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 18 hours ago
Henrik Schumacher
50.7k469145
asked 21 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 18 hours ago
Henrik Schumacher
50.7k469145
asked 21 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 18 hours ago
Henrik Schumacher
50.7k469145
asked 21 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 18 hours ago
Henrik Schumacher
50.7k469145
asked 21 hours ago
Hubble07Hubble07
2,986721
edited 18 hours ago
Henrik Schumacher
50.7k469145
asked 21 hours ago
Hubble07Hubble07
2,986721
edited 18 hours ago
Henrik Schumacher
50.7k469145
edited 18 hours ago
Henrik Schumacher
50.7k469145
edited 18 hours ago
Henrik Schumacher
50.7k469145
50.7k469145
asked 21 hours ago
Hubble07Hubble07
2,986721
asked 21 hours ago
Hubble07Hubble07
2,986721
asked 21 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 21 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 21 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 19 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469145
$endgroup$
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
18 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
18 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 21 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 21 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 21 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 21 hours ago
kglrkglr
179k9199410
edited 20 hours ago
answered 21 hours ago
kglrkglr
179k9199410
answered 21 hours ago
kglrkglr
179k9199410
answered 21 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 21 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 21 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 21 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 21 hours ago
JerryJerry
1,021112
edited 20 hours ago
answered 21 hours ago
JerryJerry
1,021112
answered 21 hours ago
JerryJerry
1,021112
answered 21 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 19 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469145
$endgroup$
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
18 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
18 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 19 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469145
$endgroup$
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
18 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
18 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 19 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469145
$endgroup$
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 19 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469145
edited 18 hours ago
answered 19 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469145
answered 19 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469145
answered 19 hours ago
Henrik SchumacherHenrik Schumacher
50.7k469145
50.7k469145
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
18 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
18 hours ago
add a comment |
$begingroup$
there's a little bug withg[n_?Integer], useg[n_Integer]org[n_?IntegerQ]instead.
$endgroup$
– Jerry
18 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
18 hours ago
$begingroup$
there's a little bug with
g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.$endgroup$
– Jerry
18 hours ago
$begingroup$
there's a little bug with
g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.$endgroup$
– Jerry
18 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
18 hours ago
$begingroup$
Good point, I added the pattern after posting...
$endgroup$
– Henrik Schumacher
18 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
