Generate this sequence more efficiently
$begingroup$
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
list-manipulation table sequence
edited Jan 18 at 10:11
Henrik Schumacher
52.6k471148
asked Jan 18 at 7:09
Hubble07Hubble07
2,988721
$endgroup$
add a comment |
$begingroup$
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
list-manipulation table sequence
edited Jan 18 at 10:11
Henrik Schumacher
52.6k471148
asked Jan 18 at 7:09
Hubble07Hubble07
2,988721
$endgroup$
add a comment |
$begingroup$
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
list-manipulation table sequence
edited Jan 18 at 10:11
Henrik Schumacher
52.6k471148
asked Jan 18 at 7:09
Hubble07Hubble07
2,988721
$endgroup$
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
list-manipulation table sequence
list-manipulation table sequence
edited Jan 18 at 10:11
Henrik Schumacher
52.6k471148
asked Jan 18 at 7:09
Hubble07Hubble07
2,988721
edited Jan 18 at 10:11
Henrik Schumacher
52.6k471148
asked Jan 18 at 7:09
Hubble07Hubble07
2,988721
edited Jan 18 at 10:11
Henrik Schumacher
52.6k471148
edited Jan 18 at 10:11
Henrik Schumacher
52.6k471148
edited Jan 18 at 10:11
Henrik Schumacher
52.6k471148
52.6k471148
asked Jan 18 at 7:09
Hubble07Hubble07
2,988721
asked Jan 18 at 7:09
Hubble07Hubble07
2,988721
asked Jan 18 at 7:09
Hubble07Hubble07
2,988721
2,988721
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
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]];
answered Jan 18 at 9:28
Henrik SchumacherHenrik Schumacher
52.6k471148
$endgroup$
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
Jan 18 at 10:01
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
Jan 18 at 10:10
add a comment |
$begingroup$
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
answered Jan 18 at 7:35
kglrkglr
182k10200415
$endgroup$
add a comment |
$begingroup$
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
$left(
begin{array}{c}
{1,2} \
{1,3,2} \
{1,3,4,2} \
{1,3,5,4,2} \
{1,3,5,6,4,2} \
{1,3,5,7,6,4,2} \
{1,3,5,7,8,6,4,2} \
{1,3,5,7,9,8,6,4,2} \
{1,3,5,7,9,10,8,6,4,2} \
end{array}
right)$
answered Jan 18 at 7:35
JerryJerry
1,385212
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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]];
answered Jan 18 at 9:28
Henrik SchumacherHenrik Schumacher
52.6k471148
$endgroup$
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
Jan 18 at 10:01
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
Jan 18 at 10:10
add a comment |
$begingroup$
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]];
answered Jan 18 at 9:28
Henrik SchumacherHenrik Schumacher
52.6k471148
$endgroup$
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
Jan 18 at 10:01
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
Jan 18 at 10:10
add a comment |
$begingroup$
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]];
answered Jan 18 at 9:28
Henrik SchumacherHenrik Schumacher
52.6k471148
$endgroup$
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]];
answered Jan 18 at 9:28
Henrik SchumacherHenrik Schumacher
52.6k471148
edited Jan 18 at 10:10
answered Jan 18 at 9:28
Henrik SchumacherHenrik Schumacher
52.6k471148
answered Jan 18 at 9:28
Henrik SchumacherHenrik Schumacher
52.6k471148
answered Jan 18 at 9:28
Henrik SchumacherHenrik Schumacher
52.6k471148
52.6k471148
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
Jan 18 at 10:01
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
Jan 18 at 10:10
add a comment |
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
Jan 18 at 10:01
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
Jan 18 at 10:10
$begingroup$
there's a little bug with
g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.$endgroup$
– Jerry
Jan 18 at 10:01
$begingroup$
there's a little bug with
g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.$endgroup$
– Jerry
Jan 18 at 10:01
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
Jan 18 at 10:10
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
Jan 18 at 10:10
add a comment |
$begingroup$
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
answered Jan 18 at 7:35
kglrkglr
182k10200415
$endgroup$
add a comment |
$begingroup$
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
answered Jan 18 at 7:35
kglrkglr
182k10200415
$endgroup$
add a comment |
$begingroup$
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
answered Jan 18 at 7:35
kglrkglr
182k10200415
$endgroup$
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
answered Jan 18 at 7:35
kglrkglr
182k10200415
edited Jan 18 at 8:27
answered Jan 18 at 7:35
kglrkglr
182k10200415
answered Jan 18 at 7:35
kglrkglr
182k10200415
answered Jan 18 at 7:35
kglrkglr
182k10200415
182k10200415
add a comment |
add a comment |
$begingroup$
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
$left(
begin{array}{c}
{1,2} \
{1,3,2} \
{1,3,4,2} \
{1,3,5,4,2} \
{1,3,5,6,4,2} \
{1,3,5,7,6,4,2} \
{1,3,5,7,8,6,4,2} \
{1,3,5,7,9,8,6,4,2} \
{1,3,5,7,9,10,8,6,4,2} \
end{array}
right)$
answered Jan 18 at 7:35
JerryJerry
1,385212
$endgroup$
add a comment |
$begingroup$
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
$left(
begin{array}{c}
{1,2} \
{1,3,2} \
{1,3,4,2} \
{1,3,5,4,2} \
{1,3,5,6,4,2} \
{1,3,5,7,6,4,2} \
{1,3,5,7,8,6,4,2} \
{1,3,5,7,9,8,6,4,2} \
{1,3,5,7,9,10,8,6,4,2} \
end{array}
right)$
answered Jan 18 at 7:35
JerryJerry
1,385212
$endgroup$
add a comment |
$begingroup$
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
$left(
begin{array}{c}
{1,2} \
{1,3,2} \
{1,3,4,2} \
{1,3,5,4,2} \
{1,3,5,6,4,2} \
{1,3,5,7,6,4,2} \
{1,3,5,7,8,6,4,2} \
{1,3,5,7,9,8,6,4,2} \
{1,3,5,7,9,10,8,6,4,2} \
end{array}
right)$
answered Jan 18 at 7:35
JerryJerry
1,385212
$endgroup$
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
$left(
begin{array}{c}
{1,2} \
{1,3,2} \
{1,3,4,2} \
{1,3,5,4,2} \
{1,3,5,6,4,2} \
{1,3,5,7,6,4,2} \
{1,3,5,7,8,6,4,2} \
{1,3,5,7,9,8,6,4,2} \
{1,3,5,7,9,10,8,6,4,2} \
end{array}
right)$
answered Jan 18 at 7:35
JerryJerry
1,385212
edited Jan 18 at 7:54
answered Jan 18 at 7:35
JerryJerry
1,385212
answered Jan 18 at 7:35
JerryJerry
1,385212
answered Jan 18 at 7:35
JerryJerry
1,385212
1,385212
add a comment |
add a comment |
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