Generate this sequence more efficiently

Multi tool use
Multi tool use












4












$begingroup$


Is there a more effecient way to generate the sequence shown below.



createOrder[n_] := 

Which[OddQ[n],

    Join[Table[2 i - 1, {i, 1, (n + 1)/2}],Reverse@Table[2 i, {i, 1, (n + 1)/2}]], 

    EvenQ[n],

    Join[Table[2 i - 1, {i, 1, n/2 + 1}],Reverse@Table[2 i, {i, 1, n/2}]]]





createOrder[#] & /@ Range[8] // MatrixForm


table






list-manipulation table sequence







share|improve this question











$endgroup$

















    4












    $begingroup$


    Is there a more effecient way to generate the sequence shown below.



    createOrder[n_] := 
    
Which[OddQ[n],
    
    Join[Table[2 i - 1, {i, 1, (n + 1)/2}],Reverse@Table[2 i, {i, 1, (n + 1)/2}]], 
    
    EvenQ[n],
    
    Join[Table[2 i - 1, {i, 1, n/2 + 1}],Reverse@Table[2 i, {i, 1, n/2}]]]
    

    

    
createOrder[#] & /@ Range[8] // MatrixForm


    table






    list-manipulation table sequence







    share|improve this question











    $endgroup$















      4












      4








      4





      $begingroup$


      Is there a more effecient way to generate the sequence shown below.



      createOrder[n_] := 
      
Which[OddQ[n],
      
    Join[Table[2 i - 1, {i, 1, (n + 1)/2}],Reverse@Table[2 i, {i, 1, (n + 1)/2}]], 
      
    EvenQ[n],
      
    Join[Table[2 i - 1, {i, 1, n/2 + 1}],Reverse@Table[2 i, {i, 1, n/2}]]]
      

      

      
createOrder[#] & /@ Range[8] // MatrixForm


      table






      list-manipulation table sequence







      share|improve this question











      $endgroup$




      Is there a more effecient way to generate the sequence shown below.



      createOrder[n_] := 
      
Which[OddQ[n],
      
    Join[Table[2 i - 1, {i, 1, (n + 1)/2}],Reverse@Table[2 i, {i, 1, (n + 1)/2}]], 
      
    EvenQ[n],
      
    Join[Table[2 i - 1, {i, 1, n/2 + 1}],Reverse@Table[2 i, {i, 1, n/2}]]]
      

      

      
createOrder[#] & /@ Range[8] // MatrixForm


      table






      list-manipulation table sequence




      list-manipulation table sequence






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 7 hours ago









      Henrik Schumacher

      50.6k469144




      50.6k469144










      asked 10 hours ago









      Hubble07Hubble07

      2,986721




      2,986721






















          3 Answers
          3






          active

          oldest

          votes


















          6












          $begingroup$

          ClearAll[f]
          
f[n_Integer] := Join[Range[1, #, 2], Reverse[Range[2, #, 2]]] & /@ Range[2, n];
          
TeXForm @ MatrixForm @ f[8]



          $left(
          begin{array}{c}
          {1,2} \
          {1,3,2} \
          {1,3,4,2} \
          {1,3,5,4,2} \
          {1,3,5,6,4,2} \
          {1,3,5,7,6,4,2} \
          {1,3,5,7,8,6,4,2} \
          end{array}
          right)$




          Also



          ClearAll[f2, f3]
          
f2[n_Integer] := SortBy[Range@#, {EvenQ, -# (-1 )^Mod[#, 2] &}] & /@ Range[2, n]
          
f3[n_] := Ordering[Transpose[{-Mod[#, 2], -# (-1 )^Mod[#, 2]} &@Range[#]]] & /@ Range[2, n]
          

          
f[8] == f2[8] == f3[8]



