < pivot value THEN swap( list, store index, i ); store index +:= 1 FI OD; swap( list, right, store index ); store index END # partition # ; INT left := LWB list, right := UPB list, result := 0; BOOL found := FALSE; WHILE NOT found DO IF left = right THEN result := list[ left ]; found := TRUE ELSE INT pivot index = partition( list, left, right, left + ENTIER ( ( random * ( right - left ) + 1 ) ) ); IF k = pivot index THEN result := list[ k ]; found := TRUE ELIF k < pivot index THEN right := pivot index - 1 ELSE left := pivot index + 1 FI FI OD; result FI # QSELECT # ; # test cases # FOR i TO 10 DO [ 1 : 10 ]INT test := []INT( 9, 8, 7, 6, 5, 0, 1, 2, 3, 4 ); print( ( whole( i, -2 ), ": ", whole( i QSELECT test, -3 ), newline ) ) OD
END</lang>
- Output:
1: 0 2: 1 3: 2 4: 3 5: 4 6: 5 7: 6 8: 7 9: 8 10: 9
AppleScript
Procedural
<lang applescript>on quickselect(theList, l, r, k)
script o property lst : theList's items -- Shallow copy. end script repeat -- Median-of-3 pivot selection. set leftValue to item l of o's lst set rightValue to item r of o's lst set pivot to item ((l + r) div 2) of o's lst set leftGreaterThanRight to (leftValue > rightValue) if (leftValue > pivot) then if (leftGreaterThanRight) then if (rightValue > pivot) then set pivot to rightValue else set pivot to leftValue end if else if (pivot > rightValue) then if (leftGreaterThanRight) then set pivot to leftValue else set pivot to rightValue end if end if -- Initialise pivot store indices and swap the already compared outer values here if necessary. set pLeft to l - 1 set pRight to r + 1 if (leftGreaterThanRight) then set item r of o's lst to leftValue set item l of o's lst to rightValue if (leftValue = pivot) then set pRight to r else if (rightValue = pivot) then set pLeft to l end if else if (leftValue = pivot) then set pLeft to l if (rightValue = pivot) then set pRight to r end if -- Continue three-way partitioning. set i to l + 1 set j to r - 1 repeat until (i > j) set leftValue to item i of o's lst repeat while (leftValue < pivot) set i to i + 1 set leftValue to item i of o's lst end repeat set rightValue to item j of o's lst repeat while (rightValue > pivot) set j to j - 1 set rightValue to item j of o's lst end repeat if (j > i) then if (leftValue = pivot) then set pRight to pRight - 1 if (pRight > j) then set leftValue to item pRight of o's lst set item pRight of o's lst to pivot end if end if if (rightValue = pivot) then set pLeft to pLeft + 1 if (pLeft < i) then set rightValue to item pLeft of o's lst set item pLeft of o's lst to pivot end if end if set item j of o's lst to leftValue set item i of o's lst to rightValue else if (i > j) then exit repeat end if set i to i + 1 set j to j - 1 end repeat -- Swap stored pivot(s) into a central partition. repeat with p from l to pLeft if (j > pLeft) then set item p of o's lst to item j of o's lst set item j of o's lst to pivot set j to j - 1 else set j to p - 1 exit repeat end if end repeat repeat with p from r to pRight by -1 if (i < pRight) then set item p of o's lst to item i of o's lst set item i of o's lst to pivot set i to i + 1 else set i to p + 1 exit repeat end if end repeat -- If k's in either of the outer partitions, repeat for that partition. Othewise return the item in slot k. if (k ≥ i) then set l to i else if (k ≤ j) then set r to j else return item k of o's lst end if end repeat
end quickselect
-- Task code: set theVector to {9, 8, 7, 6, 5, 0, 1, 2, 3, 4} set selected to {} set vectorLength to (count theVector) repeat with i from 1 to vectorLength
set end of selected to quickselect(theVector, 1, vectorLength, i)
end repeat return selected</lang>
- Output:
<lang applescript>{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}</lang>
Functional
<lang applescript>----------------------- QUICKSELECT ------------------------
-- quickSelect :: Ord a => [a] -> Int -> a on quickSelect(xxs)
script on |λ|(k) script go on |λ|(xxs, k) set {x, xs} to {item 1 of xxs, rest of xxs} set {ys, zs} to partition(gt(x), xs) set lng to length of ys if k < lng then |λ|(ys, k) else if k > lng then |λ|(zs, k - lng - 1) else x end if end if end |λ| end script if 0 ≤ k and k < length of xxs then tell go to |λ|(xxs, k) else missing value end if end |λ| end script
end quickSelect
TEST ---------------------------
on run
set xs to {9, 8, 7, 6, 5, 0, 1, 2, 3, 4} map(quickSelect(xs), enumFromTo(0, (length of xs) - 1))
end run
GENERAL AND REUSABLE PURE FUNCTIONS ------------
-- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n)
if m ≤ n then set lst to {} repeat with i from m to n set end of lst to i end repeat lst else {} end if
end enumFromTo
-- gt :: Ord a => a -> a -> Bool
on gt(x)
script on |λ|(y) x > y end |λ| end script
end gt
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
-- The list obtained by applying f -- to each element of xs. tell mReturn(f) set lng to length of xs set lst to {} repeat with i from 1 to lng set end of lst to |λ|(item i of xs, i, xs) end repeat return lst end tell
end map
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper. if script is class of f then f else script property |λ| : f end script end if
end mReturn
-- partition :: (a -> Bool) -> [a] -> ([a], [a])
on partition(p, xs)
tell mReturn(p) set {ys, zs} to {{}, {}} repeat with x in xs set v to contents of x if |λ|(v) then set end of ys to v else set end of zs to v end if end repeat end tell {ys, zs}
end partition</lang>
- Output:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
Arturo
<lang rebol>quickselect: function [a k][
arr: new a while ø [ indx: random 0 (size arr)-1 pivot: arr\[indx] remove 'arr .index indx left: select arr 'item -> item<pivot right: select arr 'item -> item>pivot
case [k] when? [= size left]-> return pivot when? [< size left]-> arr: new left else [ k: (k - size left) - 1 arr: new right ] ]
]
v: [9 8 7 6 5 0 1 2 3 4]
print map 0..(size v)-1 'i ->
quickselect v i</lang>
- Output:
0 1 2 3 4 5 6 7 8 9
AutoHotkey
(AutoHotkey1.1+)
A direct implementation of the Wikipedia pseudo-code. <lang AutoHotkey>MyList := [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] Loop, 10 Out .= Select(MyList, 1, MyList.MaxIndex(), A_Index) (A_Index = MyList.MaxIndex() ? "" : ", ") MsgBox, % Out return
Partition(List, Left, Right, PivotIndex) { PivotValue := List[PivotIndex] , Swap(List, pivotIndex, Right) , StoreIndex := Left , i := Left - 1 Loop, % Right - Left if (List[j := i + A_Index] <= PivotValue) Swap(List, StoreIndex, j) , StoreIndex++ Swap(List, Right, StoreIndex) return StoreIndex }
Select(List, Left, Right, n) { if (Left = Right) return List[Left] Loop { PivotIndex := (Left + Right) // 2 , PivotIndex := Partition(List, Left, Right, PivotIndex) if (n = PivotIndex) return List[n] else if (n < PivotIndex) Right := PivotIndex - 1 else Left := PivotIndex + 1 } }
Swap(List, i1, i2) { t := List[i1] , List[i1] := List[i2] , List[i2] := t }</lang> Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
C
<lang c>#include <stdio.h>
- include <string.h>
int qselect(int *v, int len, int k) {
- define SWAP(a, b) { tmp = v[a]; v[a] = v[b]; v[b] = tmp; }
int i, st, tmp;
for (st = i = 0; i < len - 1; i++) { if (v[i] > v[len-1]) continue; SWAP(i, st); st++; }
SWAP(len-1, st);
return k == st ?v[st] :st > k ? qselect(v, st, k) : qselect(v + st, len - st, k - st); }
int main(void) {
- define N (sizeof(x)/sizeof(x[0]))
int x[] = {9, 8, 7, 6, 5, 0, 1, 2, 3, 4}; int y[N];
int i; for (i = 0; i < 10; i++) { memcpy(y, x, sizeof(x)); // qselect modifies array printf("%d: %d\n", i, qselect(y, 10, i)); }
return 0; }</lang>
- Output:
0: 0 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9
C#
Two different implementations - one that returns only one element from the array (Nth smallest element) and second implementation that returns IEnumnerable that enumerates through element until Nth smallest element.
