Sorting algorithms/Quicksort
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
In this task, the goal is to sort an array (or list) of elements using the Quicksort algorithm. The elements must have a strict weak order and the index of the array can be of any discrete type. For languages where this is not possible, sort an array of integers. The algorithm goes like this (from the wiki):
function quicksort(array)
var list lessOrEqual, greater
if length(array) ≤ 1
return array
select a pivot value pivot from array
for each x in array
if x ≤ pivot then add x to lessOrEqual
if x > pivot then add x to greater
return concatenate(quicksort(lessOrEqual), quicksort(greater))
The "pivot" separates the dataset into two groups: those that are less than or equal to the value at the pivot and those that are greater than the pivot. The Quicksort's worst case time is O(n^2) for a completely sorted set, but otherwise it is O(n * log n). Its average time is slightly faster than that of the merge sort in most cases, even though they are both O(n * log n) sorts.
Ada
This example is implemented as a generic procedure. The procedure specification is: <ada>
-----------------------------------------------------------------------
-- Generic Quicksort procedure
-----------------------------------------------------------------------
generic
type Element_Type is private;
type Index_Type is (<>);
type Element_Array is array(Index_Type range <>) of Element_Type;
with function "<" (Left, Right : Element_Type) return Boolean is <>;
with function ">" (Left, Right : Element_Type) return Boolean is <>;
procedure Sort(Item : in out Element_Array);</ada>
The procedure body deals with any discrete index type, either an integer type or an enumerated type. <ada>
-----------------------------------------------------------------------
-- Generic Quicksort procedure
-----------------------------------------------------------------------
procedure Sort (Item : in out Element_Array) is
procedure Swap(Left, Right : in out Element_Type) is
Temp : Element_Type := Left;
begin
Left := Right;
Right := Temp;
end Swap;
Pivot_Index : Index_Type;
Pivot_Value : Element_Type;
Right : Index_Type := Item'Last;
Left : Index_Type := Item'First;
begin
if Item'Length > 1 then
Pivot_Index := Index_Type'Val((Index_Type'Pos(Item'Last) + 1 +
Index_Type'Pos(Item'First)) / 2);
Pivot_Value := Item(Pivot_Index);
loop
Left := Item'First;
Right := Item'Last;
while Left < Item'Last and then Item(Left) < Pivot_Value loop
Left := Index_Type'Succ(Left);
end loop;
while Right > Item'First and then Item(Right) > Pivot_Value loop
Right := Index_Type'Pred(Right);
end loop;
exit when Left >= Right;
Swap(Item(Left), Item(Right));
if Left < Item'Last and Right > Item'First then
Left := Index_Type'Succ(Left);
Right := Index_Type'Pred(Right);
end if;
end loop;
if Right > Item'First then
Sort(Item(Item'First..Right));
end if;
if Left < Item'Last then
Sort(Item(Left..Item'Last));
end if;
end if;
end Sort;</ada>
An example of how this procedure may be used is: <ada>
with Sort;
with Ada.Text_Io;
with Ada.Float_Text_IO; use Ada.Float_Text_IO;
procedure Sort_Test is
type Days is (Mon, Tue, Wed, Thu, Fri, Sat, Sun);
type Sales is array(Days range <>) of Float;
procedure Sort_Days is new Sort(Float, Days, Sales);
procedure Print(Item : Sales) is
begin
for I in Item'range loop
Put(Item => Item(I), Fore => 5, Aft => 2, Exp => 0);
end loop;
end Print;
Weekly_Sales : Sales := (Mon => 300.0,
Tue => 700.0,
Wed => 800.0,
Thu => 500.0,
Fri => 200.0,
Sat => 100.0,
Sun => 900.0);
begin
Print(Weekly_Sales);
Ada.Text_Io.New_Line(2);
