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### Re: Powerset short-circuit optimization

by ikegami (Pope)
 on Oct 03, 2006 at 18:17 UTC ( #576146=note: print w/replies, xml ) Need Help??

in reply to Powerset short-circuit optimization

An initial naïve solution:
```use strict;
use warnings;

sub r(&\$@) {
my \$cb = shift(@_);
my %seen;

local *_r = sub {
my @v = @_;
return if \$seen{join \$;, @v}++;
return if not \$cb->(@v);
return if @v == 1;
for (0..\$#v) {
my @v_ = @v;
splice(@v_, \$#v-\$_, 1);
_r(@v_);
}
};

_r(sort @\$_) foreach @_;
}

r { print(@_, "\n"); 1 } [ qw( A B C D   ) ],
[ qw( A B C E   ) ],
[ qw( A B C F G ) ];

Output:

```ABCD
ABC
AB
A
B
AC
C
BC
ABD
D
BD
ACD
CD
BCD
ABCE
ABE
AE
E
BE
ACE
CE
BCE
ABCFG
ABCF
ABF
AF
F
BF
ACF
CF
BCF
ABCG
ABG
AG
G
BG
ACG
CG
BCG
ABFG
AFG
FG
BFG
ACFG
CFG
BCFG

Both the implementation and the algorithm can surely be improved.

Update: The code block now returns a value. This allows the option to skip, as desired.
Update: Slightly modified to attain your ultimate goal.
Update: I can't think of another algorithm. This will likely be my last solution.

Replies are listed 'Best First'.
Re^2: Powerset short-circuit optimization
by Limbic~Region (Chancellor) on Oct 03, 2006 at 22:13 UTC
ikegami,
This is the approach I previously discussed in the CB with jdporter and blokhead. The undesireable aspect is that _r() is called 29 times to yield 15 items for A,B,C,D instead of just 15. I am not sure there is a way around this but that's why I posted it.

Cheers - L~R

The following only calls _v 15 times. ;) Of course, splice (or its optimized equivalent) and %seen are still called 29 times, but that's a far cry less than the possible 41. Also, even with the original code, the (presumably expensive) callback is only called 15 times.

```   local *_r = sub {
my @v = @_;
return if not \$cb->(@v);
return if @v == 1;
for (0..\$#v) {
my @v_ = @v;
splice(@v_, \$#v-\$_, 1);
_r(@v_) if not \$seen{join \$;, @v_}++;
}
};

It breaks the rule "A,B,C should be generated before A,C", but the following might allow you to break down the problem such that your requirements can be loosened:

```my (\$u_set1, \$u_set2, \$common) = extract_common(\$set1, \$set2);
my \$psetc = powerset(\$common);
my \$pset1 = product(\$psetc, powerset(\$u_set1));
my \$pset2 = product(\$psetc, powerset(\$u_set2));
my \$pset = union(\$pset1, \$pset2);

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