<lang csharp>// ---------------------------------------------------------------------------------------------- // // Program.cs - QuickSelect // // ----------------------------------------------------------------------------------------------
using System; using System.Collections.Generic; using System.Linq;
namespace QuickSelect {
internal static class Program { #region Static Members
private static void Main() { var inputArray = new[] {9, 8, 7, 6, 5, 0, 1, 2, 3, 4}; // Loop 10 times Console.WriteLine( "Loop quick select 10 times." ); for( var i = 0 ; i < 10 ; i++ ) { Console.Write( inputArray.NthSmallestElement( i ) ); if( i < 9 ) Console.Write( ", " ); } Console.WriteLine();
// And here is then more effective way to get N smallest elements from vector in order by using quick select algorithm // Basically we are here just sorting array (taking 10 smallest from array which length is 10) Console.WriteLine( "Just sort 10 elements." ); Console.WriteLine( string.Join( ", ", inputArray.TakeSmallest( 10 ).OrderBy( v => v ).Select( v => v.ToString() ).ToArray() ) ); // Here we are actually doing quick select once by taking only 4 smallest from array. Console.WriteLine( "Get 4 smallest and sort them." ); Console.WriteLine( string.Join( ", ", inputArray.TakeSmallest( 4 ).OrderBy( v => v ).Select( v => v.ToString() ).ToArray() ) ); Console.WriteLine( "< Press any key >" ); Console.ReadKey(); }
#endregion }
internal static class ArrayExtension { #region Static Members
/// <summary> /// Return specified number of smallest elements from array. /// </summary> /// <typeparam name="T">The type of the elements of array. Type must implement IComparable(T) interface.</typeparam> /// <param name="array">The array to return elemnts from.</param> /// <param name="count">The number of smallest elements to return. </param> /// <returns>An IEnumerable(T) that contains the specified number of smallest elements of the input array. Returned elements are NOT sorted.</returns> public static IEnumerable<T> TakeSmallest<T>( this T[] array, int count ) where T : IComparable<T> { if( count < 0 ) throw new ArgumentOutOfRangeException( "count", "Count is smaller than 0." ); if( count == 0 ) return new T[0]; if( array.Length <= count ) return array;
return QuickSelectSmallest( array, count - 1 ).Take( count ); }
/// <summary> /// Returns N:th smallest element from the array. /// </summary> /// <typeparam name="T">The type of the elements of array. Type must implement IComparable(T) interface.</typeparam> /// <param name="array">The array to return elemnt from.</param> /// <param name="n">Nth element. 0 is smallest element, when array.Length - 1 is largest element.</param> /// <returns>N:th smalles element from the array.</returns> public static T NthSmallestElement<T>( this T[] array, int n ) where T : IComparable<T> { if( n < 0 || n > array.Length - 1 ) throw new ArgumentOutOfRangeException( "n", n, string.Format( "n should be between 0 and {0} it was {1}.", array.Length - 1, n ) ); if( array.Length == 0 ) throw new ArgumentException( "Array is empty.", "array" ); if( array.Length == 1 ) return array[ 0 ];
return QuickSelectSmallest( array, n )[ n ]; }
/// <summary> /// Partially sort array such way that elements before index position n are smaller or equal than elemnt at position n. And elements after n are larger or equal. /// </summary> /// <typeparam name="T">The type of the elements of array. Type must implement IComparable(T) interface.</typeparam> /// <param name="input">The array which elements are being partially sorted. This array is not modified.</param> /// <param name="n">Nth smallest element.</param> /// <returns>Partially sorted array.</returns> private static T[] QuickSelectSmallest<T>( T[] input, int n ) where T : IComparable<T> { // Let's not mess up with our input array // For very large arrays - we should optimize this somehow - or just mess up with our input var partiallySortedArray = (T[]) input.Clone(); // Initially we are going to execute quick select to entire array var startIndex = 0; var endIndex = input.Length - 1; // Selecting initial pivot // Maybe we are lucky and array is sorted initially? var pivotIndex = n;
// Loop until there is nothing to loop (this actually shouldn't happen - we should find our value before we run out of values) var r = new Random(); while( endIndex > startIndex ) { pivotIndex = QuickSelectPartition( partiallySortedArray, startIndex, endIndex, pivotIndex ); if( pivotIndex == n ) // We found our n:th smallest value - it is stored to pivot index break; if( pivotIndex > n ) // Array before our pivot index have more elements that we are looking for endIndex = pivotIndex - 1; else // Array before our pivot index has less elements that we are looking for startIndex = pivotIndex + 1;
// Omnipotent beings don't need to roll dices - but we do... // Randomly select a new pivot index between end and start indexes (there are other methods, this is just most brutal and simplest) pivotIndex = r.Next( startIndex, endIndex ); } return partiallySortedArray; }
/// <summary> /// Sort elements in sub array between startIndex and endIndex, such way that elements smaller than or equal with value initially stored to pivot index are before /// new returned pivot value index. /// </summary> /// <typeparam name="T">The type of the elements of array. Type must implement IComparable(T) interface.</typeparam> /// <param name="array">The array that is being sorted.</param> /// <param name="startIndex">Start index of sub array.</param> /// <param name="endIndex">End index of sub array.</param> /// <param name="pivotIndex">Pivot index.</param> /// <returns>New pivot index. Value that was initially stored to <paramref name="pivotIndex"/> is stored to this newly returned index. All elements before this index are /// either smaller or equal with pivot value. All elements after this index are larger than pivot value.</returns> /// <remarks>This method modifies paremater array.</remarks> private static int QuickSelectPartition<T>( this T[] array, int startIndex, int endIndex, int pivotIndex ) where T : IComparable<T> { var pivotValue = array[ pivotIndex ]; // Initially we just assume that value in pivot index is largest - so we move it to end (makes also for loop more straight forward) array.Swap( pivotIndex, endIndex ); for( var i = startIndex ; i < endIndex ; i++ ) { if( array[ i ].CompareTo( pivotValue ) > 0 ) continue;
// Value stored to i was smaller than or equal with pivot value - let's move it to start array.Swap( i, startIndex ); // Move start one index forward startIndex++; } // Start index is now pointing to index where we should store our pivot value from end of array array.Swap( endIndex, startIndex ); return startIndex; }
private static void Swap<T>( this T[] array, int index1, int index2 ) { if( index1 == index2 ) return;
var temp = array[ index1 ]; array[ index1 ] = array[ index2 ]; array[ index2 ] = temp; }
#endregion }
}</lang>
- Output:
Loop quick select 10 times. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Just sort 10 elements. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Get 4 smallest and sort them. 0, 1, 2, 3 < Press any key >
C++
- Library
It is already provided in the standard library as std::nth_element()
. Although the standard does not explicitly mention what algorithm it must use, the algorithm partitions the sequence into those less than the nth element to the left, and those greater than the nth element to the right, like quickselect; the standard also guarantees that the complexity is "linear on average", which fits quickselect.
<lang cpp>#include <algorithm>
- include <iostream>
int main() {
for (int i = 0; i < 10; i++) { int a[] = {9, 8, 7, 6, 5, 0, 1, 2, 3, 4}; std::nth_element(a, a + i, a + sizeof(a)/sizeof(*a)); std::cout << a[i]; if (i < 9) std::cout << ", "; } std::cout << std::endl;
return 0;
}</lang>
- Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
- Implementation
A more explicit implementation: <lang cpp>#include <iterator>
- include <algorithm>
- include <functional>
- include <cstdlib>
- include <ctime>
- include <iostream>
template <typename Iterator> Iterator select(Iterator begin, Iterator end, int n) {
typedef typename std::iterator_traits<Iterator>::value_type T; while (true) { Iterator pivotIt = begin + std::rand() % std::distance(begin, end); std::iter_swap(pivotIt, end-1); // Move pivot to end pivotIt = std::partition(begin, end-1, std::bind2nd(std::less<T>(), *(end-1))); std::iter_swap(end-1, pivotIt); // Move pivot to its final place if (n == pivotIt - begin) { return pivotIt; } else if (n < pivotIt - begin) { end = pivotIt; } else { n -= pivotIt+1 - begin; begin = pivotIt+1; } }
}
int main() {
std::srand(std::time(NULL)); for (int i = 0; i < 10; i++) { int a[] = {9, 8, 7, 6, 5, 0, 1, 2, 3, 4}; std::cout << *select(a, a + sizeof(a)/sizeof(*a), i); if (i < 9) std::cout << ", "; } std::cout << std::endl;
return 0;
}</lang>
- Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
CLU
<lang clu>quick = cluster [T: type] is select
where T has lt: proctype (T,T) returns (bool) aT = array[T] sT = sequence[T] rep = null swap = proc (list: aT, a, b: int) temp: T := list[a] list[a] := list[b] list[b] := temp end swap partition = proc (list: aT, left, right, pivotIndex: int) returns (int) pivotValue: T := list[pivotIndex] swap(list, pivotIndex, right) storeIndex: int := left for i: int in int$from_to(left, right-1) do if list[i] < pivotValue then swap(list, storeIndex, i) storeIndex := storeIndex + 1 end end swap(list, right, storeIndex) return(storeIndex) end partition _select = proc (list: aT, left, right, k: int) returns (T) if left = right then return(list[left]) end pivotIndex: int := left + (right - left + 1) / 2 pivotIndex := partition(list, left, right, pivotIndex) if k = pivotIndex then return(list[k]) elseif k < pivotIndex then return(_select(list, left, pivotIndex-1, k)) else return(_select(list, pivotIndex + 1, right, k)) end end _select select = proc (list: sT, k: int) returns (T) return(_select(sT$s2a(list), 1, sT$size(list), k)) end select
end quick
start_up = proc ()
po: stream := stream$primary_output() vec: sequence[int] := sequence[int]$[9,8,7,6,5,0,1,2,3,4] for k: int in int$from_to(1, 10) do item: int := quick[int]$select(vec, k) stream$putl(po, int$unparse(k) || ": " || int$unparse(item)) end
end start_up</lang>
- Output:
1: 0 2: 1 3: 2 4: 3 5: 4 6: 5 7: 6 8: 7 9: 8 10: 9
COBOL
The following is in the Managed COBOL dialect:
<lang cobol> CLASS-ID MainProgram.