Sort_Days(Weekly_Sales);
Print(Weekly_Sales);
end Sort_Test;</ada>
ALGOL 68
From: http://en.wikibooks.org/wiki/Algorithm_implementation/Sorting/Quicksort#ALGOL_68
PROC partition =(REF [] DATA array, PROC (REF DATA, REF DATA) BOOL cmp)INT: (
INT begin:=LWB array;
INT end:=UPB array;
WHILE begin < end DO
WHILE begin < end DO
IF cmp(array[begin], array[end]) THEN
DATA tmp=array[begin];
array[begin]:=array[end];
array[end]:=tmp;
GO TO break while decr end
FI;
end -:= 1
OD;
break while decr end: SKIP;
WHILE begin < end DO
IF cmp(array[begin], array[end]) THEN
DATA tmp=array[begin];
array[begin]:=array[end];
array[end]:=tmp;
GO TO break while incr begin
FI;
begin +:= 1
OD;
break while incr begin: SKIP
OD;
begin
);
PROC qsort=(REF [] DATA array, PROC (REF DATA, REF DATA) BOOL cmp)VOID: (
IF LWB array < UPB array THEN
INT i := partition(array, cmp);
PAR ( # remove PAR for single threaded sort #
qsort(array[:i-1], cmp),
qsort(array[i+1:], cmp)
)
FI
);
MODE DATA = INT;
PROC cmp=(REF DATA a,b)BOOL: a>b;
main:(
[]DATA const l=(5,4,3,2,1);
[UPB const l]DATA l:=const l;
qsort(l,cmp);
printf(($g(3)$,l))
)
C
void quick(int *left, int *right)
{
if (right > left) {
int pivot = left[(right-left)/2];
int *r = right, *l = left;
do {
while (*l < pivot) l++;
while (*r > pivot) r--;
if (l <= r) {
int t = *l;
*l++ = *r;
*r-- = t;
}
} while (l <= r);
quick(left, r);
quick(l, right);
}
}
void sort(int *array, int length)
{
quick(array, array+length-1);
}
C++
The following implements quicksort with a median-of-three pivot. As idiomatic in C++, the argument last is a one-past-end iterator. Note that this code takes advantage of std::partition, which is O(n). Also note that it needs a random-access iterator for efficient calculation of the median-of-three pivot (more exactly, for O(1) calculation of the iterator mid).
<cpp>
- include <iterator>
- include <algorithm> // for std::partition
- include <functional> // for std::less
// helper function for median of three template<typename T>
T median(T t1, T t2, T t3)
{
if (t1 < t2)
{
if (t2 < t3)
return t2;
else if (t1 < t3)
return t3;
else
return t1;
}
else
{
if (t1 < t3)
return t1;
else if (t2 < t3)
return t3;
else
return t2;
}
}
// helper object to get <= from < template<typename Order> struct non_strict_op:
public std::binary_function<typename Order::second_argument_type,
typename Order::first_argument_type,
bool>
{
non_strict_op(Order o): order(o) {}
bool operator()(typename Order::second_argument_type arg1,
typename Order::first_argument_type arg2) const
{
return !order(arg2, arg1);
}
private:
Order order;
};
template<typename Order> non_strict_op<Order> non_strict(Order o) {
return non_strict_op<Order>(o);
}
template<typename RandomAccessIterator,
typename Order> void quicksort(RandomAccessIterator first, RandomAccessIterator last, Order order)
{
if (first != last && first+1 != last)
{
typedef typename std::iterator_traits<RandomAccessIterator>::value_type value_type;
RandomAccessIterator mid = first + (last - first)/2;
value_type pivot = median(*first, *mid, *(last-1));
RandomAccessIterator split1 = std::partition(first, last, std::bind2nd(order, pivot));
RandomAccessIterator split2 = std::partition(split1, last, std::bind2nd(non_strict(order), pivot));
quicksort(first, split1, order);
quicksort(split2, last, order);
}
}
template<typename RandomAccessIterator>
void quicksort(RandomAccessIterator first, RandomAccessIterator last)
{
quicksort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());
} </cpp>
Clojure
A very Haskell-like solution using list comprehensions and lazy evaluation.
