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 13 hours ago
Henrik Schumacher
50.7k469144
asked 16 hours ago
Hubble07Hubble07
2,986721
$endgroup$
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 13 hours ago
Henrik Schumacher
50.7k469144
asked 16 hours ago
Hubble07Hubble07
2,986721
$endgroup$
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 13 hours ago
Henrik Schumacher
50.7k469144
asked 16 hours ago
Hubble07Hubble07
2,986721
$endgroup$
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 13 hours ago
Henrik Schumacher
50.7k469144
asked 16 hours ago
Hubble07Hubble07
2,986721
edited 13 hours ago
Henrik Schumacher
50.7k469144
asked 16 hours ago
Hubble07Hubble07
2,986721
edited 13 hours ago
Henrik Schumacher
50.7k469144
edited 13 hours ago
Henrik Schumacher
50.7k469144
edited 13 hours ago
Henrik Schumacher
50.7k469144
50.7k469144
asked 16 hours ago
Hubble07Hubble07
2,986721
asked 16 hours ago
Hubble07Hubble07
2,986721
asked 16 hours ago
Hubble07Hubble07
2,986721
2,986721
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
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 16 hours ago
kglrkglr
179k9199410
$endgroup$
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 16 hours ago
JerryJerry
1,021112
$endgroup$
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 14 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469144
$endgroup$
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
13 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
13 hours ago
add a comment |
Your Answer
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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 16 hours ago
kglrkglr
179k9199410
$endgroup$
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 16 hours ago
kglrkglr
179k9199410
$endgroup$
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 16 hours ago
kglrkglr
179k9199410
$endgroup$
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 16 hours ago
kglrkglr
179k9199410
edited 15 hours ago
answered 16 hours ago
kglrkglr
179k9199410
answered 16 hours ago
kglrkglr
179k9199410
answered 16 hours ago
kglrkglr
179k9199410
179k9199410
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 16 hours ago
JerryJerry
1,021112
$endgroup$
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 16 hours ago
JerryJerry
1,021112
$endgroup$
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 16 hours ago
JerryJerry
1,021112
$endgroup$
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 16 hours ago
JerryJerry
1,021112
edited 15 hours ago
answered 16 hours ago
JerryJerry
1,021112
answered 16 hours ago
JerryJerry
1,021112
answered 16 hours ago
JerryJerry
1,021112
1,021112
add a comment |
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 14 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469144
$endgroup$
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
13 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
13 hours ago
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 14 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469144
$endgroup$
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
13 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
13 hours ago
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 14 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469144
$endgroup$
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 14 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469144
edited 13 hours ago
answered 14 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469144
answered 14 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469144
answered 14 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469144
50.7k469144
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
13 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
13 hours ago
add a comment |
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
13 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
13 hours ago
$begingroup$
there's a little bug with
g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.$endgroup$
– Jerry
13 hours ago
$begingroup$
there's a little bug with
g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.$endgroup$
– Jerry
13 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
13 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
13 hours ago
add a comment |
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StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