METHOD-ID Partition STATIC USING T. CONSTRAINTS. CONSTRAIN T IMPLEMENTS type IComparable. DATA DIVISION. LOCAL-STORAGE SECTION. 01 pivot-val T. PROCEDURE DIVISION USING VALUE arr AS T OCCURS ANY, left-idx AS BINARY-LONG, right-idx AS BINARY-LONG, pivot-idx AS BINARY-LONG RETURNING ret AS BINARY-LONG. MOVE arr (pivot-idx) TO pivot-val INVOKE self::Swap(arr, pivot-idx, right-idx) DECLARE store-idx AS BINARY-LONG = left-idx PERFORM VARYING i AS BINARY-LONG FROM left-idx BY 1 UNTIL i > right-idx IF arr (i) < pivot-val INVOKE self::Swap(arr, i, store-idx) ADD 1 TO store-idx END-IF END-PERFORM INVOKE self::Swap(arr, right-idx, store-idx) MOVE store-idx TO ret END METHOD. METHOD-ID Quickselect STATIC USING T. CONSTRAINTS. CONSTRAIN T IMPLEMENTS type IComparable. PROCEDURE DIVISION USING VALUE arr AS T OCCURS ANY, left-idx AS BINARY-LONG, right-idx AS BINARY-LONG, n AS BINARY-LONG RETURNING ret AS T. IF left-idx = right-idx MOVE arr (left-idx) TO ret GOBACK END-IF DECLARE rand AS TYPE Random = NEW Random() DECLARE pivot-idx AS BINARY-LONG = rand::Next(left-idx, right-idx) DECLARE pivot-new-idx AS BINARY-LONG = self::Partition(arr, left-idx, right-idx, pivot-idx) DECLARE pivot-dist AS BINARY-LONG = pivot-new-idx - left-idx + 1 EVALUATE TRUE WHEN pivot-dist = n MOVE arr (pivot-new-idx) TO ret WHEN n < pivot-dist INVOKE self::Quickselect(arr, left-idx, pivot-new-idx - 1, n) RETURNING ret WHEN OTHER INVOKE self::Quickselect(arr, pivot-new-idx + 1, right-idx, n - pivot-dist) RETURNING ret END-EVALUATE END METHOD. METHOD-ID Swap STATIC USING T. CONSTRAINTS. CONSTRAIN T IMPLEMENTS type IComparable. DATA DIVISION. LOCAL-STORAGE SECTION. 01 temp T. PROCEDURE DIVISION USING arr AS T OCCURS ANY, VALUE idx-1 AS BINARY-LONG, idx-2 AS BINARY-LONG. IF idx-1 <> idx-2 MOVE arr (idx-1) TO temp MOVE arr (idx-2) TO arr (idx-1) MOVE temp TO arr (idx-2) END-IF END METHOD. METHOD-ID Main STATIC. PROCEDURE DIVISION. DECLARE input-array AS BINARY-LONG OCCURS ANY = TABLE OF BINARY-LONG(9, 8, 7, 6, 5, 0, 1, 2, 3, 4) DISPLAY "Loop quick select 10 times." PERFORM VARYING i AS BINARY-LONG FROM 1 BY 1 UNTIL i > 10 DISPLAY self::Quickselect(input-array, 1, input-array::Length, i) NO ADVANCING IF i < 10 DISPLAY ", " NO ADVANCING END-IF END-PERFORM DISPLAY SPACE END METHOD. END CLASS.</lang>
Common Lisp
<lang lisp> (defun quickselect (n _list)
(let* ((ys (remove-if (lambda (x) (< (car _list) x)) (cdr _list))) (zs (remove-if-not (lambda (x) (< (car _list) x)) (cdr _list))) (l (length ys)) ) (cond ((< n l) (quickselect n ys)) ((> n l) (quickselect (- n l 1) zs)) (t (car _list))) ) )
(defparameter a '(9 8 7 6 5 0 1 2 3 4)) (format t "~a~&" (mapcar (lambda (x) (quickselect x a)) (loop for i from 0 below (length a) collect i))) </lang>
- Output:
(0 1 2 3 4 5 6 7 8 9)
Crystal
<lang ruby>def quickselect(a, k)
arr = a.dup # we will be modifying it loop do pivot = arr.delete_at(rand(arr.size)) left, right = arr.partition { |x| x < pivot } if k == left.size return pivot elsif k < left.size arr = left else k = k - left.size - 1 arr = right end end
end
v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] p v.each_index.map { |i| quickselect(v, i) }.to_a </lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
D
Standard Version
This could use a different algorithm: <lang d>void main() {
import std.stdio, std.algorithm;
auto a = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4]; foreach (immutable i; 0 .. a.length) { a.topN(i); write(a[i], " "); }
}</lang>
- Output:
0 1 2 3 4 5 6 7 8 9
Array Version
<lang d>import std.stdio, std.random, std.algorithm, std.range;
T quickSelect(T)(T[] arr, size_t n) in {
assert(n < arr.length);
} body {
static size_t partition(T[] sub, in size_t pivot) pure nothrow in { assert(!sub.empty); assert(pivot < sub.length); } body { auto pivotVal = sub[pivot]; sub[pivot].swap(sub.back); size_t storeIndex = 0; foreach (ref si; sub[0 .. $ - 1]) { if (si < pivotVal) { si.swap(sub[storeIndex]); storeIndex++; } } sub.back.swap(sub[storeIndex]); return storeIndex; }
size_t left = 0; size_t right = arr.length - 1; while (right > left) { assert(left < arr.length); assert(right < arr.length); immutable pivotIndex = left + partition(arr[left .. right + 1], uniform(0U, right - left + 1)); if (pivotIndex - left == n) { right = left = pivotIndex; } else if (pivotIndex - left < n) { n -= pivotIndex - left + 1; left = pivotIndex + 1; } else { right = pivotIndex - 1; } }
return arr[left];
}
void main() {
auto a = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4]; a.length.iota.map!(i => a.quickSelect(i)).writeln;
}</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Delphi
<lang Delphi> program Quickselect_algorithm;
{$APPTYPE CONSOLE}
uses
System.SysUtils;
function quickselect(list: TArray<Integer>; k: Integer): Integer;
procedure Swap(i, j: Integer); var tmp: Integer; begin tmp := list[i]; list[i] := list[j]; list[j] := tmp; end;
begin
repeat var px := length(list) div 2; var pv := list[px]; var last := length(list) - 1;
Swap(px, last); var i := 0; for var j := 0 to last - 1 do if list[j] < pv then begin swap(i, j); inc(i); end;
if i = k then exit(pv);
if k < i then delete(list, i, length(list)) else begin Swap(i, last); delete(list, 0, i + 1); dec(k, i + 1); end; until false;
end;
begin
var i := 0;
while True do begin var v: TArray<Integer> := [9, 8, 7, 6, 5, 0, 1, 2, 3, 4]; if i = length(v) then Break; Writeln(quickselect(v, i)); inc(i); end; Readln;
end.</lang>
Elixir
<lang elixir>defmodule Quick do
def select(k, [x|xs]) do {ys, zs} = Enum.partition(xs, fn e -> e < x end) l = length(ys) cond do k < l -> select(k, ys) k > l -> select(k - l - 1, zs) true -> x end end def test do v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] Enum.map(0..length(v)-1, fn i -> select(i,v) end) |> IO.inspect end
end
Quick.test</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Erlang
<lang erlang> -module(quickselect).
-export([test/0]).
test() ->
V = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4], lists:map( fun(I) -> quickselect(I,V) end, lists:seq(0, length(V) - 1) ).
quickselect(K, [X | Xs]) ->
{Ys, Zs} = lists:partition(fun(E) -> E < X end, Xs), L = length(Ys), if K < L -> quickselect(K, Ys); K > L -> quickselect(K - L - 1, Zs); true -> X end.
</lang>
Output:
[0,1,2,3,4,5,6,7,8,9]
F#
<lang fsharp> let rec quickselect k list =
match list with | [] -> failwith "Cannot take largest element of empty list." | [a] -> a | x::xs -> let (ys, zs) = List.partition (fun arg -> arg < x) xs let l = List.length ys if k < l then quickselect k ys elif k > l then quickselect (k-l-1) zs else x
//end quickselect
[<EntryPoint>] let main args =
let v = [9; 8; 7; 6; 5; 0; 1; 2; 3; 4] printfn "%A" [for i in 0..(List.length v - 1) -> quickselect i v] 0
</lang>
- Output:
[0; 1; 2; 3; 4; 5; 6; 7; 8; 9]
Factor
<lang factor>USING: combinators kernel make math locals prettyprint sequences ; IN: rosetta-code.quickselect
- quickselect ( k seq -- n )
seq unclip :> ( xs x ) xs [ x < ] partition :> ( ys zs ) ys length :> l { { [ k l < ] [ k ys quickselect ] } { [ k l > ] [ k l - 1 - zs quickselect ] } [ x ] } cond ;
- quickselect-demo ( -- )
{ 9 8 7 6 5 0 1 2 3 4 } dup length <iota> swap [ [ quickselect , ] curry each ] { } make . ;
MAIN: quickselect-demo</lang>
- Output:
{ 0 1 2 3 4 5 6 7 8 9 }
Fortran
Conveniently, a function was already to hand for floating-point numbers and changing the type was trivial - because the array and its associates were declared in the same statement to facilitate exactly that. The style is F77 (except for the A(1:N) usage in the DATA statement, and the END FUNCTION usage) and it did not seem worthwhile activating the MODULE protocol of F90 just to save the tedium of having to declare INTEGER FINDELEMENT in the calling routine - doing so would require four additional lines... On the other hand, a MODULE would enable the convenient development of a collection of near-clones, one for each type of array (INTEGER, REAL*4, REAL*8) which could then be collected via an INTERFACE statement into forming an apparently generic function so that one needn't have to remember FINDELEMENTI2, FINDELEMENTI4, FINDELEMENTF4, FINDELEMENTF8, and so on. With multiple parameters of various types, the combinations soon become tiresomely numerous.
Those of a delicate disposition may wish to avert their eyes from the three-way IF-statement... <lang Fortran> INTEGER FUNCTION FINDELEMENT(K,A,N) !I know I can. Chase an order statistic: FindElement(N/2,A,N) leads to the median, with some odd/even caution. Careful! The array is shuffled: for i < K, A(i) <= A(K); for i > K, A(i) >= A(K). Charles Anthony Richard Hoare devised this method, as related to his famous QuickSort.
