2016 Update
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Tina Müller
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7965 changed files with 139854 additions and 31002 deletions
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{{Sorting Algorithm}}
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In this task, the goal is to sort an array of elements using the [[wp:Shell sort|Shell sort]] algorithm, a diminishing increment sort.
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The Shell sort is named after its inventor, Donald Shell, who published the algorithm in 1959.
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Shellsort is a sequence of interleaved insertion sorts based on an increment sequence.
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;Task:
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Sort an array of elements using the [[wp:Shell sort|Shell sort]] algorithm, a diminishing increment sort.
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The Shell sort (also known as Shellsort or Shell's method) is named after its inventor, Donald Shell, who published the algorithm in 1959.
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Shell sort is a sequence of interleaved insertion sorts based on an increment sequence.
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The increment size is reduced after each pass until the increment size is 1.
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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".
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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.
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[http://www.cs.princeton.edu/~rs/shell/] Other good sequences are found at the [https://oeis.org/search?q=shell+sort On-Line Encyclopedia of Integer Sequences].
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Any sequence will sort the data as long as it ends in 1, but some work better than others.
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Empirical studies have shown a geometric increment sequence with a ratio of about 2.2 work well in practice.
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[http://www.cs.princeton.edu/~rs/shell/]
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Other good sequences are found at the [https://oeis.org/search?q=shell+sort On-Line Encyclopedia of Integer Sequences].
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<br><br>
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@ -0,0 +1,76 @@
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* Shell sort 24/06/2016
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SHELLSRT CSECT
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USING SHELLSRT,R13 base register
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B 72(R15) skip savearea
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DC 17F'0' savearea
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STM R14,R12,12(R13) prolog
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ST R13,4(R15) "
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ST R15,8(R13) "
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LR R13,R15 "
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L RK,N incr=n
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SRA RK,1 incr=n/2
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DO WHILE=(LTR,RK,P,RK) do while(incr>0)
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LA RI,1(RK) i=1+incr
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DO WHILE=(C,RI,LE,N) do i=1+incr to n
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LR RJ,RI j=i
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LR R1,RI i
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SLA R1,2 .
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L RT,A-4(R1) temp=a(i)
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LR R2,RK incr
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LA R2,1(R2) r2=incr+1
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LR R3,RJ j
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SR R3,RK j-incr
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SLA R3,2 *.
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LA R3,A-4(R3) r3=@a(j-incr)
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LR R4,RK incr
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SLA R4,2 r4=incr*4
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LR R5,RJ j
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SLA R5,2 .
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LA R5,A-4(R5) @a(j)
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* do while j-incr>=1 and a(j-incr)>temp
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DO WHILE=(CR,RJ,GE,R2,AND,C,RT,LT,0(R3))
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L R0,0(R3) a(j-incr)
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ST R0,0(R5) a(j)=a(j-incr)
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SR RJ,RK j=j-incr
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LR R5,R3 @a(j)
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SR R3,R4 @a(j-incr)=@a(j-incr)-incr*4
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ENDDO , end do
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ST RT,0(R5) a(j)=temp
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LA RI,1(RI) i=i+1
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ENDDO , end do
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IF C,RK,EQ,=F'2' if incr=2
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LA RK,1 incr=1
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ELSE , else
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LR R5,RK incr
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M R4,=F'5' *5
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D R4,=F'11' /11
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LR RK,R5 incr=incr*5/11
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ENDIF , end if
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ENDDO , end do
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LA R3,PG pgi=0
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LA RI,1 i=1
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DO WHILE=(C,RI,LE,N) do i=1 to n
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LR R1,RI i
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SLA R1,2 .
