Sorting algorithms/Shell sort

Sorting algorithms/Shell sort
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:

O(n logn) sorts

Heap sort | Merge sort | Patience sort | Quick sort

O(n log²n) sorts
Shell Sort

O(n²) sorts
Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort

other sorts
Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort

In this task, the goal is to sort an array of elements using the Shell sort algorithm, a diminishing increment sort. The Shell sort is named after its inventor, Donald Shell, who published the algorithm in 1959. Shellsort is a sequence of interleaved insertion sorts based on an increment sequence. The increment size is reduced after each pass until the increment size is 1. With an increment size of 1, the sort is a basic insertion sort, but by this time the data is guaranteed to be almost sorted, which is insertion sort's "best case". Any sequence will sort the data as long as it ends in 1, but some work better than others. Empirical studies have shown a geometric increment sequence with a ratio of about 2.2 work well in practice. [1] Other good sequences are found at the Online Encyclopedia of Integer Sequences.

Ada

This is a generic implementation of the shell sort. Ada allows arrays to be indexed by integer or enumeration types starting at any value. This version deals with any kind or value of valid index type. <lang ada>generic

  type Element_Type is digits <>;
  type Index_Type is (<>);
  type Array_Type is array(Index_Type range <>) of Element_Type;

package Shell_Sort is

  procedure Sort(Item : in out Array_Type);

end Shell_Sort;</lang> <lang ada>package body Shell_Sort is

  ----------
  -- Sort --
  ----------

  procedure Sort (Item : in out Array_Type) is
     Increment : Natural := Index_Type'Pos(Item'Last) / 2;
     J : Index_Type;
     Temp : Element_Type;
  begin
     while Increment > 0 loop
        for I in Index_Type'Val(Increment) .. Item'Last loop
           J := I;
           Temp := Item(I);
           while J > Index_Type'val(Increment) and then Item (Index_Type'Val(Index_Type'Pos(J) - Increment)) > Temp loop
              Item(J) := Item (Index_Type'Val(Index_Type'Pos(J) - Increment));
              J := Index_Type'Val(Index_Type'Pos(J) - Increment);
           end loop;
           Item(J) := Temp;
        end loop;
        if Increment = 2 then
           Increment := 1;
        else
           Increment := Increment * 5 / 11;
        end if;
     end loop;
  end Sort;

end Shell_Sort;</lang>

ALGOL 68

Translation of: python

Works with: ALGOL 68 version Standard - no extensions to language used

Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386

Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386

<lang algol68>MODE TYPE = CHAR;

PROC in place shell sort = (REF[]TYPE seq)REF[]TYPE:(

   INT inc := ( UPB seq + LWB seq + 1 ) OVER 2;
   WHILE inc NE 0 DO
       FOR index FROM LWB seq TO UPB seq DO
           INT i := index;
           TYPE el = seq[i];
           WHILE ( i  - LWB seq >= inc | seq[i - inc] > el | FALSE ) DO
               seq[i] := seq[i - inc];
               i -:= inc
           OD;
           seq[i] := el
       OD;
       inc := IF inc = 2 THEN 1 ELSE ENTIER(inc * 5 / 11) FI
   OD;
   seq

);

PROC shell sort = ([]TYPE seq)[]TYPE:

 in place shell sort(LOC[LWB seq: UPB seq]TYPE:=seq);

[]TYPE char array data = "big fjords vex quick waltz nymph"; print((shell sort(char array data), new line))</lang> Output:

     abcdefghiijklmnopqrstuvwxyz

AutoHotkey

ahk forum: discussion <lang AutoHotkey>MsgBox % ShellSort("") MsgBox % ShellSort("xxx") MsgBox % ShellSort("3,2,1") MsgBox % ShellSort("dog,000000,xx,cat,pile,abcde,1,cat,zz,xx,z") MsgBox % ShellSort("12,11,10,9,8,4,5,6,7,3,2,1,10,13,14,15,19,17,18,16,20,10")