INTEGER K,N !Find the K'th element in order of an array of N elements, not necessarily in order. INTEGER A(N),HOPE,PESTY !The array, and like associates. INTEGER L,R,L2,R2 !Fingers. L = 1 !Here we go. R = N !The bounds of the work area within which the K'th element lurks. DO WHILE (L .LT. R) !So, keep going until it is clamped. HOPE = A(K) !If array A is sorted, this will be rewarded. L2 = L !But it probably isn't sorted. R2 = R !So prepare a scan. DO WHILE (L2 .LE. R2) !Keep squeezing until the inner teeth meet. DO WHILE (A(L2) .LT. HOPE) !Pass elements less than HOPE. L2 = L2 + 1 !Note that at least element A(K) equals HOPE. END DO !Raising the lower jaw. DO WHILE (HOPE .LT. A(R2)) !Elements higher than HOPE R2 = R2 - 1 !Are in the desired place. END DO !And so we speed past them. IF (L2 - R2) 1,2,3 !How have the teeth paused? 1 PESTY = A(L2) !On grit. A(L2) > HOPE and A(R2) < HOPE. A(L2) = A(R2) !So swap the two troublemakers. A(R2) = PESTY !To be as if they had been in the desired order all along. 2 L2 = L2 + 1 !Advance my teeth. R2 = R2 - 1 !As if they hadn't paused on this pest. 3 END DO !And resume the squeeze, hopefully closing in K. IF (R2 .LT. K) L = L2 !The end point gives the order position of value HOPE. IF (K .LT. L2) R = R2 !But we want the value of order position K. END DO !Have my teeth met yet? FINDELEMENT = A(K) !Yes. A(K) now has the K'th element in order. END FUNCTION FINDELEMENT !Remember! Array A has likely had some elements moved!
PROGRAM POKE INTEGER FINDELEMENT !Not the default type for F. INTEGER N !The number of elements. PARAMETER (N = 10) !Fixed for the test problem. INTEGER A(66) !An array of integers. DATA A(1:N)/9, 8, 7, 6, 5, 0, 1, 2, 3, 4/ !The specified values.
WRITE (6,1) A(1:N) !Announce, and add a heading. 1 FORMAT ("Selection of the i'th element in order from an array.",/ 1 "The array need not be in order, and may be reordered.",/ 2 " i Val:Array elements...",/,8X,666I2)
DO I = 1,N !One by one, WRITE (6,2) I,FINDELEMENT(I,A,N),A(1:N) !Request the i'th element. 2 FORMAT (I3,I4,":",666I2) !Match FORMAT 1. END DO !On to the next trial.
END !That was easy.</lang>
To demonstrate that the array, if unsorted, will likely have elements re-positioned, the array's state after each call is shown.
Selection of the i'th element in order from an array. The array need not be in order, and may be reordered. i Val:Array elements... 9 8 7 6 5 0 1 2 3 4 1 0: 0 2 1 3 5 6 7 8 4 9 2 1: 0 1 2 3 5 6 7 8 4 9 3 2: 0 1 2 3 5 6 7 8 4 9 4 3: 0 1 2 3 5 6 7 8 4 9 5 4: 0 1 2 3 4 6 7 8 5 9 6 5: 0 1 2 3 4 5 7 8 6 9 7 6: 0 1 2 3 4 5 6 8 7 9 8 7: 0 1 2 3 4 5 6 7 8 9 9 8: 0 1 2 3 4 5 6 7 8 9 10 9: 0 1 2 3 4 5 6 7 8 9
Given an intention to make many calls on FINDELEMENT for the same array, the array might as well be fully sorted first by a routine specialising in that. Otherwise, if say going for quartiles, it would be better to start with the median and work out so as to have a better chance of avoiding unfortunate "pivot" values.
FreeBASIC
Una implementación directa del pseudocódigo de Wikipedia. <lang freebasic> Dim Shared As Long array(9), pivote
Function QuickPartition (array() As Long, izda As Long, dcha As Long, pivote As Long) As Long
Dim As Long pivotValue = array(pivote) Swap array(pivote), array(dcha) Dim As Long indice = izda For i As Long = izda To dcha-1 If array(i) < pivotValue Then Swap array(indice), array(i) indice += 1 End If Next i Swap array(dcha), array(indice) Return indice
End Function
Function QuickSelect(array() As Long, izda As Long, dcha As Long, k As Long) As Long
Do If izda = dcha Then Return array(izda) : End If pivote = izda pivote = QuickPartition(array(), izda, dcha, pivote) Select Case k Case pivote Return array(k) Case Is < pivote dcha = pivote - 1 Case Is > pivote izda = pivote + 1 End Select Loop
End Function
Dim As Long a = Lbound(array), b = Ubound(array) Print "Array desordenado: "; For i As Long = a To b
Read array(i) Print array(i);
Next i Data 9, 8, 7, 6, 5, 0, 1, 2, 3, 4
Print !"\n\n Array ordenado: "; For i As Long = a To b
Print QuickSelect(array(), a, b, i);
Next i Sleep </lang>
- Output:
Array desordenado: 9 8 7 6 5 0 1 2 3 4 Array ordenado: 0 1 2 3 4 5 6 7 8 9
Go
<lang go>package main
import "fmt"
func quickselect(list []int, k int) int {
for { // partition px := len(list) / 2 pv := list[px] last := len(list) - 1 list[px], list[last] = list[last], list[px] i := 0 for j := 0; j < last; j++ { if list[j] < pv { list[i], list[j] = list[j], list[i] i++ } } // select if i == k { return pv } if k < i { list = list[:i] } else { list[i], list[last] = list[last], list[i] list = list[i+1:] k -= i + 1 } }
}
func main() {
for i := 0; ; i++ { v := []int{9, 8, 7, 6, 5, 0, 1, 2, 3, 4} if i == len(v) { return } fmt.Println(quickselect(v, i)) }
}</lang>
- Output:
0 1 2 3 4 5 6 7 8 9
A more generic version that works for any container that conforms to sort.Interface
:
<lang go>package main
import (
"fmt" "sort" "math/rand"
)
func partition(a sort.Interface, first int, last int, pivotIndex int) int {
a.Swap(first, pivotIndex) // move it to beginning left := first+1 right := last for left <= right { for left <= last && a.Less(left, first) { left++ } for right >= first && a.Less(first, right) { right-- } if left <= right { a.Swap(left, right) left++ right-- } } a.Swap(first, right) // swap into right place return right
}
func quickselect(a sort.Interface, n int) int {
first := 0 last := a.Len()-1 for { pivotIndex := partition(a, first, last,
rand.Intn(last - first + 1) + first)
if n == pivotIndex { return pivotIndex } else if n < pivotIndex { last = pivotIndex-1 } else { first = pivotIndex+1 } } panic("bad index")
}
func main() {
for i := 0; ; i++ { v := []int{9, 8, 7, 6, 5, 0, 1, 2, 3, 4} if i == len(v) { return } fmt.Println(v[quickselect(sort.IntSlice(v), i)]) }
}</lang>
- Output:
0 1 2 3 4 5 6 7 8 9
Haskell
<lang haskell>import Data.List (partition)
quickselect
:: Ord a => [a] -> Int -> a
quickselect (x:xs) k
| k < l = quickselect ys k | k > l = quickselect zs (k - l - 1) | otherwise = x where (ys, zs) = partition (< x) xs l = length ys
main :: IO () main =
print ((fmap . quickselect) <*> zipWith const [0 ..] $ [9, 8, 7, 6, 5, 0, 1, 2, 3, 4])</lang>
- Output:
[0,1,2,3,4,5,6,7,8,9]
Icon and Unicon
The following works in both languages. <lang unicon>procedure main(A)
every writes(" ",select(1 to *A, A, 1, *A)|"\n")
end
procedure select(k,A,min,max)
repeat { pNI := partition(?(max-min)+min, A, min, max) pD := pNI - min + 1 if pD = k then return A[pNI] if k < pD then max := pNI-1 else (k -:= pD, min := pNI+1) }
end
procedure partition(pivot,A,min,max)
pV := (A[max] :=: A[pivot]) sI := min every A[i := min to max-1] <= pV do (A[sI] :=: A[i], sI +:= 1) A[max] :=: A[sI] return sI
end</lang>
Sample run:
->qs 9 8 7 6 5 0 1 2 3 4 0 1 2 3 4 5 6 7 8 9 ->
J
Caution: as defined, we should expect performance on this task to be bad. Quickselect is optimized for selecting a single element from a list, with best-case performance of O(n) and worst case performance of O(n^2). If we use it to select most of the items from a list, the overall task performance will be O(n^2) best case and O(n^3) worst case. If we really wanted to perform this task efficiently, we would first sort the list and then extract the desired elements. But we do not really want to be efficient here, and maybe that is the point.
Further caution: this task asks us to select "the first, second, third, ... up to the tenth largest member of the vector". But we also cannot know, apriori, what value is the first, second, third, ... largest member. So to accomplish this task we are first going to have to sort the list. But We Will Use Quickselect - that is the specification, after all. Perhaps this task should be taken as an illustration of how silly specifications can sometimes be. We need to have a good sense of humor, after all.
Another caution: quick select simply selects a value that matches. So in the simple case it's an identity operation. When we select a 5 from a list, we get a 5 back out. We can imagine that there might be cases where the thing we get back out is a more complicated data structure. But whether that is really efficient, or not, depends on other factors.
Final caution: a brute-force linear scan of a list is O(n) best case and O(n) worst case. A binary search on an ordered list tends to be faster. So when you hear someone talking about efficiency, you might want to ask "efficient at what?" In this case, I think there might be room for further clarification of that issue (but that makes this a good object lesson - in the real world there are many examples of presentations of ideas which sound great but where other alternatives might be significantly better).
