⚠️ Warning: This is a draft ⚠️
This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.
{{task}} Use the [[wp:Quickselect|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: Quick''sort'' has a separate [[Sorting algorithms/Quicksort|task]].
ALGOL 68
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
{{out}}
1: 0
2: 1
3: 2
4: 3
5: 4
6: 5
7: 6
8: 7
9: 8
10: 9
AutoHotkey
{{works with|AutoHotkey_L}} (AutoHotkey1.1+) A direct implementation of the Wikipedia pseudo-code.
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
}
'''Output:'''
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
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; }
{{out}}
0: 0
1: 1
2: 2
3: 3
4: 4
5: 5
6: 6
7: 7
8: 8
9: 9
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.
#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; }
{{out}}
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
;Implementation
A more explicit implementation:
#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; }
{{out}}
0, 1, 2, 3, 4, 5, 6, 7, 8, 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.
// ---------------------------------------------------------------------------------------------- // // 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 } }
{{out}}
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 >
COBOL
The following is in the Managed COBOL dialect: {{works with|Visual 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.
Common Lisp
{{trans|Haskell}}
(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)))
{{out}}
(0 1 2 3 4 5 6 7 8 9)
Crystal
{{trans|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
{{out}}
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
D
Standard Version
This could use a different algorithm:
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], " "); } }
{{out}}
0 1 2 3 4 5 6 7 8 9
Array Version
{{trans|Java}}
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; }
{{out}}
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Elixir
{{trans|Erlang}}
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
{{out}}
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Erlang
{{trans|Haskell}}
-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.
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 usage of a PARAMETER statement in TEST to set up the specific test, and 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, REAL4, REAL8) 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...
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.
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.
=={{header|F Sharp|F#}}== {{trans|Haskell}}
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
{{out}}
[0; 1; 2; 3; 4; 5; 6; 7; 8; 9]
Factor
{{trans|Haskell}}
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
{{out}}
{ 0 1 2 3 4 5 6 7 8 9 }
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)) } }
{{out}}
0
1
2
3
4
5
6
7
8
9
A more generic version that works for any container that conforms to sort.Interface:
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)]) } }
{{out}}
0
1
2
3
4
5
6
7
8
9
Haskell
import Data.List (partition) quickselect :: Ord a => Int -> [a] -> a quickselect k (x:xs) | k < l = quickselect k ys | k > l = quickselect (k-l-1) zs | otherwise = x where (ys, zs) = partition (< x) xs l = length ys main :: IO () main = do let v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] print $ map (\i -> quickselect i v) [0 .. length v-1]
{{out}}
[0,1,2,3,4,5,6,7,8,9]
=={{header|Icon}} and {{header|Unicon}}==
The following works in both languages.
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
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:
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.
)
"Proof" that it works:
8 quickselect 9, 8, 7, 6, 5, 0, 1, 2, 3, 4
8
And, the required task example:
((10 {./:~) quickselect"0 1 ]) 9, 8, 7, 6, 5, 0, 1, 2, 3, 4
0 1 2 3 4 5 6 7 8 9
(Insert here: puns involving greater transparency, the emperor's new clothes, burlesque and maybe the dance of the seven veils.)
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(); } }
{{out}}
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Javascript
ES5
// 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); } }
'''Example''':
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) });
{{out}}
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9];
ES6
{{Trans|Haskell}}
(() => { '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)); })();
{{Out}}
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
jq
{{works with|jq|1.4}}
# 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;
'''Example''': Notice that values of k that are too large or too small generate nothing.
(0, 12, range(1;11)) as $k
| [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] | quickselect($k)
| "k=\($k) => \(.)"
{{out}}
$ 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 $
Julia
{{works with|Julia|0.6}}
Using builtin function select:
v = [9, 8, 7, 6, 5, 0, 1, 2, 3, 4] @show v select(v, 1:10)
{{out}}
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
// 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() }
{{out}}
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
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
{{out}}
1 0
2 1
3 2
4 3
5 4
6 5
7 6
8 7
9 8
10 9
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)):
{{Out|Example}}
5 4 2 1 3 6 8 11 11 11 8 11 9 11 16 20 20 18 17 16
8
11
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
{{out}}
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
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)
Output:
0: 0
1: 1
2: 2
3: 3
4: 4
5: 5
6: 6
7: 7
8: 8
9: 9
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
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
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)
)
};
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 } }
{{out}}
0 1 2 3 4 5 6 7 8 9
Perl 6
{{trans|Python}} {{works with|rakudo|2015-10-20}}
;
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;
}
}
}
}
{{out}}
0 1 2 3 4 5 6 7 8 9
Phix
Note the (three) commented-out multiple assignments are nowhere near as performant as the long-hand equivalents; perhaps there may be a way to narrow down the divide in some future release of the compiler...
global function quick_select(sequence s, integer k)
integer left = 1, right = length(s), pos
object pivotv, tmp
while left<right do
pivotv = s[k];
-- {s[k], s[right]} = {s[right], s[k]}
tmp = s[k]
s[k] = s[right]
s[right]=tmp
pos = left
for i=left to right do
if s[i]<pivotv then
-- {s[i], s[pos]} = {s[pos], s[i]}
tmp = s[i]
s[i] = s[pos]
s[pos]=tmp
pos += 1
end if
end for
-- {s[right], s[pos]} = {s[pos], s[right]}
tmp = s[right]
s[right] = s[pos]
s[pos]=tmp
if pos==k then exit end if
if pos<k then
left = pos + 1
else
right = pos - 1
end if
end while
return {s,s[k]}
end function
sequence s = {9, 8, 7, 6, 5, 0, 1, 2, 3, 4}
integer r
for i=1 to 10 do
{s,r} = quick_select(s,i)
printf(1," %d",r)
end for
{} = wait_key()
{{out}}
0 1 2 3 4 5 6 7 8 9
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) ) ) )
{{out}}
(0 1 2 3 4 5 6 7 8 9)
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;
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
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)"
Output:
0 1 2 3 4 5 6 7 8 9
PureBasic
A direct implementation of the Wikipedia pseudo-code.
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
{{out}}
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.
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)])
{{out}}
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Composition of pure functions
{{Trans|Haskell}} {{Works with|Python|3}}
'''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()
{{Out}}
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
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)))) ", "))
{{out}}
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
REXX
===uses in-line swap===
/*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; [email protected]
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*/
'''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
/*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; [email protected]
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.*/
'''output''' is the identical to the 1st REXX version.
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
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) }
{{out}}
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
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(", ")) } }
{{out}}
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Sidef
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)};
{{out}}
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Standard ML
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
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
(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()
{{out}}
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Tcl
{{trans|Python}}
# 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}] } } }
Demonstrating:
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]" }
{{out}}
1 => 0
2 => 1
3 => 2
4 => 3
5 => 4
6 => 5
7 => 6
8 => 7
9 => 8
10 => 9
VBA
{{trans|Phix}}
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
{{out}}
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
zkl
{{trans|Wikipedia}} 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)
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);
}
list:=T(10, 9, 8, 7, 6, 1, 2, 3, 4, 5);
foreach nth in (list.len()){ println(nth,": ",qselect(list,nth)) }
{{out}}
0: 1
1: 2
2: 3
3: 4
4: 5
5: 6
6: 7
7: 8
8: 9
9: 10