ShellSort(var) {  ; SORT COMMA SEPARATED LIST

  StringSplit a, var, `,                ; make array (length = a0)
  inc := a0
  While inc:=round(inc/2.2)             ; geometric gap sequence
     Loop % a0-inc {                    ; insertion sort:
        i := A_Index+inc, t := a%i%, j := i, k := j-inc
        While j > inc && a%k% > t
           a%j% := a%k%, j := k, k -= inc
        a%j% := t
     }
  Loop % a0                             ; construct string from sorted array
     s .= "," . a%A_Index%
  Return SubStr(s,2)                    ; drop leading comma

}</lang>

AWK

Translation of: Fortran

<lang awk>{

 line[NR] = $0

} END { # sort it with shell sort

 increment = int(NR / 2)
 while ( increment > 0 ) {
   for(i=increment+1; i <= NR; i++) {
     j = i
     temp = line[i]
     while ( (j >= increment+1) && (line[j-increment] > temp) ) {

line[j] = line[j-increment] j -= increment

     }
     line[j] = temp
   }
   if ( increment == 2 )
     increment = 1
   else 
     increment = int(increment*5/11)
 }
 #print it
 for(i=1; i <= NR; i++) {
   print line[i]
 }

}</lang>

C

This implementation uses an array of pre-defined increments <lang c>#include <ansi_c.h>

1. define ARRAYSIZE 100000 /* or whatever */

void shellsort (int a[], int length);

int main (int argc, char *argv[]) {

 int intArray[ARRAYSIZE], i;

 for(i=0; i<ARRAYSIZE; i++)
   intArray[i] = rand();
 shellsort(intArray, ARRAYSIZE);

}

void shellsort (int a[], int length) {

 int i, j, k, temp, increment;
 static int incSequence[] = {412771, 165103, 66041, 26417, 10567,
                             4231, 1693, 673, 269, 107, 43, 17, 7, 3, 1};

 for (k = 0; k < sizeof(incSequence)/sizeof(int); k++)
 {
   if (incSequence[k]*2 > length) continue;
   increment = incSequence[k];
   for (i=increment; i < length; i++)
   {
     temp = a[i];
     for (j = i - increment; j >= 0; j -= increment)
     {
       if (a[j] <= temp) break;
       a[j + increment] = a[j];
     }
     a[j + increment] = temp;
   }
 }

}</lang>

Common Lisp

<lang lisp>(defun gap-insertion-sort (array predicate gap)

 (let ((length (length array)))
   (if (< length 2) array
     (do ((i 1 (1+ i))) ((eql i length) array)
       (do ((x (aref array i))
            (j i (- j gap)))
           ((or (< (- j gap) 0)
                (not (funcall predicate x (aref array (1- j)))))
            (setf (aref array j) x))
         (setf (aref array j) (aref array (- j gap))))))))

(defconstant +gaps+

 '(1750 701 301 132 57 23 10 4 1)
 "The best sequence of gaps, according to Marcin Ciura.")

(defun shell-sort (array predicate &optional (gaps +gaps+))

 (assert (eql 1 (car (last gaps))) (gaps)
   "Last gap of ~w is not 1." gaps)
 (dolist (gap gaps array)
   (gap-insertion-sort array predicate gap)))</lang>

D

From the Python version, uses Phobos of D 1. <lang d>import std.stdio: writefln;

void shell(T)(T[] seq) {

   int inc = seq.length / 2;
   while (inc) {
       foreach (i, el; seq) {
           while (i >= inc && seq[i - inc] > el) {
               seq[i] = seq[i - inc];
               i -= inc;
           }
           seq[i] = el;
       }
       inc = inc == 2 ? 1 : cast(int)(inc * 5.0 / 11);
   }

}

void main() {

   int[] data = [22, 7, 2, -5, 8, 4].dup;
   shell(data);
   writefln(data); // [-5, 2, 4, 7, 8, 22]

