File Coverage

blib/lib/Math/GrahamFunction.pm

Criterion	Covered	Total	%
statement	128	128	100.0
branch	34	36	94.4
condition	8	9	88.8
subroutine	26	26	100.0
pod	1	1	100.0
total	197	200	98.5

package Math::GrahamFunction;
$Math::GrahamFunction::VERSION = '0.02003';
use warnings;
use strict;

use 5.008;


use parent qw(Math::GrahamFunction::Object);

use Math::GrahamFunction::SqFacts;
use Math::GrahamFunction::SqFacts::Dipole;

__PACKAGE__->mk_accessors(
    qw(
        _base
        n
        _n_vec
        next_id
        _n_sq_factors
        primes_to_ids_map
        )
);

sub _initialize
{
    my $self = shift;
    my $args = shift;

    $self->n( $args->{n} )
        or die "n was not specified";

    $self->primes_to_ids_map( {} );

    return 0;
}


sub _get_num_facts
{
    my ( $self, $number ) = @_;

    return Math::GrahamFunction::SqFacts->new( { 'n' => $number } );
}

sub _get_facts
{
    my ( $self, $factors ) = @_;

    return Math::GrahamFunction::SqFacts->new(
        { 'factors' => ( ref($factors) eq "ARRAY" ? $factors : [$factors] ) } );
}

sub _get_num_dipole
{
    my ( $self, $number ) = @_;

    return Math::GrahamFunction::SqFacts::Dipole->new(
        {
            'result'  => $self->_get_num_facts($number),
            'compose' => $self->_get_facts($number),
        }
    );

}

sub _calc_n_sq_factors
{
    my $self = shift;

    $self->_n_sq_factors( $self->_get_num_dipole( $self->n ) );
}

sub _check_largest_factor_in_between
{
    my $self = shift;

    my $n = $self->n();

    # Cheating:
    # Check if between n and n+largest_factor we can fit
    # a square of SqFact{n*(n+largest_factor)}. If so, return
    # n+largest_factor.
    #
    # So, for instance, if n = p than n+largest_factor = 2p
    # and so SqFact{p*(2p)} = 2 and it is possible to see if
    # there's a 2*i^2 between p and 2p. That way, p*2*i^2*2p is
    # a square number.

    my $largest_factor = $self->_n_sq_factors()->last();

    my ( $lower_bound, $lb_sq_factors );

    $lower_bound = $self->n() + $largest_factor;
    while (1)
    {
        $lb_sq_factors = $self->_get_num_facts($lower_bound);
        if ( $lb_sq_factors->exists($largest_factor) )
        {
            last;
        }
        $lower_bound += $largest_factor;
    }

    my $n_times_lb = $self->_n_sq_factors->result->mult($lb_sq_factors);

    my $rest_of_factors_product = $n_times_lb->product();

    my $low_square_val = int( sqrt( $n / $rest_of_factors_product ) );
    my $high_square_val =
        int( sqrt( $lower_bound / $rest_of_factors_product ) );

    if ( $low_square_val != $high_square_val )
    {
        my @factors = (
            $n,
            ( $low_square_val + 1 ) *
                ( $low_square_val + 1 ) *
                $rest_of_factors_product,
            $lower_bound
        );

        # TODO - possibly convert to Dipole
        # return ($lower_bound, $self->_get_facts(\@factors));
        return \@factors;
    }
    else
    {
        return;
    }
}

sub _get_next_id
{
    my $self = shift;
    return $self->next_id( $self->next_id() + 1 );
}

sub _get_prime_id
{
    my $self = shift;
    my $p    = shift;
    return $self->primes_to_ids_map()->{$p};
}

sub _register_prime
{
    my ( $self, $p ) = @_;
    $self->primes_to_ids_map()->{$p} = $self->_get_next_id();
}

sub _prime_exists
{
    my ( $self, $p ) = @_;
    return exists( $self->primes_to_ids_map->{$p} );
}

sub _get_min_id
{
    my ( $self, $vec ) = @_;

    my $min_id = -1;
    my $min_p  = 0;

    foreach my $p ( @{ $vec->result()->factors() } )
    {
        my $id = $self->_get_prime_id($p);
        if ( ( $min_id < 0 ) || ( $min_id > $id ) )
        {
            $min_id = $id;
            $min_p  = $p;
        }
    }

    return ( $min_id, $min_p );
}

sub _try_to_form_n
{
    my $self = shift;

    while ( !$self->_n_vec->is_square() )
    {
        # Calculating $id as the minimal ID of the squaring factors of $p
        my ( $id, undef ) = $self->_get_min_id( $self->_n_vec );