          True







          share|improve this answer











          $endgroup$





















            5












            $begingroup$

               fGetList[n_]:= (Select[Range[#], OddQ]~Join~Reverse@Select[Range[#], EvenQ]) & /@Range[n] // Rest
            

            
   fGetList[10] // MatrixForm // TeXForm


            $
            left(
            begin{array}{c}
            {1,2} \
            {1,3,2} \
            {1,3,4,2} \
            {1,3,5,4,2} \
            {1,3,5,6,4,2} \
            {1,3,5,7,6,4,2} \
            {1,3,5,7,8,6,4,2} \
            {1,3,5,7,9,8,6,4,2} \
            {1,3,5,7,9,10,8,6,4,2} \
            end{array}
            right)$



            another version



            fGetList2[n_?IntegerQ] := 
            
 Flatten@MapAt[Reverse, GatherBy[Range[#], OddQ], 2] & /@ Range[2, n]
            

            
fGetList2[10] // MatrixForm // TeXForm


            $left(
            begin{array}{c}
            {1,2} \
            {1,3,2} \
            {1,3,4,2} \
            {1,3,5,4,2} \
            {1,3,5,6,4,2} \
            {1,3,5,7,6,4,2} \
            {1,3,5,7,8,6,4,2} \
            {1,3,5,7,9,8,6,4,2} \
            {1,3,5,7,9,10,8,6,4,2} \
            end{array}
            right)$






            share|improve this answer











            $endgroup$





















              3












              $begingroup$

              cg = Compile[{{a, _Integer, 1}, {b, _Integer, 1}, {i, _Integer}},
              
   Join[a[[1 ;; Quotient[i + 1, 2]]], b[[-Quotient[i, 2] ;; -1]]],
              
   CompilationTarget -> "WVM",
              
   RuntimeAttributes -> {Listable},
              
   Parallelization -> True
              
   ];
              
g[n_Integer] := cg[Range[1, n + 1, 2], Range[n + Mod[n, 2], 2, -2], Range[2, n + 1]];





              share|improve this answer











              $endgroup$













              • $begingroup$
                there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                $endgroup$
                – Jerry
                7 hours ago












              • $begingroup$
                Good point, I added the pattern after posting...
                $endgroup$
                – Henrik Schumacher
                7 hours ago











              Your Answer





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              3 Answers
              3






              active

              oldest

              votes








              3 Answers
              3






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              6












              $begingroup$

              ClearAll[f]
              
f[n_Integer] := Join[Range[1, #, 2], Reverse[Range[2, #, 2]]] & /@ Range[2, n];
              
TeXForm @ MatrixForm @ f[8]



              $left(
              begin{array}{c}
              {1,2} \
              {1,3,2} \
              {1,3,4,2} \
              {1,3,5,4,2} \
              {1,3,5,6,4,2} \
              {1,3,5,7,6,4,2} \
              {1,3,5,7,8,6,4,2} \
              end{array}
              right)$




              Also



              ClearAll[f2, f3]
              
f2[n_Integer] := SortBy[Range@#, {EvenQ, -# (-1 )^Mod[#, 2] &}] & /@ Range[2, n]
              
f3[n_] := Ordering[Transpose[{-Mod[#, 2], -# (-1 )^Mod[#, 2]} &@Range[#]]] & /@ Range[2, n]
              

              
f[8] == f2[8] == f3[8]



              True







              share|improve this answer











              $endgroup$


















                6












                $begingroup$

                ClearAll[f]
                
f[n_Integer] := Join[Range[1, #, 2], Reverse[Range[2, #, 2]]] & /@ Range[2, n];
                
TeXForm @ MatrixForm @ f[8]



                $left(
                begin{array}{c}
                {1,2} \
                {1,3,2} \
                {1,3,4,2} \
                {1,3,5,4,2} \
                {1,3,5,6,4,2} \
                {1,3,5,7,6,4,2} \
                {1,3,5,7,8,6,4,2} \
                end{array}
                right)$




                Also



                ClearAll[f2, f3]
                
f2[n_Integer] := SortBy[Range@#, {EvenQ, -# (-1 )^Mod[#, 2] &}] & /@ Range[2, n]
                
f3[n_] := Ordering[Transpose[{-Mod[#, 2], -# (-1 )^Mod[#, 2]} &@Range[#]]] & /@ Range[2, n]
                

                
f[8] == f2[8] == f3[8]



                True







                share|improve this answer











                $endgroup$
















                  6












                  6








                  6





                  $begingroup$

                  ClearAll[f]
                  
f[n_Integer] := Join[Range[1, #, 2], Reverse[Range[2, #, 2]]] & /@ Range[2, n];
                  