With that out of the way, here's a pedantic (and laughably inefficient) implementation of quickselect:
<lang J>quickselect=:4 :0
if. 0=#y do. _ return. end. n=.?#y m=.n{y if. x < m do. x quickselect (m>y)#y else. if. x > m do. x quickselect (m<y)#y else. m end. end.
)</lang>
"Proof" that it works:
<lang J> 8 quickselect 9, 8, 7, 6, 5, 0, 1, 2, 3, 4 8</lang>
And, the required task example:
<lang J> ((10 {./:~) quickselect"0 1 ]) 9, 8, 7, 6, 5, 0, 1, 2, 3, 4 0 1 2 3 4 5 6 7 8 9</lang>
(Insert here: puns involving greater transparency, the emperor's new clothes, burlesque and maybe the dance of the seven veils.)
Java
<lang java>import java.util.Random;
public class QuickSelect {
private static <E extends Comparable<? super E>> int partition(E[] arr, int left, int right, int pivot) { E pivotVal = arr[pivot]; swap(arr, pivot, right); int storeIndex = left; for (int i = left; i < right; i++) { if (arr[i].compareTo(pivotVal) < 0) { swap(arr, i, storeIndex); storeIndex++; } } swap(arr, right, storeIndex); return storeIndex; }
private static <E extends Comparable<? super E>> E select(E[] arr, int n) { int left = 0; int right = arr.length - 1; Random rand = new Random(); while (right >= left) { int pivotIndex = partition(arr, left, right, rand.nextInt(right - left + 1) + left); if (pivotIndex == n) { return arr[pivotIndex]; } else if (pivotIndex < n) { left = pivotIndex + 1; } else { right = pivotIndex - 1; } } return null; }
private static void swap(Object[] arr, int i1, int i2) { if (i1 != i2) { Object temp = arr[i1]; arr[i1] = arr[i2]; arr[i2] = temp; } }
public static void main(String[] args) { for (int i = 0; i < 10; i++) { Integer[] input = {9, 8, 7, 6, 5, 0, 1, 2, 3, 4}; System.out.print(select(input, i)); if (i < 9) System.out.print(", "); } System.out.println(); }
}</lang>
- Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
JavaScript
ES5
<lang javascript>// this just helps make partition read better function swap(items, firstIndex, secondIndex) {
var temp = items[firstIndex]; items[firstIndex] = items[secondIndex]; items[secondIndex] = temp;
};
// many algorithms on this page violate // the constraint that partition operates in place function partition(array, from, to) {
// https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/random var pivotIndex = getRandomInt(from, to), pivot = array[pivotIndex]; swap(array, pivotIndex, to); pivotIndex = from;
for(var i = from; i <= to; i++) { if(array[i] < pivot) { swap(array, pivotIndex, i); pivotIndex++; } }; swap(array, pivotIndex, to);
return pivotIndex;
};
// later versions of JS have TCO so this is safe function quickselectRecursive(array, from, to, statistic) {
if(array.length === 0 || statistic > array.length - 1) { return undefined; };
var pivotIndex = partition(array, from, to); if(pivotIndex === statistic) { return array[pivotIndex]; } else if(pivotIndex < statistic) { return quickselectRecursive(array, pivotIndex, to, statistic); } else if(pivotIndex > statistic) { return quickselectRecursive(array, from, pivotIndex, statistic); }
};
function quickselectIterative(array, k) {
if(array.length === 0 || k > array.length - 1) { return undefined; };
var from = 0, to = array.length, pivotIndex = partition(array, from, to);
while(pivotIndex !== k) { pivotIndex = partition(array, from, to); if(pivotIndex < k) { from = pivotIndex; } else if(pivotIndex > k) { to = pivotIndex; } };
return array[pivotIndex];
};
KthElement = {
find: function(array, element) { var k = element - 1; return quickselectRecursive(array, 0, array.length, k); // you can also try out the Iterative version // return quickselectIterative(array, k); }
}</lang>
Example: <lang Javascript> var array = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4],
ks = Array.apply(null, {length: 10}).map(Number.call, Number);
ks.map(k => { KthElement.find(array, k) });</lang>
- Output:
<lang JavaScript>[0, 1, 2, 3, 4, 5, 6, 7, 8, 9];</lang>
ES6
<lang JavaScript>(() => {
'use strict';
// QUICKSELECT ------------------------------------------------------------
// quickselect :: Ord a => Int -> [a] -> a const quickSelect = (k, xxs) => { const [x, xs] = uncons(xxs), [ys, zs] = partition(v => v < x, xs), l = length(ys);
return (k < l) ? ( quickSelect(k, ys) ) : (k > l) ? ( quickSelect(k - l - 1, zs) ) : x; };
// GENERIC FUNCTIONS ------------------------------------------------------
// enumFromTo :: Int -> Int -> [Int] const enumFromTo = (m, n) => Array.from({ length: Math.floor(n - m) + 1 }, (_, i) => m + i);
// length :: [a] -> Int const length = xs => xs.length;
// map :: (a -> b) -> [a] -> [b] const map = (f, xs) => xs.map(f);
// partition :: Predicate -> List -> (Matches, nonMatches) // partition :: (a -> Bool) -> [a] -> ([a], [a]) const partition = (p, xs) => xs.reduce((a, x) => p(x) ? [a[0].concat(x), a[1]] : [a[0], a[1].concat(x)], [ [], [] ]);
// uncons :: [a] -> Maybe (a, [a]) const uncons = xs => xs.length ? [xs[0], xs.slice(1)] : undefined;
// TEST ------------------------------------------------------------------- const v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4];
return map(i => quickSelect(i, v), enumFromTo(0, length(v) - 1));
})();</lang>
- Output:
<lang JavaScript>[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]</lang>
jq
<lang jq># 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;</lang>
Example: Notice that values of k that are too large or too small generate nothing. <lang jq>(0, 12, range(1;11)) as $k
| [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] | quickselect($k) | "k=\($k) => \(.)"</lang>
- Output:
<lang sh>$ jq -n -r -f quickselect.jq k=1 => 0 k=2 => 1 k=3 => 2 k=4 => 3 k=5 => 4 k=6 => 5 k=7 => 6 k=8 => 7 k=9 => 8 k=10 => 9 $</lang>
Julia
Using builtin function select
:
<lang julia>v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4]
@show v select(v, 1:10)
</lang>
- Output:
v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] select(v, 1:10) = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Kotlin
<lang scala>// version 1.1.2
const val MAX = Int.MAX_VALUE val rand = java.util.Random()
fun partition(list:IntArray, left: Int, right:Int, pivotIndex: Int): Int {
val pivotValue = list[pivotIndex] list[pivotIndex] = list[right] list[right] = pivotValue var storeIndex = left for (i in left until right) { if (list[i] < pivotValue) { val tmp = list[storeIndex] list[storeIndex] = list[i] list[i] = tmp storeIndex++ } } val temp = list[right] list[right] = list[storeIndex] list[storeIndex] = temp return storeIndex
}
tailrec fun quickSelect(list: IntArray, left: Int, right: Int, k: Int): Int {
if (left == right) return list[left] var pivotIndex = left + Math.floor((rand.nextInt(MAX) % (right - left + 1)).toDouble()).toInt() pivotIndex = partition(list, left, right, pivotIndex) if (k == pivotIndex) return list[k] else if (k < pivotIndex) return quickSelect(list, left, pivotIndex - 1, k) else return quickSelect(list, pivotIndex + 1, right, k)
}
fun main(args: Array<String>) {
val list = intArrayOf(9, 8, 7, 6, 5, 0, 1, 2, 3, 4) val right = list.size - 1 for (k in 0..9) { print(quickSelect(list, 0, right, k)) if (k < 9) print(", ") } println()
}</lang>
- Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Lua
<lang Lua>function partition (list, left, right, pivotIndex)
local pivotValue = list[pivotIndex] list[pivotIndex], list[right] = list[right], list[pivotIndex] local storeIndex = left for i = left, right do if list[i] < pivotValue then list[storeIndex], list[i] = list[i], list[storeIndex] storeIndex = storeIndex + 1 end end list[right], list[storeIndex] = list[storeIndex], list[right] return storeIndex
end
function quickSelect (list, left, right, n)
local pivotIndex while 1 do if left == right then return list[left] end pivotIndex = math.random(left, right) pivotIndex = partition(list, left, right, pivotIndex) if n == pivotIndex then return list[n] elseif n < pivotIndex then right = pivotIndex - 1 else left = pivotIndex + 1 end end
end
math.randomseed(os.time()) local vec = {9, 8, 7, 6, 5, 0, 1, 2, 3, 4} for i = 1, 10 do print(i, quickSelect(vec, 1, #vec, i) .. " ") end</lang>
- Output:
1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9
Maple
<lang Maple>part := proc(arr, left, right, pivot) local val,safe,i: val := arr[pivot]: arr[pivot], arr[right] := arr[right], arr[pivot]: safe := left: for i from left to right do if arr[i] < val then arr[safe], arr[i] := arr[i], arr[safe]: safe := safe + 1: end if: end do: arr[right], arr[safe] := arr[safe], arr[right]: return safe: end proc:
quickselect := proc(arr,k) local pivot,left,right: left,right := 1,numelems(arr): while(true)do if left = right then return arr[left]: end if: pivot := trunc((left+right)/2); pivot := part(arr, left, right, pivot): if k = pivot then return arr[k]: elif k < pivot then right := pivot-1: else left := pivot+1: end if: end do: end proc: roll := rand(1..20): demo := Array([seq(roll(), i=1..20)]); map(x->printf("%d ", x), demo): print(quickselect(demo,7)): print(quickselect(demo,14)):</lang>
- Example:
5 4 2 1 3 6 8 11 11 11 8 11 9 11 16 20 20 18 17 16 8 11
Mathematica / Wolfram Language
<lang Mathematica>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]</lang>
