lexorder
test for lexicographical order
Calling Sequence
Parameters
Description
Thread Safety
Examples
lexorder(s1, s2)
s1, s2
-
strings or unevaluated symbols
The procedure lexorder returns true if s1 occurs before s2 in lexicographical order, or if s1 is equal to s2. Otherwise, it returns false.
The lexicographical order depends in part on the ordering of the underlying character set, which is system-dependent.
For strings and symbols consisting of ordinary letters, lexicographical order is the standard alphabetical order.
The most common use of lexorder is as the second (optional) argument to the sort command. This allows you to sort a list of strings (or symbols) lexicographically. Note, however, that it is the symbol lexorder rather than the lexorder procedure that should be used as an option to sort. Both will work, with identical results, but the symbol lexorder is recognized by sort, causing it to use a builtin algorithm that is faster than the one that calls the lexorder procedure. (See the example below.)
The lexorder command is thread-safe as of Maple 15.
For more information on thread safety, see index/threadsafe.
lexorder⁡a,b
true
lexorder⁡A,a
lexorder⁡ a,a
lexorder⁡greatest,great
false
lexorder⁡`*`,`^`
lexorder⁡first,second
sort⁡first,second,third,fourth,fifth,lexorder
fifth,first,fourth,second,third
Calling the builtin procedure lexorder() directly is slower than using the 'lexorder' algorithm that is built in to sort().
L≔seq⁡StringTools:-Random⁡1000,alnum,i=1..10000:
time⁡sort⁡L,lexorder
0.003
time⁡sort⁡L,eval⁡lexorder
0.121
Reversing the sense of the comparison is more costly still, because a full Maple procedure call is incurred for each comparison.
time⁡sort⁡L,a,b↦lexorder⁡b,a
0.169
A better way to do this is to use a linear reversal algorithm after sorting the list with the builtin algorithm. Since sorting dominates at O(n*ln(n)), using the sorting algorithm with the smaller constant factor delivers better performance.
revsort := proc( los::list(string) )::list(string); local L; L := sort( los, 'lexorder' ); [ seq( L[ -i ], i = 1 .. nops( L ) ) ] end proc:
time⁡revsort⁡L
0.005
evalb⁡revsort⁡L=sort⁡L,a,b↦lexorder⁡b,a
See Also
eval
evalb
list
nops
seq
sort
string
StringTools,Random
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