(defn qsort [L]
(if (nil? L)
'()
(let [[pivot & L2] L]
(lazy-cat (qsort (for [y L2 :when (<= y pivot)] y))
(list pivot)
(qsort (for [y L2 :when (> y pivot)] y))))))
D
An implementation much similar to the C one is possible too, this is slower and simpler, derived from the Python one. This is a function template:
import std.stdio;
T[] quickSort(T)(T[] items) {
T[] less, more;
if (items.length <= 1)
return items;
else {
T pivot = items[0];
foreach(el; items[1 .. $])
if (el < pivot)
less ~= el;
else
more ~= el;
return quickSort(less) ~ pivot ~ quickSort(more);
}
}
void main() {
auto a1 = [4, 65, 2, -31, 0, 99, 2, 83, 782, 1];
writefln(quickSort(a1));
auto a2 = [4.0,65.0,2.0,-31.0,0.0,99.0,2.0,83.0,782.0,1.0];
writefln(quickSort(a2));
}
Erlang
like haskell
qsort([]) -> []; qsort([X|Xs]) -> qsort([ Y || Y <- Xs, Y < X]) ++ [X] ++ qsort([ Y || Y <- Xs, Y >= X]).
Forth
defer lessthan ( a@ b@ -- ? ) ' < is lessthan
: mid ( l r -- mid ) over - 2/ -cell and + ;
: exch ( addr1 addr2 -- ) dup @ >r over @ swap ! r> swap ! ;
: partition ( l r -- l r r2 l2 )
2dup mid @ >r ( r: pivot )
2dup begin
swap begin dup @ r@ lessthan while cell+ repeat
swap begin r@ over @ lessthan while cell- repeat
2dup <= if 2dup exch >r cell+ r> cell- then
2dup > until r> drop ;
: qsort ( l r -- )
partition swap rot
\ 2over 2over - + < if 2swap then
2dup < if recurse else 2drop then
2dup < if recurse else 2drop then ;
: sort ( array len -- )
dup 2 < if 2drop exit then
1- cells over + qsort ;
Fortran
MODULE Qsort_Module
IMPLICIT NONE
CONTAINS
RECURSIVE SUBROUTINE Qsort(a)
INTEGER, INTENT(IN OUT) :: a(:)
INTEGER :: split
IF(size(a) > 1) THEN
CALL Partition(a, split)
CALL Qsort(a(:split-1))
CALL Qsort(a(split:))
END IF
END SUBROUTINE Qsort
SUBROUTINE Partition(a, marker)
INTEGER, INTENT(IN OUT) :: a(:)
INTEGER, INTENT(OUT) :: marker
INTEGER :: left, right, pivot, temp
pivot = (a(1) + a(size(a))) / 2 ! Average of first and last elements to prevent quadratic
left = 0 ! behavior with sorted or reverse sorted data
right = size(a) + 1
DO WHILE (left < right)
right = right - 1
DO WHILE (a(right) > pivot)
right = right-1
END DO
left = left + 1
DO WHILE (a(left) < pivot)
left = left + 1
END DO
IF (left < right) THEN
temp = a(left)
a(left) = a(right)
a(right) = temp
END IF
END DO
IF (left == right) THEN
marker = left + 1
ELSE
marker = left
END IF
END SUBROUTINE Partition
END MODULE Qsort_Module
PROGRAM Quicksort
USE Qsort_Module
IMPLICIT NONE
INTEGER, PARAMETER :: n = 100
INTEGER :: array(n)
INTEGER :: i
REAL :: x
CALL RANDOM_SEED
DO i = 1, n
CALL RANDOM_NUMBER(x)
array(i) = INT(x * 10000)
END DO
WRITE (*, "(A)") "array is :-"
WRITE (*, "(10I5)") array
CALL Qsort(array)
WRITE (*,*)
WRITE (*, "(A)") "sorted array is :-"
WRITE (*,"(10I5)") array
END PROGRAM Quicksort
Haskell
The famous two-liner, reflecting the underlying algorithm directly:
qsort [] = [] qsort (x:xs) = qsort [y | y <- xs, y <= x] ++ [x] ++ qsort [y | y <- xs, y > x]
A more efficient version, doing only one comparison per element:
import Data.List qsort [] = [] qsort (x:xs) = qsort ys ++ x : qsort zs where (ys, zs) = partition (<= x) xs
IDL
IDL has a powerful optimized sort() built-in. The following is thus merely for demonstration.
