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Permutation.hh
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Permutation.hh
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#ifndef PERMUTATION_HH
#define PERMUTATION_HH
#include <set>
#include <utility>
template< typename Element,
auto set,
template< typename,
typename > typename Map >
class Permutation
{
private:
Map< Element, Element > m;
bool
element_of_set( Element q )
{
for( Element element : set )
{
if( q == element )
{
return true;
}
}
return false;
}
bool
without_repeating_elements( )
{
for( std::set< Element > s;
auto element : set )
{
if( 1u == s.count( element ) )
{
return false;
}
s.insert( element );
}
return true;
}
bool
injectiveness( )
{
for( std::set< Element > destinations;
Element element : set )
{
if( false == destinations.insert( operator()( element ) ).second )
{
return false;
}
}
return true;
}
bool
surjectiveness( )
{
std::set< Element > destinations;
for( const Element element : set )
{
destinations.insert( operator()( element ) );
}
return set.size( ) == destinations.size( );
}
public:
Permutation( )
{
assert( without_repeating_elements( ) );
for( const Element element : set )
{
m[ element ] = element;
}
}
Permutation( std::vector<
std::pair<
Element,
Element >
> transitions )
: Permutation( )
{
for( std::set< Element > sources,
destinations;
auto [ source, destination ] : transitions )
{
assert( true == sources.insert( source ).second );
assert( true == destinations.insert( destination ).second );
}
for( auto [ source, destination ] : transitions )
{
m[ source ] = destination;
assert( element_of_set( source ) &&
element_of_set( destination ) );
}
assert( true == injectiveness( ) &&
true == surjectiveness( ) );
}
Element
operator()( const Element q )
{
assert( element_of_set( q ) );
return m.at( q );
}
template< typename Permutation >
Permutation
operator*( Permutation q ) const
{
static_assert(
std::is_same_v< Permutation,
std::decay_t< decltype( *this ) >
>
);
std::vector<
std::pair<
Element,
Element >
> r;
for( const auto [ source, destination ] : m )
{
r.emplace_back( source, q( destination ) );
}
return Permutation( r );
}
};
#endif