TeXForm @ MatrixForm @ f[8]



                  $left(
                  begin{array}{c}
                  {1,2} \
                  {1,3,2} \
                  {1,3,4,2} \
                  {1,3,5,4,2} \
                  {1,3,5,6,4,2} \
                  {1,3,5,7,6,4,2} \
                  {1,3,5,7,8,6,4,2} \
                  end{array}
                  right)$




                  Also



                  ClearAll[f2, f3]
                  
f2[n_Integer] := SortBy[Range@#, {EvenQ, -# (-1 )^Mod[#, 2] &}] & /@ Range[2, n]
                  
f3[n_] := Ordering[Transpose[{-Mod[#, 2], -# (-1 )^Mod[#, 2]} &@Range[#]]] & /@ Range[2, n]
                  

                  
f[8] == f2[8] == f3[8]



                  True







                  share|improve this answer











                  $endgroup$



                  ClearAll[f]
                  
f[n_Integer] := Join[Range[1, #, 2], Reverse[Range[2, #, 2]]] & /@ Range[2, n];
                  
TeXForm @ MatrixForm @ f[8]



                  $left(
                  begin{array}{c}
                  {1,2} \
                  {1,3,2} \
                  {1,3,4,2} \
                  {1,3,5,4,2} \
                  {1,3,5,6,4,2} \
                  {1,3,5,7,6,4,2} \
                  {1,3,5,7,8,6,4,2} \
                  end{array}
                  right)$




                  Also



                  ClearAll[f2, f3]
                  
f2[n_Integer] := SortBy[Range@#, {EvenQ, -# (-1 )^Mod[#, 2] &}] & /@ Range[2, n]
                  
f3[n_] := Ordering[Transpose[{-Mod[#, 2], -# (-1 )^Mod[#, 2]} &@Range[#]]] & /@ Range[2, n]
                  

                  
f[8] == f2[8] == f3[8]



                  True








                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 9 hours ago

























                  answered 10 hours ago









                  kglrkglr

                  179k9199410




                  179k9199410























                      5












                      $begingroup$

                         fGetList[n_]:= (Select[Range[#], OddQ]~Join~Reverse@Select[Range[#], EvenQ]) & /@Range[n] // Rest
                      

                      
   fGetList[10] // MatrixForm // TeXForm


                      $
                      left(
                      begin{array}{c}
                      {1,2} \
                      {1,3,2} \
                      {1,3,4,2} \
                      {1,3,5,4,2} \
                      {1,3,5,6,4,2} \
                      {1,3,5,7,6,4,2} \
                      {1,3,5,7,8,6,4,2} \
                      {1,3,5,7,9,8,6,4,2} \
                      {1,3,5,7,9,10,8,6,4,2} \
                      end{array}
                      right)$



                      another version



                      fGetList2[n_?IntegerQ] := 
                      
 Flatten@MapAt[Reverse, GatherBy[Range[#], OddQ], 2] & /@ Range[2, n]
                      

                      
fGetList2[10] // MatrixForm // TeXForm


                      $left(
                      begin{array}{c}
                      {1,2} \
                      {1,3,2} \
                      {1,3,4,2} \
                      {1,3,5,4,2} \
                      {1,3,5,6,4,2} \
                      {1,3,5,7,6,4,2} \
                      {1,3,5,7,8,6,4,2} \
                      {1,3,5,7,9,8,6,4,2} \
                      {1,3,5,7,9,10,8,6,4,2} \
                      end{array}
                      right)$






                      share|improve this answer











                      $endgroup$


















                        5












                        $begingroup$

                           fGetList[n_]:= (Select[Range[#], OddQ]~Join~Reverse@Select[Range[#], EvenQ]) & /@Range[n] // Rest
                        

                        
   fGetList[10] // MatrixForm // TeXForm


                        $
                        left(
                        begin{array}{c}
                        {1,2} \
                        {1,3,2} \
                        {1,3,4,2} \
                        {1,3,5,4,2} \
                        {1,3,5,6,4,2} \
                        {1,3,5,7,6,4,2} \
                        {1,3,5,7,8,6,4,2} \
                        {1,3,5,7,9,8,6,4,2} \
                        {1,3,5,7,9,10,8,6,4,2} \
                        end{array}
                        right)$