function qs, arr if (count = n_elements(arr)) lt 2 then return,arr pivot = total(arr) / count ; use the average for want of a better choice return,[qs(arr[where(arr le pivot)]),qs(arr[where(arr gt pivot)])] end
Example:
IDL> print,qs([3,17,-5,12,99])
-5 3 12 17 99
J
sel=: 1 : 'x # ['
quicksort=: 3 : 0
if. 1 >: #y do. y else. (quicksort y <sel e),(y =sel e),quicksort y >sel e=.y{~?#y end.
)
To actually sort data in J, it is more convenient and more efficient to use /:~ .
Java
<java>public static <E extends Comparable<? super E>> LinkedList<E> quickSort(LinkedList<E> arr){ LinkedList<E> less= new LinkedList<E>(); LinkedList<E> pivotList= new LinkedList<E>(); LinkedList<E> more= new LinkedList<E>(); if(arr.size() <= 1) return arr; E pivot= arr.getFirst(); //This pivot can change to get faster results for(E i: arr){ if(i.compareTo(pivot)<0) less.add(i); else if(i.compareTo(pivot)>0) more.add(i); else pivotList.add(i); } less= quickSort(less); more= quickSort(more); less.addAll(pivotList); less.addAll(more); return less; }</java>
JavaScript
<javascript>function sort(a,less) {
function swap(i,j) { var t=a[i]; a[i]=a[j]; a[j]=t }
function qs(l,r) {
if (l<r) {
var pivot = a[(l+r)>>1];
var l2=l, r2=r;
do {
while (less(a[l2], pivot) ++l2;
while (less(pivot, a[r2]) --r2;
if (l2 <= r2) swap(l2++, r2--);
} while (l2 <= r2);
qs(l, r2);
qs(l2, r);
}
}
qs(0, a.length-1);
return a;
}</javascript>
Joy
DEFINE qsort == [small] [] [uncons [>] split] [[swap] dip cons concat] binrec .
Lucid
qsort(a) = if eof(first a) then a else follow(qsort(b0),qsort(b1)) fi
where
p = first a < a;
b0 = a whenever p;
b1 = a whenever not p;
follow(x,y) = if xdone then y upon xdone else x fi
where
xdone = iseod x fby xdone or iseod x;
end;
end
MAXScript
fn quickSort arr =
(
less = #()
pivotList = #()
more = #()
if arr.count <= 1 then
(
arr
)
else
(
pivot = arr[arr.count/2]
for i in arr do
(
case of
(
(i < pivot): (append less i)
(i == pivot): (append pivotList i)
(i > pivot): (append more i)
)
)
less = quickSort less
more = quickSort more
less + pivotList + more
)
)
a = #(4, 89, -3, 42, 5, 0, 2, 889)
a = quickSort a
Nial
quicksort is fork [ >= [1 first,tally],
pass,
link [
quicksort sublist [ < [pass, first], pass ],
sublist [ match [pass,first],pass ],
quicksort sublist [ > [pass,first], pass ]
]
]
Using it.