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L R2,A-4(R1) a(i)
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XDECO R2,XDEC edit a(i)
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MVC 0(4,R3),XDEC+8 output a(i)
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LA R3,4(R3) pgi=pgi+4
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LA RI,1(RI) i=i+1
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ENDDO , end do
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XPRNT PG,L'PG print buffer
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L R13,4(0,R13) epilog
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LM R14,R12,12(R13) "
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XR R15,R15 "
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BR R14 exit
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A DC F'4',F'65',F'2',F'-31',F'0',F'99',F'2',F'83',F'782',F'1'
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DC F'45',F'82',F'69',F'82',F'104',F'58',F'88',F'112',F'89',F'74'
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N DC A((N-A)/L'A) number of items of a
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PG DC CL80' ' buffer
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XDEC DS CL12 temp for xdeco
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YREGS
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RI EQU 6 i
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RJ EQU 7 j
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RK EQU 8 incr
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RT EQU 9 temp
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END SHELLSRT
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@ -0,0 +1,37 @@
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defmodule Sort do
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def shell_sort(list) when length(list)<=1, do: list
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def shell_sort(list), do: shell_sort(list, div(length(list),2))
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defp shell_sort(list, inc) do
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gb = Enum.with_index(list) |> Enum.group_by(fn {_,i} -> rem(i,inc) end)
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wk = Enum.map(0..inc-1, fn i ->
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Enum.map(gb[i], fn {x,_} -> x end) |> insert_sort([])
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end)
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|> merge
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if sorted?(wk), do: wk, else: shell_sort( wk, max(trunc(inc / 2.2), 1) )
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end
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defp merge(lists) do
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len = length(hd(lists))
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Enum.map(lists, fn list -> if length(list)<len, do: list++[nil], else: list end)
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|> List.zip
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|> Enum.flat_map(fn tuple -> Tuple.to_list(tuple) end)
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|> Enum.filter(&(&1)) # remove nil
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end
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defp sorted?(list) do
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Enum.chunk(list,2,1) |> Enum.all?(fn [a,b] -> a <= b end)
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end
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defp insert_sort(list), do: insert_sort(list, [])
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defp insert_sort([], sorted), do: sorted
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defp insert_sort([h | t], sorted), do: insert_sort(t, insert(h, sorted))
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defp insert(x, []), do: [x]
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defp insert(x, sorted) when x < hd(sorted), do: [x | sorted]
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defp insert(x, [h | t]), do: [h | insert(x, t)]
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end
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list = [0, 14, 11, 8, 13, 15, 5, 7, 16, 17, 1, 6, 12, 2, 10, 4, 19, 9, 18, 3]
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IO.inspect Sort.shell_sort(list)
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@ -2,7 +2,7 @@ shellSort[ lst_ ] := Module[ {list = lst, incr, temp, i, j},
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incr = Round[Length[list]/2];
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While[incr > 0,
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For[i = incr + 1, i < Length[list], i++,
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For[i = incr + 1, i <= Length[list], i++,
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temp = list[[i]]; j = i;
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@ -1,48 +1,48 @@
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/*REXX program sorts a stemmed array using the shell sort algorithm. */
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call gen /*generate the array elements. */
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call show 'before sort' /*display the before array elements. */
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say copies('▒',75) /*displat a separator line (a fence). */
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call shellSort # /*invoke the shell sort. */
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call show ' after sort' /*display the after array elements. */
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────GEN subroutine────────────────────────────*/
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gen: @.= /*assign a default value to stem array.*/
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@.1='3 character abbreviations for states of the USA' /*predates ZIP code.*/
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@.2='==============================================='
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@.3='RHO Rhode Island and Providence Plantations' ; @.36='NMX New Mexico'
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@.4='CAL California' ; @.20='NEV Nevada' ; @.37='IND Indiana'
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@.5='KAN Kansas' ; @.21='TEX Texas' ; @.38='MOE Missouri'
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@.6='MAS Massachusetts' ; @.22='VGI Virginia' ; @.39='COL Colorado'
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@.7='WAS Washington' ; @.23='OHI Ohio' ; @.40='CON Connecticut'
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@.8='HAW Hawaii' ; @.24='NHM New Hampshire'; @.41='MON Montana'
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@.9='NCR North Carolina'; @.25='MAE Maine' ; @.42='LOU Louisiana'
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@.10='SCR South Carolina'; @.26='MIC Michigan' ; @.43='IOW Iowa'
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@.11='IDA Idaho' ; @.27='MIN Minnesota' ; @.44='ORE Oregon'