}</lang>

E

Translation of: Python

<lang e>/** Shell sort (in-place) */ def shellSort(array) {

   var inc := array.size() // 2
   while (inc.aboveZero()) {
       for var i => a in array {
           while (i >= inc && (def b := array[i - inc]) > a) {
               array[i] := b
               i -= inc
           }
           array[i] := a
       }
       inc := if (inc <=> 2) { 1 } else { (inc * 5.0 / 11).floor() }
   }

}</lang>

Forth

Works with: GNU Forth

<lang forth>defer less? ' < is less?

shell { array len -- }

 1 begin dup len u<= while 2* 1+ repeat { gap }
 begin gap 2/ dup to gap while
   len gap do
     array i cells +
     dup @ swap         ( temp last )
     begin gap cells -
           array over u<=
     while 2dup @ less?
     while dup gap cells + over @ swap !
     repeat then
     gap cells + !
   loop
 repeat ;

create array 8 , 1 , 4 , 2 , 10 , 3 , 7 , 9 , 6 , 5 ,

array 10 shell array 10 cells dump</lang>

Fortran

Works with: Fortran version 90 and later

<lang fortran>MODULE sort

CONTAINS

SUBROUTINE Shell_Sort(a)

 IMPLICIT NONE
 INTEGER :: i, j, increment
 REAL :: temp
 REAL, INTENT(in out) :: a(:)

 increment = SIZE(a) / 2
 DO WHILE (increment > 0)
     DO i = increment+1, SIZE(a)
        j = i
        temp = a(i)
        DO WHILE (j >= increment+1 .AND. a(j-increment) > temp)
           a(j) = a(j-increment)
           j = j - increment
        END DO
        a(j) = temp
     END DO
     IF (increment == 2) THEN
  	  increment = 1
     ELSE
        increment = increment * 5 / 11
     END IF      
 END DO

END SUBROUTINE Shell_Sort

END MODULE sort

PROGRAM Shellsort

USE sort

 IMPLICIT NONE
 REAL :: array(1000)
    
 CALL RANDOM_SEED
 CALL RANDOM_NUMBER(array)

 WRITE (*,*) "Unsorted array"
 WRITE (*,*) array
 WRITE (*,*) 
 CALL Shell_Sort(array)
 WRITE (*,*) "Sorted array"
 WRITE (*,*) array
 

END PROGRAM Shellsort</lang>

Haskell

Adapted version from [2]

<lang haskell>import Data.List

shellSort xs = foldr (invColumnize (map (foldr insert []))) xs gaps

 where gaps = takeWhile (< length xs) $ iterate (succ.(3*)) 1
       invColumnize f k = concat. transpose. f. transpose
                          . takeWhile (not.null). unfoldr (Just. splitAt k)</lang>

Java

Translation of: Fortran

This method will sort in place. If you want to preserve your unsorted array, use a copy of the array as an argument to this method. <lang java>public static void shell(int[] a) { int increment = a.length / 2; while (increment > 0) { for (int i = increment; i < a.length; i++) { int j = i; int temp = a[i]; while (j >= increment && a[j - increment] > temp) { a[j] = a[j - increment]; j -= increment; } a[j] = temp; } if (increment == 2) { increment = 1; } else { increment *= (5.0 / 11); } } }</lang>

Lisaac

<lang Lisaac>Section Header

+ name := SHELL_SORT;

- external := `#include <time.h>`;

Section Public

- main <- (

 + a : ARRAY[INTEGER];

 a := ARRAY[INTEGER].create 0 to 100;
 `srand(time(NULL))`;
 0.to 100 do { i : INTEGER;
   a.put `rand()`:INTEGER to i;
 };

 shell a;

 a.foreach { item : INTEGER;
   item.print;
   '\n'.print;
 };

);

- shell a : ARRAY[INTEGER] <- (

 + lower, length, increment, temp : INTEGER;

 lower := a.lower;
 length := a.upper - lower + 1;
 increment := length;
 {
   increment := increment / 2;
   increment > 0
 }.while_do {
   increment.to (length - 1) do { i : INTEGER; + j : INTEGER;
     temp := a.item(lower + i);
     j := i - increment;
     { (j >= 0) && { a.item(lower + j) > temp } }.while_do {
       a.put (a.item(lower + j)) to (lower + j + increment);
       j := j - increment;
     };
     a.put temp to (lower + j + increment);
   };
 };