        # Multiply by the controlling vector of this ID if it exists
        # or terminate if it doesn't.
        return 0 if ( !defined( $self->_base->[$id] ) );
        $self->_n_vec->mult_by( $self->_base->[$id] );
    }

    return 1;
}

sub _get_final_factors
{
    my $self = shift;

    $self->_calc_n_sq_factors();

    # The graham number of a perfect square is itself.
    if ( $self->_n_sq_factors->is_square() )
    {
        return $self->_n_sq_factors->_get_ret();
    }
    elsif ( defined( my $ret = $self->_check_largest_factor_in_between() ) )
    {
        return $ret;
    }
    else
    {
        return $self->_main_solve();
    }
}

sub solve
{
    my $self = shift;

    return { factors => $self->_get_final_factors() };
}

sub _main_init
{
    my $self = shift;

    $self->next_id(0);

    $self->_base( [] );

    # Register all the primes in the squaring factors of $n
    foreach my $p ( @{ $self->_n_sq_factors->factors() } )
    {
        $self->_register_prime($p);
    }

    # $self->_n_vec is used to determine if $n can be composed out of the
    # base's vectors.
    $self->_n_vec( $self->_n_sq_factors->clone() );

    return;
}


sub _update_base
{
    my ( $self, $final_vec ) = @_;

    # Get the minimal ID and its corresponding prime number
    # in $final_vec.
    my ( $min_id, $min_p ) = $self->_get_min_id($final_vec);

    if ( $min_id >= 0 )
    {
        # Assign $final_vec as the controlling vector for this prime
        # number
        $self->_base->[$min_id] = $final_vec;

        # Canonicalize the rest of the vectors with the new vector.
    CANON_LOOP:
        for my $j ( keys @{ $self->_base } )
        {
            if ( ( $j == $min_id ) || ( !defined( $self->_base->[$j] ) ) )
            {
                next CANON_LOOP;
            }
            if ( $self->_base->[$j]->exists($min_p) )
            {
                $self->_base->[$j]->mult_by($final_vec);
            }
        }
    }
}

sub _get_final_composition
{
    my ( $self, $i_vec ) = @_;

    # $final_vec is the new vector to add after it was
    # stair-shaped by all the controlling vectors in the base.

    my $final_vec = $i_vec;

    foreach my $p ( @{ $i_vec->factors() } )
    {
        if ( !$self->_prime_exists($p) )
        {
            $self->_register_prime($p);
        }
        else
        {
            my $id = $self->_get_prime_id($p);
            if ( defined( $self->_base->[$id] ) )
            {
                $final_vec->mult_by( $self->_base->[$id] );
            }
        }
    }

    return $final_vec;
}

sub _get_i_vec
{
    my ( $self, $i ) = @_;

    my $i_vec = $self->_get_num_dipole($i);

    # Skip perfect squares - they do not add to the solution
    if ( $i_vec->is_square() )
    {
        return;
    }

    # Check if $i is a prime number
    # We need n > 2 because for n == 2 it does include a prime number.
    #
    # Prime numbers cannot be included because 2*n is an upper bound
    # to G(n) and so if there is a prime p > n than its next multiple
    # will be greater than G(n).
    if ( ( $self->n() > 2 ) && ( $i_vec->first() == $i ) )
    {
        return;
    }

    return $i_vec;
}

sub _solve_iteration
{
    my ( $self, $i ) = @_;

    my $i_vec = $self->_get_i_vec($i)
        or return;

    my $final_vec = $self->_get_final_composition($i_vec);

    $self->_update_base($final_vec);

    # Check if we can form $n
    if ( $self->_try_to_form_n() )
    {
        return $self->_n_vec->_get_ret();
    }
    else
    {
        return;
    }
}

sub _main_solve
{
    my $self = shift;

    $self->_main_init();

    for ( my $i = $self->n() + 1 ; ; ++$i )
    {
        if ( defined( my $ret = $self->_solve_iteration($i) ) )
        {
            return $ret;
        }
    }
}


1;    # End of Math::GrahamFunction

__END__