                        another version



                        fGetList2[n_?IntegerQ] := 
                        
 Flatten@MapAt[Reverse, GatherBy[Range[#], OddQ], 2] & /@ Range[2, n]
                        

                        
fGetList2[10] // MatrixForm // TeXForm


                        $left(
                        begin{array}{c}
                        {1,2} \
                        {1,3,2} \
                        {1,3,4,2} \
                        {1,3,5,4,2} \
                        {1,3,5,6,4,2} \
                        {1,3,5,7,6,4,2} \
                        {1,3,5,7,8,6,4,2} \
                        {1,3,5,7,9,8,6,4,2} \
                        {1,3,5,7,9,10,8,6,4,2} \
                        end{array}
                        right)$






                        share|improve this answer











                        $endgroup$
















                          5












                          5








                          5





                          $begingroup$

                             fGetList[n_]:= (Select[Range[#], OddQ]~Join~Reverse@Select[Range[#], EvenQ]) & /@Range[n] // Rest
                          

                          
   fGetList[10] // MatrixForm // TeXForm


                          $
                          left(
                          begin{array}{c}
                          {1,2} \
                          {1,3,2} \
                          {1,3,4,2} \
                          {1,3,5,4,2} \
                          {1,3,5,6,4,2} \
                          {1,3,5,7,6,4,2} \
                          {1,3,5,7,8,6,4,2} \
                          {1,3,5,7,9,8,6,4,2} \
                          {1,3,5,7,9,10,8,6,4,2} \
                          end{array}
                          right)$



                          another version



                          fGetList2[n_?IntegerQ] := 
                          
 Flatten@MapAt[Reverse, GatherBy[Range[#], OddQ], 2] & /@ Range[2, n]
                          

                          
fGetList2[10] // MatrixForm // TeXForm


                          $left(
                          begin{array}{c}
                          {1,2} \
                          {1,3,2} \
                          {1,3,4,2} \
                          {1,3,5,4,2} \
                          {1,3,5,6,4,2} \
                          {1,3,5,7,6,4,2} \
                          {1,3,5,7,8,6,4,2} \
                          {1,3,5,7,9,8,6,4,2} \
                          {1,3,5,7,9,10,8,6,4,2} \
                          end{array}
                          right)$






                          share|improve this answer











                          $endgroup$



                             fGetList[n_]:= (Select[Range[#], OddQ]~Join~Reverse@Select[Range[#], EvenQ]) & /@Range[n] // Rest
                          

                          
   fGetList[10] // MatrixForm // TeXForm


                          $
                          left(
                          begin{array}{c}
                          {1,2} \
                          {1,3,2} \
                          {1,3,4,2} \
                          {1,3,5,4,2} \
                          {1,3,5,6,4,2} \
                          {1,3,5,7,6,4,2} \
                          {1,3,5,7,8,6,4,2} \
                          {1,3,5,7,9,8,6,4,2} \
                          {1,3,5,7,9,10,8,6,4,2} \
                          end{array}
                          right)$



                          another version



                          fGetList2[n_?IntegerQ] := 
                          
 Flatten@MapAt[Reverse, GatherBy[Range[#], OddQ], 2] & /@ Range[2, n]
                          

                          
fGetList2[10] // MatrixForm // TeXForm


                          $left(
                          begin{array}{c}
                          {1,2} \
                          {1,3,2} \
                          {1,3,4,2} \
                          {1,3,5,4,2} \
                          {1,3,5,6,4,2} \
                          {1,3,5,7,6,4,2} \
                          {1,3,5,7,8,6,4,2} \
                          {1,3,5,7,9,8,6,4,2} \
                          {1,3,5,7,9,10,8,6,4,2} \
                          end{array}
                          right)$







