type_recognition_heuristic.h

// ---------------------------------------------------------------------------
//
//  This file is part of PermLib.
//
// Copyright (c) 2009-2012 Thomas Rehn <thomas@carmen76.de>
// All rights reserved.
// 
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
// 1. Redistributions of source code must retain the above copyright
//    notice, this list of conditions and the following disclaimer.
// 2. Redistributions in binary form must reproduce the above copyright
//    notice, this list of conditions and the following disclaimer in the
//    documentation and/or other materials provided with the distribution.
// 3. The name of the author may not be used to endorse or promote products
//    derived from this software without specific prior written permission.
// 
// THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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// ---------------------------------------------------------------------------
 
 
#ifndef TYPERECOGNITIONHEURISTIC_H_
#define TYPERECOGNITIONHEURISTIC_H_
 
#include <list>
#include <vector>
 
#include <boost/iterator/counting_iterator.hpp>
#include <boost/pending/disjoint_sets.hpp>
 
namespace permlib {


template <class PERM>
class SymmetricGroupRecognitionHeuristic {
public:
        SymmetricGroupRecognitionHeuristic(unsigned int n, bool storeUnusedGenerators = false);
        

        bool addGenerator(const PERM& p);

        void symmetricGroupOrbits(std::vector<std::list<dom_int> >& orbits);
        
        const std::list<PERM>& unusedGenerators() { return m_unusedGenerators; }
private:
        bool addUnusedGenerator(const PERM& p);
        
        unsigned int m_n;
        bool m_storeUnusedGenerators;
        std::list<PERM> m_unusedGenerators;
        
        std::vector<dom_int> m_rank;
        std::vector<dom_int> m_parent;
        boost::disjoint_sets<dom_int*,dom_int*> m_components;
        
};
 
//
//     ----       IMPLEMENTATION
//
 
template <class PERM>
SymmetricGroupRecognitionHeuristic<PERM>::SymmetricGroupRecognitionHeuristic(unsigned int n, bool storeUnusedGenerators) 
        : m_n(n), m_storeUnusedGenerators(storeUnusedGenerators), m_rank(n), m_parent(n), m_components(&m_rank[0], &m_parent[0])
{ 
        for (dom_int i = 0; i < n; ++i)
                m_components.make_set(i);
}
 
 
template <class PERM>
bool SymmetricGroupRecognitionHeuristic<PERM>::addGenerator(const PERM& p) {
        BOOST_ASSERT( p.size() == m_n );
        
        dom_int cycle[2];
        unsigned int cycleIndex = 0;
        
        for (unsigned int i = 0; i < p.size(); ++i) {
                if (p.at(i) != i) {
                        if (cycleIndex >= 2)
                                return addUnusedGenerator(p);
                        
                        cycle[cycleIndex++] = i;
                }
        }
        
        if (cycleIndex == 0)
                // discard identity
                return true;
        
        BOOST_ASSERT(cycleIndex == 2);
        
        m_components.union_set(cycle[0], cycle[1]);
        return true;
}
 
 
template <class PERM>
void SymmetricGroupRecognitionHeuristic<PERM>::symmetricGroupOrbits(std::vector<std::list<dom_int> >& orbits) {
        m_components.compress_sets(boost::counting_iterator<dom_int>(0), boost::counting_iterator<dom_int>(m_n));
        
        std::vector<unsigned int> componentSizes(m_n);
        for (unsigned int i = 0; i < m_n; ++i) {
                ++componentSizes[ m_components.find_set(i) ];
        }
        
        std::vector<int> nonTrivialComponentMap(m_n, -1);
        unsigned int nonTrivialIndex = 0;
        for (unsigned int i = 0; i < m_n; ++i) {
                if (componentSizes[i] > 1)
                        nonTrivialComponentMap[i] = nonTrivialIndex++;
        }
        
        orbits.clear();
        orbits.resize(nonTrivialIndex);
        
        for (unsigned int i = 0; i < m_n; ++i) {
                unsigned int componentIndex = m_components.find_set(i);
                if (nonTrivialComponentMap[componentIndex] >= 0)
                        orbits[ nonTrivialComponentMap[componentIndex] ].push_back(i);
        }
}
 
 
template <class PERM>
bool SymmetricGroupRecognitionHeuristic<PERM>::addUnusedGenerator(const PERM& p) {
        m_unusedGenerators.push_back(p);
        return false;
}
 
} // end NS
 
#endif // -- TYPERECOGNITIONHEURISTIC_H_