- Output:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
NetRexx
<lang NetRexx>/* NetRexx */ options replace format comments java crossref symbols nobinary /** @see <a href="http://en.wikipedia.org/wiki/Quickselect">http://en.wikipedia.org/wiki/Quickselect</a> */
runSample(arg) return
-- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ method qpartition(list, ileft, iright, pivotIndex) private static
pivotValue = list[pivotIndex] list = swap(list, pivotIndex, iright) -- Move pivot to end storeIndex = ileft loop i_ = ileft to iright - 1 if list[i_] <= pivotValue then do list = swap(list, storeIndex, i_) storeIndex = storeIndex + 1 end end i_ list = swap(list, iright, storeIndex) -- Move pivot to its final place return storeIndex
-- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ method qselectInPlace(list, k_, ileft = -1, iright = -1) public static
if ileft = -1 then ileft = 1 if iright = -1 then iright = list[0]
loop label inplace forever pivotIndex = Random().nextInt(iright - ileft + 1) + ileft -- select pivotIndex between left and right pivotNewIndex = qpartition(list, ileft, iright, pivotIndex) pivotDist = pivotNewIndex - ileft + 1 select when pivotDist = k_ then do returnVal = list[pivotNewIndex] leave inplace end when k_ < pivotDist then iright = pivotNewIndex - 1 otherwise do k_ = k_ - pivotDist ileft = pivotNewIndex + 1 end end end inplace return returnVal
-- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ method swap(list, i1, i2) private static
if i1 \= i2 then do t1 = list[i1] list[i1] = list[i2] list[i2] = t1 end return list
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method runSample(arg) private static
parse arg samplelist if samplelist = | samplelist = '.' then samplelist = 9 8 7 6 5 0 1 2 3 4 items = samplelist.words say 'Input:' say ' 'samplelist.space(1, ',').changestr(',', ', ') say
say 'Using in-place version of the algorithm:' iv = loop k_ = 1 to items iv = iv qselectInPlace(buildIndexedString(samplelist), k_) end k_ say ' 'iv.space(1, ',').changestr(',', ', ') say
say 'Find the 4 smallest:' iv = loop k_ = 1 to 4 iv = iv qselectInPlace(buildIndexedString(samplelist), k_) end k_ say ' 'iv.space(1, ',').changestr(',', ', ') say
say 'Find the 3 largest:' iv = loop k_ = items - 2 to items iv = iv qselectInPlace(buildIndexedString(samplelist), k_) end k_ say ' 'iv.space(1, ',').changestr(',', ', ') say
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method buildIndexedString(samplelist) private static
list = 0 list[0] = samplelist.words() loop k_ = 1 to list[0] list[k_] = samplelist.word(k_) end k_ return list </lang>
- Output:
Input: 9, 8, 7, 6, 5, 0, 1, 2, 3, 4 Using in-place version of the algorithm: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Find the 4 smallest: 0, 1, 2, 3 Find the 3 largest: 7, 8, 9
Nim
<lang nim>proc qselect[T](a: var openarray[T]; k: int, inl = 0, inr = -1): T =
var r = if inr >= 0: inr else: a.high var st = 0 for i in 0 ..< r: if a[i] > a[r]: continue swap a[i], a[st] inc st
swap a[r], a[st]
if k == st: a[st] elif st > k: qselect(a, k, 0, st - 1) else: qselect(a, k, st, inr)
let x = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4]
for i in 0..9:
var y = x echo i, ": ", qselect(y, i)</lang>
Output:
0: 0 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9
OCaml
<lang ocaml>let rec quickselect k = function
[] -> failwith "empty" | x :: xs -> let ys, zs = List.partition ((>) x) xs in let l = List.length ys in if k < l then quickselect k ys else if k > l then quickselect (k-l-1) zs else x</lang>
Usage:
# let v = [9; 8; 7; 6; 5; 0; 1; 2; 3; 4];; val v : int list = [9; 8; 7; 6; 5; 0; 1; 2; 3; 4] # Array.init 10 (fun i -> quickselect i v);; - : int array = [|0; 1; 2; 3; 4; 5; 6; 7; 8; 9|]
PARI/GP
<lang parigp>part(list, left, right, pivotIndex)={
my(pivotValue=list[pivotIndex],storeIndex=left,t); t=list[pivotIndex]; list[pivotIndex]=list[right]; list[right]=t; for(i=left,right-1, if(list[i] <= pivotValue, t=list[storeIndex]; list[storeIndex]=list[i]; list[i]=t; storeIndex++ ) ); t=list[right]; list[right]=list[storeIndex]; list[storeIndex]=t; storeIndex
}; quickselect(list, left, right, n)={
if(left==right,return(list[left])); my(pivotIndex=part(list, left, right, random(right-left)+left)); if(pivotIndex==n,return(list[n])); if(n < pivotIndex, quickselect(list, left, pivotIndex - 1, n) , quickselect(list, pivotIndex + 1, right, n) )
};</lang>
Perl
<lang Perl>my @list = qw(9 8 7 6 5 0 1 2 3 4); print join ' ', map { qselect(\@list, $_) } 1 .. 10 and print "\n";
sub qselect {
my ($list, $k) = @_; my $pivot = @$list[int rand @{ $list } - 1]; my @left = grep { $_ < $pivot } @$list; my @right = grep { $_ > $pivot } @$list; if ($k <= @left) { return qselect(\@left, $k); } elsif ($k > @left + 1) { return qselect(\@right, $k - @left - 1); } else { $pivot }
}</lang>
- Output:
0 1 2 3 4 5 6 7 8 9
Phix
sequence s = {9, 8, 7, 6, 5, 0, 1, 2, 3, 4} function quick_select(integer k) integer left = 1, right = length(s) while left<right do object pivotv = s[k]; {s[k], s[right]} = {s[right], s[k]} integer pos = left for i=left to right do if s[i]<pivotv then {s[i], s[pos]} = {s[pos], s[i]} pos += 1 end if end for {s[right], s[pos]} = {s[pos], s[right]} if pos==k then exit end if if pos<k then left = pos + 1 else right = pos - 1 end if end while return s[k] end function for i=1 to 10 do integer r = quick_select(i) printf(1," %d",r) end for {} = wait_key()
- Output:
0 1 2 3 4 5 6 7 8 9
PicoLisp
<lang PicoLisp>(seed (in "/dev/urandom" (rd 8))) (de swapL (Lst X Y)
(let L (nth Lst Y) (swap L (swap (nth Lst X) (car L)) ) ) )
(de partition (Lst L R P)
(let V (get Lst P) (swapL Lst R P) (for I (range L R) (and (> V (get Lst I)) (swapL Lst L I) (inc 'L) ) ) (swapL Lst L R) L ) )
(de quick (Lst N L R)
(default L (inc N) R (length Lst)) (if (= L R) (get Lst L) (let P (partition Lst L R (rand L R)) (cond ((= N P) (get Lst N)) ((> P N) (quick Lst N L P)) (T (quick Lst N P R)) ) ) ) )
(let Lst (9 8 7 6 5 0 1 2 3 4)
(println (mapcar '((N) (quick Lst N)) (range 0 9) ) ) )</lang>
- Output:
(0 1 2 3 4 5 6 7 8 9)
PL/I
<lang PL/I> quick: procedure options (main); /* 4 April 2014 */
partition: procedure (list, left, right, pivot_Index) returns (fixed binary);
declare list (*) fixed binary; declare (left, right, pivot_index) fixed binary; declare (store_index, pivot_value) fixed binary; declare I fixed binary;
pivot_Value = list(pivot_Index); call swap (pivot_Index, right); /* Move pivot to end */ store_Index = left; do i = left to right-1; if list(i) < pivot_Value then do; call swap (store_Index, i); store_Index = store_index + 1; end; end; call swap (right, store_Index); /* Move pivot to its final place */ return (store_Index);
swap: procedure (i, j);
declare (i, j) fixed binary; declare t fixed binary;
t = list(i); list(i) = list(j); list(j) = t;
end swap; end partition;
/* Returns the n-th smallest element of list within left..right inclusive */ /* (i.e. left <= n <= right). */ quick_select: procedure (list, left, right, n) recursive returns (fixed binary);
declare list(*) fixed binary; declare (left, right, n) fixed binary; declare pivot_index fixed binary;
if left = right then /* If the list contains only one element */ return ( list(left) ); /* Return that element */ pivot_Index = (left+right)/2; /* select a pivot_Index between left and right, */ /* e.g. left + Math.floor(Math.random() * (right - left + 1)) */ pivot_Index = partition(list, left, right, pivot_Index); /* The pivot is in its final sorted position. */ if n = pivot_Index then return ( list(n) ); else if n < pivot_Index then return ( quick_select(list, left, pivot_Index - 1, n) ); else return ( quick_select(list, pivot_Index + 1, right, n) );
end quick_select;
declare a(10) fixed binary static initial (9, 8, 7, 6, 5, 0, 1, 2, 3, 4); declare I fixed binary;
do i = 1 to 10; put skip edit ('The ', trim(i), '-th element is ', quick_select((a), 1, 10, (i) )) (a); end;
end quick;</lang> Output:
The 1-th element is 0 The 2-th element is 1 The 3-th element is 2 The 4-th element is 3 The 5-th element is 4 The 6-th element is 5 The 7-th element is 6 The 8-th element is 7 The 9-th element is 8 The 10-th element is 9
PowerShell
<lang PowerShell>
function partition($list, $left, $right, $pivotIndex) { $pivotValue = $list[$pivotIndex] $list[$pivotIndex], $list[$right] = $list[$right], $list[$pivotIndex] $storeIndex = $left foreach ($i in $left..($right-1)) { if ($list[$i] -lt $pivotValue) { $list[$storeIndex],$list[$i] = $list[$i], $list[$storeIndex] $storeIndex += 1 } } $list[$right],$list[$storeIndex] = $list[$storeIndex], $list[$right] $storeIndex
}
function rank($list, $left, $right, $n) {
if ($left -eq $right) {$list[$left]} else { $pivotIndex = Get-Random -Minimum $left -Maximum $right $pivotIndex = partition $list $left $right $pivotIndex if ($n -eq $pivotIndex) {$list[$n]} elseif ($n -lt $pivotIndex) {(rank $list $left ($pivotIndex - 1) $n)} else {(rank $list ($pivotIndex+1) $right $n)} }
}
function quickselect($list) {
$right = $list.count-1 foreach($left in 0..$right) {rank $list $left $right $left}
} $arr = @(9, 8, 7, 6, 5, 0, 1, 2, 3, 4) "$(quickselect $arr)" </lang> Output:
0 1 2 3 4 5 6 7 8 9
PureBasic
A direct implementation of the Wikipedia pseudo-code. <lang PureBasic> Procedure QuickPartition (Array L(1), left, right, pivotIndex)
pivotValue = L(pivotIndex) Swap L(pivotIndex) , L(right); Move pivot To End storeIndex = left For i=left To right-1 If L(i) < pivotValue Swap L(storeIndex),L(i) storeIndex+1 EndIf Next i Swap L(right), L(storeIndex) ; Move pivot To its final place ProcedureReturn storeIndex EndProcedure
Procedure QuickSelect(Array L(1), left, right, k)
Repeat If left = right:ProcedureReturn L(left):EndIf pivotIndex.i= left; Select pivotIndex between left And right pivotIndex= QuickPartition(L(), left, right, pivotIndex) If k = pivotIndex ProcedureReturn L(k) ElseIf k < pivotIndex right= pivotIndex - 1 Else left= pivotIndex + 1 EndIf ForEver
EndProcedure Dim L.i(9) For i=0 To 9
Read L(i)
Next i DataSection
Data.i 9, 8, 7, 6, 5, 0, 1, 2, 3, 4
EndDataSection For i=0 To 9
Debug QuickSelect(L(),0,9,i)
Next i</lang>
- Output:
0 1 2 3 4 5 6 7 8 9
Python
Procedural
A direct implementation of the Wikipedia pseudo-code, using a random initial pivot. I added some input flexibility allowing sensible defaults for left and right function arguments. <lang python>import random
def partition(vector, left, right, pivotIndex):
pivotValue = vector[pivotIndex] vector[pivotIndex], vector[right] = vector[right], vector[pivotIndex] # Move pivot to end storeIndex = left for i in range(left, right): if vector[i] < pivotValue: vector[storeIndex], vector[i] = vector[i], vector[storeIndex] storeIndex += 1 vector[right], vector[storeIndex] = vector[storeIndex], vector[right] # Move pivot to its final place return storeIndex
def _select(vector, left, right, k):
"Returns the k-th smallest, (k >= 0), element of vector within vector[left:right+1] inclusive." while True: pivotIndex = random.randint(left, right) # select pivotIndex between left and right pivotNewIndex = partition(vector, left, right, pivotIndex) pivotDist = pivotNewIndex - left if pivotDist == k: return vector[pivotNewIndex] elif k < pivotDist: right = pivotNewIndex - 1 else: k -= pivotDist + 1 left = pivotNewIndex + 1
def select(vector, k, left=None, right=None):
"""\ 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 """ if left is None: left = 0 lv1 = len(vector) - 1 if right is None: right = lv1 assert vector and k >= 0, "Either null vector or k < 0 " assert 0 <= left <= lv1, "left is out of range" assert left <= right <= lv1, "right is out of range" return _select(vector, left, right, k)
if __name__ == '__main__':
v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] print([select(v, i) for i in range(10)])</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Composition of pure functions
<lang python>Quick select
from functools import reduce
- quickselect :: Ord a => Int -> [a] -> a
def quickSelect(k):
The kth smallest element in the unordered list xs. def go(k, xs): x = xs[0]
def ltx(y): return y < x ys, zs = partition(ltx)(xs[1:]) n = len(ys) return go(k, ys) if k < n else ( go(k - n - 1, zs) if k > n else x ) return lambda xs: go(k, xs) if xs else None
- TEST ----------------------------------------------------
- main :: IO ()
def main():
Test
v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] print(list(map( flip(quickSelect)(v), range(0, len(v)) )))
- GENERIC -------------------------------------------------
- flip :: (a -> b -> c) -> b -> a -> c
def flip(f):
The (curried) function f with its arguments reversed. return lambda a: lambda b: f(b)(a)
- partition :: (a -> Bool) -> [a] -> ([a], [a])
def partition(p):
The pair of lists of those elements in xs which respectively do, and don't satisfy the predicate p. def go(a, x): ts, fs = a return (ts + [x], fs) if p(x) else (ts, fs + [x]) return lambda xs: reduce(go, xs, ([], []))
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Racket
<lang racket>(define (quickselect A k)
(define pivot (list-ref A (random (length A)))) (define A1 (filter (curry > pivot) A)) (define A2 (filter (curry < pivot) A)) (cond [(<= k (length A1)) (quickselect A1 k)] [(> k (- (length A) (length A2))) (quickselect A2 (- k (- (length A) (length A2))))] [else pivot]))
(define a '(9 8 7 6 5 0 1 2 3 4)) (display (string-join (map number->string (for/list ([k 10]) (quickselect a (+ 1 k)))) ", ")) </lang>
- Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Raku
(formerly Perl 6)
<lang perl6>my @v = <9 8 7 6 5 0 1 2 3 4>; say map { select(@v, $_) }, 1 .. 10;
sub partition(@vector, $left, $right, $pivot-index) {
my $pivot-value = @vector[$pivot-index]; @vector[$pivot-index, $right] = @vector[$right, $pivot-index]; my $store-index = $left; for $left ..^ $right -> $i { if @vector[$i] < $pivot-value { @vector[$store-index, $i] = @vector[$i, $store-index]; $store-index++; } } @vector[$right, $store-index] = @vector[$store-index, $right]; return $store-index;
}
sub select( @vector,
\k where 1 .. @vector, \l where 0 .. @vector = 0, \r where l .. @vector = @vector.end ) { my ($k, $left, $right) = k, l, r; loop { my $pivot-index = ($left..$right).pick; my $pivot-new-index = partition(@vector, $left, $right, $pivot-index); my $pivot-dist = $pivot-new-index - $left + 1; given $pivot-dist <=> $k { when Same { return @vector[$pivot-new-index]; } when More { $right = $pivot-new-index - 1; } when Less { $k -= $pivot-dist; $left = $pivot-new-index + 1; } } }
}</lang>
- Output:
0 1 2 3 4 5 6 7 8 9
REXX
uses in-line swap
<lang rexx>/*REXX program sorts a list (which may be numbers) by using the quick select algorithm.*/ parse arg list; if list= then list= 9 8 7 6 5 0 1 2 3 4 /*Not given? Use default.*/ say right('list: ', 22) list
- = words(list)
do i=1 for #; @.i= word(list, i) /*assign all the items ──► @. (array). */ end /*i*/ /* [↑] #: number of items in the list.*/
say
do j=1 for # /*show 1 ──► # items place and value.*/ say right('item', 20) right(j, length(#))", value: " qSel(1, #, j) end /*j*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ qPart: procedure expose @.; parse arg L 1 ?,R,X; xVal= @.X
parse value @.X @.R with @.R @.X /*swap the two names items (X and R). */ do k=L to R-1 /*process the left side of the list. */ if @.k>xVal then iterate /*when an item > item #X, then skip it.*/ parse value @.? @.k with @.k @.? /*swap the two named items (? and K). */ ?= ? + 1 /*bump the item number (point to next).*/ end /*k*/ parse value @.R @.? with @.? @.R /*swap the two named items (R and ?). */ return ? /*return the item number to invoker. */
/*──────────────────────────────────────────────────────────────────────────────────────*/ qSel: procedure expose @.; parse arg L,R,z; if L==R then return @.L /*only one item?*/
do forever /*keep searching until we're all done. */ new= qPart(L, R, (L+R) % 2) /*partition the list into roughly ½. */ $= new - L + 1 /*calculate pivot distance less L+1. */ if $==z then return @.new /*we're all done with this pivot part. */ else if z<$ then R= new-1 /*decrease the right half of the array.*/ else do; z= z-$ /*decrease the distance. */ L= new+1 /*increase the left half *f the array.*/ end end /*forever*/</lang>
- output when using the default input:
list: 9 8 7 6 5 0 1 2 3 4 item 1, value: 0 item 2, value: 1 item 3, value: 2 item 4, value: 3 item 5, value: 4 item 6, value: 5 item 7, value: 6 item 8, value: 7 item 9, value: 8 item 10, value: 9
uses swap subroutine
<lang rexx>/*REXX program sorts a list (which may be numbers) by using the quick select algorithm. */ parse arg list; if list= then list= 9 8 7 6 5 0 1 2 3 4 /*Not given? Use default.*/ say right('list: ', 22) list
- = words(list)
do i=1 for #; @.i= word(list, i) /*assign all the items ──► @. (array). */ end /*i*/ /* [↑] #: number of items in the list.*/
say
do j=1 for # /*show 1 ──► # items place and value.*/ say right('item', 20) right(j, length(#))", value: " qSel(1, #, j) end /*j*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ qPart: procedure expose @.; parse arg L 1 ?,R,X; xVal= @.X
call swap X,R /*swap the two named items (X and R). */ do k=L to R-1 /*process the left side of the list. */ if @.k>xVal then iterate /*when an item > item #X, then skip it.*/ call swap ?,k /*swap the two named items (? and K). */ ?= ? + 1 /*bump the item number (point to next).*/ end /*k*/ call swap R,? /*swap the two named items (R and ?). */ return ? /*return the item number to invoker. */
/*──────────────────────────────────────────────────────────────────────────────────────*/ qSel: procedure expose @.; parse arg L,R,z; if L==R then return @.L /*only one item?*/
do forever /*keep searching until we're all done. */ new= qPart(L, R, (L+R) % 2) /*partition the list into roughly ½. */ $= new - L + 1 /*calculate the pivot distance less L+1*/ if $==z then return @.new /*we're all done with this pivot part. */ else if z<$ then R= new-1 /*decrease the right half of the array.*/ else do; z= z-$ /*decrease the distance. */ L= new+1 /*increase the left half of the array.*/ end end /*forever*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ swap: parse arg _1,_2; parse value @._1 @._2 with @._2 @._1; return /*swap 2 items.*/</lang>
- output is the identical to the 1st REXX version.
