I believe this can be reduced to LCS which is O(much better).

I concur. My assessment was of the OPs somewhat naive approach to the problem, not the optimal solution.

reduced to LCS

Careful. LCS can mean either: longest common substring; or -- as is applicable here -- longest common subsequence.

And actually, the OPs problem can be further specialised to Longest increasing subsequence, and tackled with a very straight forward algorithm that is O(n log n).

wow... so I implemented the wiki page's pseudocode, and benchmarked my code vs the Longest Increasing Subsequence:

<Reveal this spoiler or all in this thread>

results:

20 [953 317 563 582 789 629 613 918 9 680 276 163 119 915 967 426 820 
+227 256 650]
lis: [ 317 563 582 613 680 915 967 ]
pryrt: [ 317 563 582 629 680 915 967 ]
Benchmark:
running
  lis, pryrt
 for at least 10 CPU seconds
...

       lis: 10 wallclock secs (10.51 usr +  0.00 sys = 10.51 CPU) @ 25
+210.27/s (n=265086)

       pryrt: 11 wallclock secs (11.26 usr +  0.00 sys = 11.26 CPU) @ 
+ 0.18/s (n=2)

            (warning: too few iterations for a reliable count)

         s/iter       pryrt     lis
pryrt      5.63        --     -100%
lis   3.97e-005 14197064%        --
[download]

With a random list just twenty elements long, it went from 5-6s per run for my code, to better than 25_000 runs per second with the efficient algorithm: that's almost 150_000 times faster, and that's just with 20 elements in the array. (My original benchmark tried cmpthese() on random length arrays, using the defaults to my genarray() function, but after a minute, I didn't feel like waiting that long, so switched to a 10sec timethese()/cmpthese() pair. Multiple runs give similar results.)

When run-time is money, it pays to search for known-good algorithms, rather than just trusting that you've thought of an efficient algorithm!

Thanks ++gilthoniel for an interesting thread, and ++BrowserUK, for once again bringing his knowledge of efficient coding practices to help us all.

To all who come upon this thread: definitely use the efficient code, rather than my original code!

I also implemented the wiki pseudo-code, resulting almost identical code:

<Reveal this spoiler or all in this thread>

Though I pass the data in via a reference for efficiency.

I've been trying to wrap my brain around the mentioned Knuth optimisation without success.

One comment on your code. This return wantarray ? @S : [@S]; throws away the advantage of returning a reference, by constructing a list from the existing array, which is then used to construct another (anonymous) array, a reference to which is returned.

Better to just do return wantarray ? @S : \@S;

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