# Commits

committed c0caea3

Add the non-terminating solution to #110.

It does not finish in time.

# project-euler/110/euler-110.pl

+#!/usr/bin/perl
+
+use strict;
+use warnings;
+
+=head1 DESCRIPTION:
+
+In the following equation x, y, and n are positive integers:
+
+1/x + 1/y = 1/n
+
+For n = 4 there are exactly three distinct solutions:
+
+* 1/5 + 1/20 = 1/4
+
+* 1/6 + 1/12 = 1/4
+
+* 1/8 + 1/8 = 1/4
+
+What is the least value of n for which the number of distinct solutions exceeds one-thousand?
+
+=head1 ANALYSIS
+
+ny + nx = xy
+
+n (x+y) = xy
+
+n = xy / (x+y)
+
+x,y > n
+
+1/y = 1/n-1/x = (x-n)/nx
+
+y = nx/(x-n)
+
+If t = x-n ; x = t + n
+
+y = n*(t+n) / t = n + [ n^2 / t ]
+
+t \in [1 .. n]
+
+If n = p1^e1 * p2^e2 * p3^e3 ....
+
+Then the number of t's is (2*e1+1)*(2*e2+1)*(2*e3+1)*(2*e4+1)/2
+
+=cut
+
+
+=begin Removed
+
+use integer;
+
+for (my $n = 1_000; ;$n++)
+{
+    my $count = 0; + my$n_sq = $n *$n;
+
+    for my $t (1 ..$n)
+    {
+        if (! ($n_sq %$t))
+        {
+            $count++; + } + } + print "Reached$n [$count]\n"; + if ($count > 1_000)
+    {
+        print "N = $n\n"; + exit(0); + } +} + +=end Removed + +=cut + +use Math::GMP; + +use Heap::Fibonacci; +use Heap::Elem::Num qw(NumElem); + +use List::Util qw(reduce); + +my$heap = Heap::Fibonacci->new;
+
+my $limit = 4_000_000; +my$num_divisors = ($limit * 2 -1); + +my$primes_list = '';
+
+{
+    open my $fh, "primes 2 |"; + for my$i (0 .. $limit) + { + my$p = <$fh>; + chomp($p);
+        vec($primes_list,$i, 32) = $p; + } + close($fh);
+}
+
+my %decomposition = ('1' => []);
+
+$heap->add(NumElem(1)); + +while (my$elem = $heap->extract_top) { + my$n = $elem->val; + + my$composition = $decomposition{"$n"};
+    if ((reduce { $a *$b } 1, map { Math::GMP->new($_ * 2 + 1) } @$composition) > $num_divisors + ) + { + print "Found$n\n";
+        exit(0);
+    }
+    else
+    {
+        foreach my $idx ( + 0  + ..  + ((@$composition == $limit) + ? ($#$composition) + : ($#$composition+1) + ) + ) + { + my @new = @$composition;
+            $new[$idx]++;
+            my $new_n =  + reduce {$a * $b } 1,  + map { Math::GMP->new(vec($primes_list, $_, 32)) **$new[$_] } (0 ..$#new)
+                ;
+            if (! exists($decomposition{"$new_n"}))
+            {
+                $decomposition{"$new_n"} = \@new;
+                $heap->add( NumElem($new_n) );
+            }
+        }
+    }
+}