It's probably a bit late to post this but since the code is now written I might as well. Corion's mention of a binary counter made me think of this thread in which I ventured this solution. I can use this to generate all strings of, say, three ones and two zeros and then use a regex and pos to generate an array of elements to sum. Because the iterator returns strings in this order for the above example
use 5.026;
use warnings;
use List::Util qw{ sum };
use Data::Dumper;
my @tests = (
5,
[ 1 ],
[ 1, 2 ],
[ 1, 2, 3 ],
[ 1, 2, 3, 4 ],
[ 1, 2, 3, 4, 5 ],
[ 4, 17, 9, 23, 1, 14 ],
);
foreach my $test ( @tests )
{
my $raRes = allSums( $test ) or do {
warn qq{$test: Not an array ref.\n};
say q{-} x 25;
next;
};
print Data::Dumper
->new( [ $test, $raRes ], [ qw{ test raRes }] )
->Indent( 1 )
->Dumpxs();
say q{-} x 25;
}
sub allSums
{
my $raNumbers = shift;
return 0 unless ref( $raNumbers ) eq q{ARRAY};
my $raSums = [ [], [], ];
my $nElems = scalar @{ $raNumbers };
if ( $nElems < 3 )
{
return $raSums;
}
foreach my $sumsOf ( 2 .. $nElems - 1 )
{
my $nZeros = $nElems - $sumsOf;
my $rcNext = permutary( $nZeros, $sumsOf );
while ( my $str = $rcNext->() )
{
my @posns;
push @posns, pos $str while $str =~ m{(?=1)}g;
unshift @{ $raSums->[ $sumsOf ] },
{
join( q{+}, @{ $raNumbers }[ @posns ] ),
sum @{ $raNumbers }[ @posns ]
};
}
}
return $raSums;
}
sub permutary
{
no warnings qw{ portable };
my ( $numZeros, $numOnes ) = @_;
my $format = q{%0} . ( $numZeros + $numOnes ) . q{b};
my $start = oct( q{0b} . q{1} x $numOnes );
my $limit = oct( q{0b} . q{1} x $numOnes . q{0} x $numZeros );
return sub
{
return undef if $start > $limit;
my $binStr = sprintf $format, $start;
die qq{Error: $binStr not $numOnes ones\n}
unless $numOnes == $binStr =~ tr{1}{};
my $jump = 0;
if ( $binStr =~ m{(1+)$} )
{
$jump = 2 ** ( length($1) - 1 );
}
elsif ( $binStr =~ m{(1+)(0+)$} )
{
$jump = 2 ** ( length($1) - 1 ) + 1;
$jump += 2 ** $_ for 1 .. length( $2 ) - 1;
}
else
{
die qq{Error: $binStr seems malformed\n};
}
$start += $jump;
return $binStr;
};
}
5: Not an array ref.
-------------------------
$test = [
1
];
$raRes = [
[],
[]
];
-------------------------
$test = [
1,
2
];
$raRes = [
[],
[]
];
-------------------------
$test = [
1,
2,
3
];
$raRes = [
[],
[],
[
{
'1+2' => 3
},
{
'1+3' => 4
},
{
'2+3' => 5
}
]
];
-------------------------
$test = [
1,
2,
3,
4
];
$raRes = [
[],
[],
[
{
'1+2' => 3
},
{
'1+3' => 4
},
{
'1+4' => 5
},
{
'2+3' => 5
},
{
'2+4' => 6
},
{
'3+4' => 7
}
],
[
{
'1+2+3' => 6
},
{
'1+2+4' => 7
},
{
'1+3+4' => 8
},
{
'2+3+4' => 9
}
]
];
-------------------------
$test = [
1,
2,
3,
4,
5
];
$raRes = [
[],
[],
[
{
'1+2' => 3
},
{
'1+3' => 4
},
{
'1+4' => 5
},
{
'1+5' => 6
},
{
'2+3' => 5
},
{
'2+4' => 6
},
{
'2+5' => 7
},
{
'3+4' => 7
},
{
'3+5' => 8
},
{
'4+5' => 9
}
],
[
{
'1+2+3' => 6
},
{
'1+2+4' => 7
},
{
'1+2+5' => 8
},
{
'1+3+4' => 8
},
{
'1+3+5' => 9
},
{
'1+4+5' => 10
},
{
'2+3+4' => 9
},
{
'2+3+5' => 10
},
{
'2+4+5' => 11
},
{
'3+4+5' => 12
}
],
[
{
'1+2+3+4' => 10
},
{
'1+2+3+5' => 11
},
{
'1+2+4+5' => 12
},
{
'1+3+4+5' => 13
},
{
'2+3+4+5' => 14
}
]
];
-------------------------
$test = [
4,
17,
9,
23,
1,
14
];
$raRes = [
[],
[],
[
{
'4+17' => 21
},
{
'4+9' => 13
},
{
'4+23' => 27
},
{
'4+1' => 5
},
{
'4+14' => 18
},
{
'17+9' => 26
},
{
'17+23' => 40
},
{
'17+1' => 18
},
{
'17+14' => 31
},
{
'9+23' => 32
},
{
'9+1' => 10
},
{
'9+14' => 23
},
{
'23+1' => 24
},
{
'23+14' => 37
},
{
'1+14' => 15
}
],
[
{
'4+17+9' => 30
},
{
'4+17+23' => 44
},
{
'4+17+1' => 22
},
{
'4+17+14' => 35
},
{
'4+9+23' => 36
},
{
'4+9+1' => 14
},
{
'4+9+14' => 27
},
{
'4+23+1' => 28
},
{
'4+23+14' => 41
},
{
'4+1+14' => 19
},
{
'17+9+23' => 49
},
{
'17+9+1' => 27
},
{
'17+9+14' => 40
},
{
'17+23+1' => 41
},
{
'17+23+14' => 54
},
{
'17+1+14' => 32
},
{
'9+23+1' => 33
},
{
'9+23+14' => 46
},
{
'9+1+14' => 24
},
{
'23+1+14' => 38
}
],
[
{
'4+17+9+23' => 53
},
{
'4+17+9+1' => 31
},
{
'4+17+9+14' => 44
},
{
'4+17+23+1' => 45
},
{
'4+17+23+14' => 58
},
{
'4+17+1+14' => 36
},
{
'4+9+23+1' => 37
},
{
'4+9+23+14' => 50
},
{
'4+9+1+14' => 28
},
{
'4+23+1+14' => 42
},
{
'17+9+23+1' => 50
},
{
'17+9+23+14' => 63
},
{
'17+9+1+14' => 41
},
{
'17+23+1+14' => 55
},
{
'9+23+1+14' => 47
}
],
[
{
'4+17+9+23+1' => 54
},
{
'4+17+9+23+14' => 67
},
{
'4+17+9+1+14' => 45
},
{
'4+17+23+1+14' => 59
},
{
'4+9+23+1+14' => 51
},
{
'17+9+23+1+14' => 64
}
]
];
-------------------------
I hope this is of interest.