);</lang>

OCaml

Translation of: C

<lang ocaml>let shellsort a =

 let len = Array.length a in
 let incSequence = [| 412771; 165103; 66041; 26417; 10567;
                      4231; 1693; 673; 269; 107; 43; 17; 7; 3; 1 |] in

 Array.iter (fun increment ->
   if (increment * 2) <= len then
     for i = increment to pred len do
       let temp = a.(i) in
       let rec loop j =
         if j < 0 || a.(j) <= temp then (j)
         else begin
           a.(j + increment) <- a.(j);
           loop (j - increment)
         end
       in
       let j = loop (i - increment) in
       a.(j + increment) <- temp;
     done;
 ) incSequence;

</lang>

and the main: <lang ocaml>let () =

 let arraysize = 1000 in  (* or whatever *)
 Random.self_init();
 let intArray =
   Array.init arraysize (fun _ -> Random.int 4000)
 in
 shellsort intArray;
 Array.iter (Printf.printf " %d") intArray;
 print_newline();

</lang>

Perl

Translation of: Java

<lang perl>use strict; use warnings; sub shell { # (int[a])

   my @iary = @_;
   my $inc = int(($#iary+1) / 2);
   while ($inc > 0) {
       foreach my $i (0 .. $#iary) {
           my $temp = $iary[$i];
           while ($i >= $inc && $iary[$i-$inc] > $temp) {
               $iary[$i] = $iary[$i-$inc];
               $i -= $inc;
           }
           $iary[$i] = $temp;
       }    
       if ($inc == 2) {
           $inc = 1;
       } else { 
          $inc *= (5.0 / 11);
          $inc = int($inc);
       }
   }
   return @iary;

} my @data = (22, 7, 2, -5, 8, 4); print "input =@data\n"; @data=shell(@data); print "output=@data\n"; # [-5, 2, 4, 7, 8, 22]</lang>

Python

Translation of: Java

This method sorts in place. If you want to preserve your unsorted list, copy it first. <lang python>def shell(seq):

   inc = len(seq) // 2
   while inc:
       for i, el in enumerate(seq):
           while i >= inc and seq[i - inc] > el:
               seq[i] = seq[i - inc]
               i -= inc
           seq[i] = el
       inc = 1 if inc == 2 else int(inc * 5.0 / 11)

data = [22, 7, 2, -5, 8, 4] shell(data) print data # [-5, 2, 4, 7, 8, 22]</lang>

Ruby

Translation of: Java

This method sorts in place. If you want to preserve your unsorted list, copy it first. <lang ruby>class Array

 def shellsort!
   inc = length / 2
   while inc != 0
     each_with_index do |el, i|
       while i >= inc and self[i - inc] > el
         self[i] = self[i - inc]
         i -= inc
       end
       self[i] = el
     end
     inc = (inc == 2 ? 1 : (inc * 5.0 / 11).to_i)
   end
 end

end

data = [22, 7, 2, -5, 8, 4] data.shellsort! p data # [-5, 2, 4, 7, 8, 22]</lang>

Tcl

<lang tcl>package require Tcl 8.5

proc shellsort {m} {

   set len [llength $m]
   set inc [expr {$len / 2}]
   while {$inc > 0} {
       for {set i $inc} {$i < $len} {incr i} {
           set j $i
           set temp [lindex $m $i]
           while {$j >= $inc && [set val [lindex $m [expr {$j - $inc}]]] > $temp} {
               lset m $j $val
               incr j -$inc
           }
           lset m $j $temp
       }
       set inc [expr {$inc == 2 ? 1 : $inc * 5 / 11}]
   }
   return $m

}

puts [shellsort {8 6 4 2 1 3 5 7 9}] ;# => 1 2 3 4 5 6 7 8 9</lang>