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@.12='NDK North Dakota' ; @.28='MIS Mississippi' ; @.45='ARK Arkansas'
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@.13='SDK South Dakota' ; @.29='WIS Wisconsin' ; @.46='ARZ Arizona'
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@.14='NEB Nebraska' ; @.30='OKA Oklahoma' ; @.47='UTH Utah'
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@.15='DEL Delaware' ; @.31='ALA Alabama' ; @.48='KTY Kentucky'
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@.16='PEN Pennsylvania' ; @.32='FLA Florida' ; @.49='WVG West Virginia'
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@.17='TEN Tennessee' ; @.33='MLD Maryland' ; @.50='NWJ New Jersey'
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@.18='GEO Georgia' ; @.34='ALK Alaska' ; @.51='NYK New York'
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@.19='VER Vermont' ; @.35='ILL Illinois' ; @.52='WYO Wyoming'
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do #=1 while @.#\==''; end; #=#-1 /*determine number of entries in array.*/
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return
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/*──────────────────────────────────SHELLSORT subroutine──────────────────────*/
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shellSort: procedure expose @.; parse arg N
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i=N%2 /*% is integer division in REXX. */
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do while i\==0
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do j=i+1 to N; k=j; p=k-i /*P: previous item*/
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_=@.j
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do while k>=i+1 & @.p>_; @.k=@.p
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k=k-i; p=k-i
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end /*while k≥i+1*/
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@.k=_
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end /*j*/
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/*REXX program sorts a stemmed array using the shell sort (shellsort) algorithm. */
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call gen /*generate the array elements. */
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call show 'before sort' /*display the before array elements. */
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say copies('▒', 75) /*displat a separator line (a fence). */
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call shellSort # /*invoke the shell sort. */
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call show ' after sort' /*display the after array elements. */
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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gen: @.= /*assign a default value to stem array.*/
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@.1='3 character abbreviations for states of the USA' /*predates ZIP code.*/
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@.2='==============================================='
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@.3='RHO Rhode Island and Providence Plantations' ; @.36='NMX New Mexico'
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@.4='CAL California' ; @.20='NEV Nevada' ; @.37='IND Indiana'
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@.5='KAN Kansas' ; @.21='TEX Texas' ; @.38='MOE Missouri'
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@.6='MAS Massachusetts' ; @.22='VGI Virginia' ; @.39='COL Colorado'
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@.7='WAS Washington' ; @.23='OHI Ohio' ; @.40='CON Connecticut'
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@.8='HAW Hawaii' ; @.24='NHM New Hampshire'; @.41='MON Montana'
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@.9='NCR North Carolina'; @.25='MAE Maine' ; @.42='LOU Louisiana'
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@.10='SCR South Carolina'; @.26='MIC Michigan' ; @.43='IOW Iowa'
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@.11='IDA Idaho' ; @.27='MIN Minnesota' ; @.44='ORE Oregon'
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@.12='NDK North Dakota' ; @.28='MIS Mississippi' ; @.45='ARK Arkansas'
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@.13='SDK South Dakota' ; @.29='WIS Wisconsin' ; @.46='ARZ Arizona'
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@.14='NEB Nebraska' ; @.30='OKA Oklahoma' ; @.47='UTH Utah'
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@.15='DEL Delaware' ; @.31='ALA Alabama' ; @.48='KTY Kentucky'
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@.16='PEN Pennsylvania' ; @.32='FLA Florida' ; @.49='WVG West Virginia'
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@.17='TEN Tennessee' ; @.33='MLD Maryland' ; @.50='NWJ New Jersey'
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@.18='GEO Georgia' ; @.34='ALK Alaska' ; @.51='NYK New York'
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@.19='VER Vermont' ; @.35='ILL Illinois' ; @.52='WYO Wyoming'
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do #=1 while @.#\==''; end; #=#-1 /*determine number of entries in array.*/
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return
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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shellSort: procedure expose @.; parse arg N /*obtain the N from the argument list*/
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i=N%2 /*% is integer division in REXX. */
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do while i\==0
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do j=i+1 to N; k=j; p=k-i /*P: previous item*/
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_=@.j
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do while k>=i+1 & @.p>_; @.k=@.p
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k=k-i; p=k-i
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end /*while k≥i+1*/
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@.k=_
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end /*j*/
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if i==2 then i=1
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else i=i*5%11
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end /*while i¬==0*/
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return
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/*──────────────────────────────────SHOW subroutine───────-───────────────────*/
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show: do j=1 for #; say 'element' right(j,length(#)) arg(1)': ' @.j; end; return
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if i==2 then i=1
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else i=i*5 % 11
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end /*while i¬==0*/
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return
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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show: do j=1 for #; say 'element' right(j,length(#)) arg(1)": " @.j; end; return
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