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### Re: Coming soon: Algorithm::Loops (puzzle2)

by Abigail-II (Bishop)
 on Apr 12, 2003 at 23:25 UTC ( #250094=note: print w/replies, xml ) Need Help??

in reply to Re^2: Coming soon: Algorithm::Loops (puzzle2)
in thread Coming soon: Algorithm::Loops

Sorry, I hadn't studied the code well enough that you intended to find years with a unique solution, and the solution requiring six terms. A modified version of my program finds 5106 and 5328.

Also, my modified versions no longer has three digits hardcoded. You can now give the number of digits on the command line - you can also give the minimum number of terms in the unique solution, and the range of years to investigate. Unfortunally, doing it for 4 digits takes a long time. There are about 12 billion sums to consider, compared to about 14 thousand for 3 digits.

Abigail

```#!/usr/bin/perl

use strict;
use warnings;

use Getopt::Long;

GetOptions  'digits=i' => \my \$digits, # Number of digits.
'min=i'    => \my \$min,    # Minimum sum.
'max=i'    => \my \$max,    # Maximum sum.
'terms=i'  => \my \$terms,  # Minimum number of terms in su
+m.
;

\$digits    ||=          3;
\$min       ||=          0;
\$max       ||= 0x7FFFFFFF;
\$terms     ||=          6;

#
# Return all permutations of a set.
#
sub perms;
sub perms {
@_ ? map {my \$i = \$_; map {[\$_ [\$i] => @\$_]}
perms @_ [0 .. \$i - 1, \$i + 1 .. \$#_]} 0 .. \$#_ : [];
}

#
# Return the powerset of a set.
#
sub power_set;
sub power_set {
@_ ? do {my @r = power_set @_ [1 .. \$#_];
[\$_ ] => @r => map {[\$_  => @\$_]} @r} : ()
}

my %answers;
sub try {
local \$" = " + ";
foreach my \$set (power_set @_) {
my \$sum = eval "@\$set";
push @{\$answers {\$sum}} => \$set;
}
}

OUTER:
foreach (("0" x \$digits) .. ("9" x \$digits)) {
my @digits = split //;
for (my \$i = 1; \$i < @digits; \$i ++) {
next OUTER if \$digits [\$i] < \$digits [\$i - 1]
}
my %seen;
try grep {!\$seen {\$_} ++}
map  {\$_ = join "" => @\$_; s/^0*(?=\d)//; \$_} perms @digit
+s;
}

foreach my \$sum (sort {\$a <=> \$b} keys %answers) {
next unless \$sum >= \$min && \$sum < \$max;
next unless @{\$answers {\$sum}}     ==      1;
next unless @{\$answers {\$sum} } >= \$terms;

local \$" = " + ";
print "\$sum == @{\$answers{\$sum}}\n";
}
__END__
[download]```

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