|quicksort [5, 8, 7, 4, 3] =3 4 5 7 8
OCaml
let rec quicksort gt = function
| [] -> []
| x::xs ->
let ys, zs = List.partition (gt x) xs in
quicksort gt ys @ x :: quicksort gt zs
let _ =
quicksort (>) [4; 65; 2; -31; 0; 99; 83; 782; 1]
Perl
sub quick_sort {
$arr = shift;
local $less = [];
local $pivot_list = [];
local $more = [];
if ($#{$arr} <= 0) {
return $arr;
} else {
$pivot = $arr->[0];
foreach my $i (@{$arr}) {
if ($i < $pivot) {
push @{$less}, $i;
} elsif ($i > $pivot) {
push @{$more}, $i;
} else {
push @{$pivot_list}, $i;
}
}
$less = quick_sort($less);
$more = quick_sort($more);
return [@{$less}, @{$pivot_list}, @{$more}];
}
}
print join(' ', @{quick_sort([4, 65, 2, -31, 0, 99, 83, 782, 1])}), "\n";
Output:
-31 0 1 2 4 65 83 99 782
Python
def quickSort(arr):
less = []
pivotList = []
more = []
if len(arr) <= 1:
return arr
else:
pivot = arr[0]
for i in arr:
if i < pivot:
less.append(i)
elif i > pivot:
more.append(i)
else:
pivotList.append(i)
less = quickSort(less)
more = quickSort(more)
return less + pivotList + more
a = [4, 65, 2, -31, 0, 99, 83, 782, 1]
a = quickSort(a)
In a Haskell fashion: <python> def qsort(L):
return (qsort([y for y in L[1:] if y <= L[0]]) +
L[:1] +
qsort([y for y in L[1:] if y > L[0]])) if len(L) > 1 else L
</python>
Scheme
(define (split-by l p)
(let loop ((low (list)) (high (list)) (l l))
(if (null? l)
(cons low high)
(if (p (car l))
(loop low (cons (car l) high) (cdr l))
(loop (cons (car l) low) high (cdr l))))))
(define (quicksort l gt?)
(let q ((l l))
(if (null? l)
l
(let ((s (split-by (cdr l) (lambda (x) (gt? x (car l))))))
(append (q (car s)) (list (car l)) (q (cdr s)))))))
(quicksort (list 1 3 5 7 9 8 6 4 2) >)
Seed7
const proc: quickSort (inout array elemType: arr, in integer: left, in integer: right) is func
local
var elemType: compare_elem is elemType.value;
var integer: less_idx is 0;
var integer: greater_idx is 0;
var elemType: help is elemType.value;
begin
if right > left then
compare_elem := arr[right];
less_idx := pred(left);
greater_idx := right;
repeat
repeat
incr(less_idx);
until arr[less_idx] >= compare_elem;
repeat
decr(greater_idx);
until arr[greater_idx] <= compare_elem or greater_idx = left;
if less_idx < greater_idx then
help := arr[less_idx];
arr[less_idx] := arr[greater_idx];
arr[greater_idx] := help;
end if;
until less_idx >= greater_idx;
arr[right] := arr[less_idx];
arr[less_idx] := compare_elem;
quickSort(arr, left, pred(less_idx));
quickSort(arr, succ(less_idx), right);
end if;
end func;
const proc: quickSort (inout array elemType: arr) is func
begin
quickSort(arr, 1, length(arr));
end func;
Original source: [2]
SML
fun quicksort nil : int list = nil
| quicksort (x::xs) =
let
val part = List.partition (fn y => y<x) xs
val left = #1 part
val right = #2 part
in
quicksort left @ [x] @ quicksort right
end
UnixPipes
split() {
(while read n ; do
test $1 -gt $n && echo $n > $2 || echo $n > $3
done)
}
qsort() {
(read p; test -n "$p" && (
lc="1.$1" ; gc="2.$1"
split $p >(qsort $lc >$lc) >(qsort $gc >$gc);
cat $lc <(echo $p) $gc
rm -f $lc $gc;
))
}
cat to.sort | qsort
V
[qsort
[joinparts [p [*l1] [*l2] : [*l1 p *l2]] view].
[split_on_first uncons [>] split].
[small?]
[]
[split_on_first [l1 l2 : [l1 qsort l2 qsort joinparts]] view i]
ifte].
The way of joy (using binrec)
[qsort
[small?] []
[uncons [>] split]
[[p [*l] [*g] : [*l p *g]] view]
binrec].