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

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:

#! perl -slw
use strict;
use Time::HiRes qw[ time ];
use Data::Dump qw[ pp ]; $Data::Dump::WIDTH = 500;

our $S //= 0; srand $S if $S;
our $N //= 20;

sub LIS {
    my $X = shift;
    my( @P, @M );

    my $L = 0;
    for my $i ( 0 .. $#$X ) {
        ## Binary search for the largest positive j = L such that X[M[
+j]] < X[i]
        my $lo = 1;
        my $hi = $L;
        while( $lo <= $hi ) {
            my $mid = int( ( $lo + $hi ) / 2 );
            if( $X->[ $M[ $mid ] ] < $X->[ $i ] ) {
                $lo = $mid + 1;
            }
            else{
                $hi = $mid - 1;
            }
        }
        ## After searching, lo is 1 greater than the length of the lon
+gest prefix of X[i]
        my $newL = $lo;

        ## The predecessor of X[i] is the last index of the subsequenc
+e of length newL-1
        $P[ $i ] = $M[ $newL - 1 ];
        $M[ $newL ] = $i;

        if( $newL > $L ) {
            ## If we found a subsequence longer than any we've found y
+et, update L
            $L = $newL;
        }
    }
    ## Reconstruct the longest increasing subsequence
    my @S;
    my $k = $M[ $L ];
    for my $i ( reverse 0 .. $L-1 ) {
        $S[ $i ] = $X->[ $k ];
        $k = $P[ $k ];
    }
    return @S;
}


my @data = map int( rand $N ), 1 .. $N;

my $start = time;
my @best = LIS( \@data );
printf "best(%d): @best\n", scalar @best;
printf "Took %.3f seconds\n", time() - $start;
[download]

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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