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#!/usr/local/bin/perl
use strict;
use warnings;
use feature qw(say);
use Data::Dumper qw(Dumper);
use Math::Prime::Util qw(is_prime primes);
my @TESTS = (
[ 5,2], [4,2], [18,2], [19,3], [100,9],
[40,5], [328,15], [96,2], [97,3], [100,4],
[129,10], [160,11],
);
my @t;
say "*** @{$_}\n", _dump( first_partition(@{$_}) ), "\n--\n", _dump( partition(@{$_}) ), "\n" for @TESTS;
if(0){
say '===============================';
for my $s (1..200) { printf '%4d',scalar(@t = partition($s,$_)) for 1..12; say ''; }
say '===============================';
for my $s (1..15) { (@t=partition($_,$s)) ? ( print int(log@t/log 4) ) : print ' ' for 1..320; say ''; }
say '===============================';
}
sub partition {
my ( $m, $n, $p ) = (@_,0);
$n > 1
? map { $p = $_;
map { [ $p, @{$_} ] }
partition( $m-$p, $n-1, $p )
} @{ primes $p+1, int( ($m-$n/2+1/2)/$n) }
: $m > $p && is_prime $m ? [$m] : ();
}
sub first_partition {
my ( $m, $n, $p ) = (@_,0);
$n > 1
? map { $p = $_;
map { return [$p, @{$_}] }
first_partition( $m-$p, $n-1, $p )
} @{ primes $p+1, int( ($m-$n/2+1/2)/$n) }
: $m > $p && is_prime $m ? [$m] : ();
}
sub _dump {
@_ ? join ', ', map { '[ '. join(', ', @{$_}).' ]' } @_ : '-- no solutions --';
}
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