Concise way to do lexicographic ordering

Question

I want to order a bunch of number sequences lexicographically. Did this with

lexo[x_, y_] := x == {} || 
    y != {} && (First[x] < First[y] || First[x] == First[y] && lexo[Rest[x], Rest[y]])
Sort[mysequences, lexo]

and it works, but it is presumably not very efficient, because of recursive self-calls.

There is also a version in one of the answers here which might be better. But maybe Mathematica has something built in for that?

I suspect this since there turns out to be something called Lexicographic for which I could not find any documentation. Also, Combinatorica has things like LexicographicSubsets and LexicographicPermutations except that I want something more general, working for any sequences of numbers.

(1) Lexicographic is an option value for the MonomialOrder option in GroebnerBasis. Nowadays it would be a string but at the time this was designed we really didn't do option settings that way. (2) Coincidently, implementing a LexicographicOrder for usage in Sort and related is on my immediate to-do list. — Daniel Lichtblau, Mar 17 '21 at 13:17
@kglr Tried it on Subsets[Range[3]], throws an error message because of the empty set, and sorts like this {{1},{1,2},{1,3},{1,2,3},{2},{2,3},{3},{}} which is not quite lexicographic: {1,2,3} must go before {1,3} — მამუკა ჯიბლაძე, Mar 17 '21 at 23:10
maybe SortBy[x \[Function] PadRight[x, Max[Length /@ #]]]@# &@ Subsets[Range@3]? — kglr, Mar 17 '21 at 23:22
... or (x \[Function] SortBy[x, PadRight[#, Max[Length /@ x]] &])@ Subsets[Range@3]? — kglr, Mar 17 '21 at 23:26
@kglr Thank you, these both seem to work correctly. Could you make an answer please? — მამუკა ჯიბლაძე, Mar 18 '21 at 05:13
მამუკაჯიბლაძე, posted the comments as an answer. — kglr, Mar 18 '21 at 05:27

score 2 · Accepted Answer · answered Mar 18 '21 at 05:27

ClearAll[lexSort1, lexSort2]

lexSort1 = SortBy[x \[Function] PadRight[x, Max[Length /@ #]]]@# &;

lexSort2 = Function[x, SortBy[x, PadRight[#, Max[Length /@ x]] &]];

Examples:

lexSort1 @ Subsets[Range@3]

 {{}, {1}, {1, 2}, {1, 2, 3}, {1, 3}, {2}, {2, 3}, {3}}

lexSort2 @ Subsets[Range@3]

 {{}, {1}, {1, 2}, {1, 2, 3}, {1, 3}, {2}, {2, 3}, {3}}

Concise way to do lexicographic ordering

1 Answers1