Ring
<lang ring> aList = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] see partition(aList, 9, 4, 2) + nl
func partition list, left, right, pivotIndex
pivotValue = list[pivotIndex] temp = list[pivotIndex] list[pivotIndex] = list[right] list[right] = temp storeIndex = left for i = left to right-1 if list[i] < pivotValue temp = list[storeIndex] list[storeIndex] = list[i] list[i] = temp storeIndex++ ok temp = list[right] list[right] = list[storeIndex] list[storeIndex] = temp next return storeIndex
</lang>
Ruby
<lang ruby>def quickselect(a, k)
arr = a.dup # we will be modifying it loop do pivot = arr.delete_at(rand(arr.length)) left, right = arr.partition { |x| x < pivot } if k == left.length return pivot elsif k < left.length arr = left else k = k - left.length - 1 arr = right end end
end
v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] p v.each_index.map { |i| quickselect(v, i) }</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Rust
<lang rust>// See https://en.wikipedia.org/wiki/Quickselect
fn partition<T: PartialOrd>(a: &mut [T], left: usize, right: usize, pivot: usize) -> usize {
a.swap(pivot, right); let mut store_index = left; for i in left..right { if a[i] < a[right] { a.swap(store_index, i); store_index += 1; } } a.swap(right, store_index); store_index
}
fn pivot_index(left: usize, right: usize) -> usize {
return left + (right - left) / 2;
}
fn select<T: PartialOrd>(a: &mut [T], mut left: usize, mut right: usize, n: usize) {
loop { if left == right { break; } let mut pivot = pivot_index(left, right); pivot = partition(a, left, right, pivot); if n == pivot { break; } else if n < pivot { right = pivot - 1; } else { left = pivot + 1; } }
}
// Rearranges the elements of 'a' such that the element at index 'n' is // the same as it would be if the array were sorted, smaller elements are // to the left of it and larger elements are to its right. fn nth_element<T: PartialOrd>(a: &mut [T], n: usize) {
select(a, 0, a.len() - 1, n);
}
fn main() {
let a = vec![9, 8, 7, 6, 5, 0, 1, 2, 3, 4]; for n in 0..a.len() { let mut b = a.clone(); nth_element(&mut b, n); println!("n = {}, nth element = {}", n + 1, b[n]); }
}</lang>
- Output:
n = 1, nth element = 0 n = 2, nth element = 1 n = 3, nth element = 2 n = 4, nth element = 3 n = 5, nth element = 4 n = 6, nth element = 5 n = 7, nth element = 6 n = 8, nth element = 7 n = 9, nth element = 8 n = 10, nth element = 9
Scala
<lang scala>import scala.util.Random
object QuickSelect {
def quickSelect[A <% Ordered[A]](seq: Seq[A], n: Int, rand: Random = new Random): A = { val pivot = rand.nextInt(seq.length); val (left, right) = seq.partition(_ < seq(pivot)) if (left.length == n) { seq(pivot) } else if (left.length < n) { quickSelect(right, n - left.length, rand) } else { quickSelect(left, n, rand) } } def main(args: Array[String]): Unit = { val v = Array(9, 8, 7, 6, 5, 0, 1, 2, 3, 4) println((0 until v.length).map(quickSelect(v, _)).mkString(", ")) }
}</lang>
- Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Sidef
<lang ruby>func quickselect(a, k) {
var pivot = a.pick; var left = a.grep{|i| i < pivot}; var right = a.grep{|i| i > pivot};
given(var l = left.len) { when (k) { pivot } case (k < l) { __FUNC__(left, k) } default { __FUNC__(right, k - l - 1) } }
}
var v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4]; say v.range.map{|i| quickselect(v, i)};</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Standard ML
<lang sml>fun quickselect (_, _, []) = raise Fail "empty"
| quickselect (k, cmp, x :: xs) = let val (ys, zs) = List.partition (fn y => cmp (y, x) = LESS) xs val l = length ys in if k < l then quickselect (k, cmp, ys) else if k > l then quickselect (k-l-1, cmp, zs) else x end</lang>
Usage:
- val v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4]; val v = [9,8,7,6,5,0,1,2,3,4] : int list - List.tabulate (10, fn i => quickselect (i, Int.compare, v)); val it = [0,1,2,3,4,5,6,7,8,9] : int list
Swift
<lang swift>func select<T where T : Comparable>(var elements: [T], n: Int) -> T {
var r = indices(elements) while true { let pivotIndex = partition(&elements, r) if n == pivotIndex { return elements[pivotIndex] } else if n < pivotIndex { r.endIndex = pivotIndex } else { r.startIndex = pivotIndex+1 } }
}
for i in 0 ..< 10 {
let a = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] print(select(a, i)) if i < 9 { print(", ") }
} println()</lang>
- Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Tcl
<lang tcl># Swap the values at two indices of a list proc swap {list i j} {
upvar 1 $list l set tmp [lindex $l $i] lset l $i [lindex $l $j] lset l $j $tmp
}
proc quickselect {vector k {left 0} {right ""}} {
set last [expr {[llength $vector] - 1}] if {$right eq ""} {
set right $last
} # Sanity assertions if {![llength $vector] || $k <= 0} {
error "Either empty vector, or k <= 0"
} elseif {![tcl::mathop::<= 0 $left $last]} {
error "left is out of range"
} elseif {![tcl::mathop::<= $left $right $last]} {
error "right is out of range"
}
# the _select core, inlined while 1 {
set pivotIndex [expr {int(rand()*($right-$left))+$left}]
# the partition core, inlined set pivotValue [lindex $vector $pivotIndex] swap vector $pivotIndex $right set storeIndex $left for {set i $left} {$i <= $right} {incr i} { if {[lindex $vector $i] < $pivotValue} { swap vector $storeIndex $i incr storeIndex } } swap vector $right $storeIndex set pivotNewIndex $storeIndex
set pivotDist [expr {$pivotNewIndex - $left + 1}] if {$pivotDist == $k} { return [lindex $vector $pivotNewIndex] } elseif {$k < $pivotDist} { set right [expr {$pivotNewIndex - 1}] } else { set k [expr {$k - $pivotDist}] set left [expr {$pivotNewIndex + 1}] }
}
}</lang> Demonstrating: <lang tcl>set v {9 8 7 6 5 0 1 2 3 4} foreach i {1 2 3 4 5 6 7 8 9 10} {
puts "$i => [quickselect $v $i]"
}</lang>
- Output:
1 => 0 2 => 1 3 => 2 4 => 3 5 => 4 6 => 5 7 => 6 8 => 7 9 => 8 10 => 9
VBA
<lang vb>Dim s As Variant
Private Function quick_select(ByRef s As Variant, k As Integer) As Integer
Dim left As Integer, right As Integer, pos As Integer Dim pivotValue As Integer, tmp As Integer left = 1: right = UBound(s) Do While left < right pivotValue = s(k) tmp = s(k) s(k) = s(right) s(right) = tmp pos = left For i = left To right If s(i) < pivotValue Then tmp = s(i) s(i) = s(pos) s(pos) = tmp pos = pos + 1 End If Next i tmp = s(right) s(right) = s(pos) s(pos) = tmp If pos = k Then Exit Do End If If pos < k Then left = pos + 1 Else right = pos - 1 End If Loop quick_select = s(k)
End Function Public Sub main()
Dim r As Integer, i As Integer s = [{9, 8, 7, 6, 5, 0, 1, 2, 3, 4}] For i = 1 To 10 r = quick_select(s, i) 's is ByRef parameter Debug.Print IIf(i < 10, r & ", ", "" & r); Next i
End Sub
</lang>
- Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Wren
The Find.quick method in the above module implements the quickselect algorithm. <lang ecmascript>import "/sort" for Find
var a = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] for (k in 0..9) {
System.write(Find.quick(a, k)) if (k < 9) System.write(", ")
} System.print()</lang>
- Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
zkl
This is the in place version rather than the much more concise copy-partition functional method. A copy of the input list is made to cover the case it is immutable (or the input shouldn't be changed) <lang zkl>fcn qselect(list,nth){ // in place quick select
fcn(list,left,right,nth){ if (left==right) return(list[left]); pivotIndex:=(left+right)/2; // or median of first,middle,last
// partition pivot:=list[pivotIndex]; list.swap(pivotIndex,right); // move pivot to end pivotIndex := left; i:=left; do(right-left){ // foreach i in ([left..right-1])
if (list[i] < pivot){ list.swap(i,pivotIndex); pivotIndex += 1; } i += 1;
} list.swap(pivotIndex,right); // move pivot to final place
if (nth==pivotIndex) return(list[nth]); if (nth<pivotIndex) return(self.fcn(list,left,pivotIndex-1,nth)); return(self.fcn(list,pivotIndex+1,right,nth)); }(list.copy(),0,list.len()-1,nth);
}</lang> <lang zkl>list:=T(10, 9, 8, 7, 6, 1, 2, 3, 4, 5); foreach nth in (list.len()){ println(nth,": ",qselect(list,nth)) }</lang>
- Output:
0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10
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