                          share|improve this answer














                          share|improve this answer



                          share|improve this answer








                          edited 9 hours ago

























                          answered 10 hours ago









                          JerryJerry

                          999112




                          999112























                              3












                              $begingroup$

                              cg = Compile[{{a, _Integer, 1}, {b, _Integer, 1}, {i, _Integer}},
                              
   Join[a[[1 ;; Quotient[i + 1, 2]]], b[[-Quotient[i, 2] ;; -1]]],
                              
   CompilationTarget -> "WVM",
                              
   RuntimeAttributes -> {Listable},
                              
   Parallelization -> True
                              
   ];
                              
g[n_Integer] := cg[Range[1, n + 1, 2], Range[n + Mod[n, 2], 2, -2], Range[2, n + 1]];





                              share|improve this answer











                              $endgroup$













                              • $begingroup$
                                there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                                $endgroup$
                                – Jerry
                                7 hours ago












                              • $begingroup$
                                Good point, I added the pattern after posting...
                                $endgroup$
                                – Henrik Schumacher
                                7 hours ago
















                              3












                              $begingroup$

                              cg = Compile[{{a, _Integer, 1}, {b, _Integer, 1}, {i, _Integer}},
                              
   Join[a[[1 ;; Quotient[i + 1, 2]]], b[[-Quotient[i, 2] ;; -1]]],
                              
   CompilationTarget -> "WVM",
                              
   RuntimeAttributes -> {Listable},
                              
   Parallelization -> True
                              
   ];
                              
g[n_Integer] := cg[Range[1, n + 1, 2], Range[n + Mod[n, 2], 2, -2], Range[2, n + 1]];





                              share|improve this answer











                              $endgroup$













                              • $begingroup$
                                there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                                $endgroup$
                                – Jerry
                                7 hours ago












                              • $begingroup$
                                Good point, I added the pattern after posting...
                                $endgroup$
                                – Henrik Schumacher
                                7 hours ago














                              3












                              3








                              3





                              $begingroup$

                              cg = Compile[{{a, _Integer, 1}, {b, _Integer, 1}, {i, _Integer}},
                              
   Join[a[[1 ;; Quotient[i + 1, 2]]], b[[-Quotient[i, 2] ;; -1]]],
                              
   CompilationTarget -> "WVM",
                              
   RuntimeAttributes -> {Listable},
                              
   Parallelization -> True
                              
   ];
                              
g[n_Integer] := cg[Range[1, n + 1, 2], Range[n + Mod[n, 2], 2, -2], Range[2, n + 1]];





                              share|improve this answer











                              $endgroup$



                              cg = Compile[{{a, _Integer, 1}, {b, _Integer, 1}, {i, _Integer}},
                              
   Join[a[[1 ;; Quotient[i + 1, 2]]], b[[-Quotient[i, 2] ;; -1]]],
                              
   CompilationTarget -> "WVM",
                              
   RuntimeAttributes -> {Listable},
                              
   Parallelization -> True
                              
   ];
                              
g[n_Integer] := cg[Range[1, n + 1, 2], Range[n + Mod[n, 2], 2, -2], Range[2, n + 1]];






                              share|improve this answer














                              share|improve this answer



                              share|improve this answer








                              edited 7 hours ago

























                              answered 8 hours ago









                              Henrik SchumacherHenrik Schumacher

                              50.6k469144




                              50.6k469144












                              • $begingroup$
                                there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                                $endgroup$
                                – Jerry
                                7 hours ago












                              • $begingroup$
                                Good point, I added the pattern after posting...
                                $endgroup$
                                – Henrik Schumacher
                                7 hours ago


















                              • $begingroup$
                                there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                                $endgroup$
                                – Jerry
                                7 hours ago












                              • $begingroup$
                                Good point, I added the pattern after posting...
                                $endgroup$
                                – Henrik Schumacher
                                7 hours ago
















                              $begingroup$
                              there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                              $endgroup$
                              – Jerry
                              7 hours ago






                              $begingroup$
                              there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                              $endgroup$
                              – Jerry
                              7 hours ago














                              $begingroup$
                              Good point, I added the pattern after posting...
                              $endgroup$
                              – Henrik Schumacher
                              7 hours ago




                              $begingroup$
                              Good point, I added the pattern after posting...
                              $endgroup$
                              – Henrik Schumacher
                              7 hours ago


















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