/** \file
 * \brief Calculate one or all Maximum Adjacency Ordering(s) of a given simple undirected graph.
 *
 * \author Sebastian Semper
 *
 * \par License:
 * This file is part of the Open Graph Drawing Framework (OGDF).
 *
 * \par
 * Copyright (C)<br>
 * See README.md in the OGDF root directory for details.
 *
 * \par
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * Version 2 or 3 as published by the Free Software Foundation;
 * see the file LICENSE.txt included in the packaging of this file
 * for details.
 *
 * \par
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * \par
 * You should have received a copy of the GNU General Public
 * License along with this program; if not, see
 * http://www.gnu.org/copyleft/gpl.html
 */

#pragma once

#include <ogdf/basic/Graph.h>
#include <ogdf/basic/basic.h>

namespace ogdf {
class GraphAttributes;
template<class E>
class ListPure;

/**
 * \brief Calculate one or all Maximum Adjacency Ordering(s) of a given simple undirected graph.
 *
 *
 * The class MaxAdjOrdering provides one algorithm to calculate a MAO or all MAOs of a given graph.
 * It returns a ListPure of nodes or a list of ListPures that contain the ordering.
 *
 * @ingroup ga-connectivity
 */
class OGDF_EXPORT MaxAdjOrdering {
private:
	/**
	 * \brief This method gets called recursively to generate all MAOs
	 * via backtracking
	 * @param n Number of nodes
	 * @param currentOrder The partial MAO to this point
	 * @param currentUnsorted Nodes that are still left to sort
	 * @param r Values on the nodes that count the edges to the partial MAO
	 * @param MAOs The list of all MAOs to this point
	 */
	void m_calcAllMAOs_recursion(int n, ListPure<node> currentOrder, ListPure<node> currentUnsorted,
			NodeArray<int> r, ListPure<ListPure<node>>* MAOs);

	/**
	 * \brief This method gets called recursively to generate all MAOs and their
	 * induced forest decompositions of the edges
	 * via backtracking
	 * @param n Number of nodes
	 * @param currentOrder The partial MAO to this point
	 * @param currentForest The partial forest decomposition to this point
	 * @param currentUnsorted Nodes that are still left to sort
	 * @param r Values on the nodes that count the edges to the partial MAO
	 * @param MAOs The list of all MAOs to this point
	 * @param Fs The list of all forests to this point
	 */
	void m_calcAllMAOs_recursion(int n, ListPure<node> currentOrder,
			ListPure<ListPure<edge>> currentForest, ListPure<node> currentUnsorted, NodeArray<int> r,
			ListPure<ListPure<node>>* MAOs, ListPure<ListPure<ListPure<edge>>>* Fs);

public:
	/**
	 * \brief Standard constructor
	 */
	MaxAdjOrdering();
	/**
	 * \brief Standard destructor
	 */
	~MaxAdjOrdering();

	/**
	 * \brief Calculates one MAO starting with the node with index 0
	 * @param G is the Graph to work on
	 * @param MAO is the pointer to a list that stores the MAO
	 */
	void calc(const Graph* G, ListPure<node>* MAO);
	/**
	 * \brief Calculates one MAO starting with the node with index 0
	 * and lex-bfs tie breaking.
	 * @param G is the Graph to work on
	 * @param MAO is the pointer to a list that stores the MAO
	 */
	void calcBfs(const Graph* G, ListPure<node>* MAO);

	/**
	 * \brief Calculates one MAO starting with a given node
	 * @param G is the Graph to work on
	 * @param s Node to start the MAO with
	 * @param MAO is the pointer to a list that stores the MAO
	 */
	void calc(const Graph* G, node s, ListPure<node>* MAO);

	/**
	 * \brief Calculates one MAO starting with the node with index 0
	 * @param G is the Graph to work on
	 * @param MAO is the pointer to a list that stores the MAO
	 * @param Forests is the pointer to a list that stores the forest decomposition associated with the MAO
	 */
	void calc(const Graph* G, ListPure<node>* MAO, ListPure<ListPure<edge>>* Forests);

	/**
	 * \brief Calculates one MAO starting with a given node
	 * @param G is the Graph to work on
	 * @param s Node to start the MAO with
	 * @param MAO is the pointer to a list that stores the MAO
	 * @param Forests is the pointer to a list that stores the forest decomposition associated with the MAO
	 */
	void calc(const Graph* G, node s, ListPure<node>* MAO, ListPure<ListPure<edge>>* Forests);

	/**
	 * \brief Calculates all MAOs of a given graph
	 * @param G is the Graph to work on
	 * @param MAOs List of all MAOs. So it must be a list of lists
	 */
	void calcAll(const Graph* G, ListPure<ListPure<node>>* MAOs);

	/**
	 * \brief Calculates all MAOs including their associated forest decompositions of a given graph
	 * @param G is the graph to work on
	 * @param MAOs List of all MAOs. So it must be a list of lists of vertices.
	 * @param Fs List of all forest decompositions. So it must be a list of lists of lists of edges.
	 */
	void calcAll(const Graph* G, ListPure<ListPure<node>>* MAOs,
			ListPure<ListPure<ListPure<edge>>>* Fs);

	/**
	 * \brief Calculates the associated forest decomposition of a given MAO of a graph
	 * @param G is the given graph
	 * @param MAO contains the MAO of \p G, given as a list of vertices
	 * @param F stores the computed forest decomposition and is a list of edge lists
	 */
	void calcForest(const Graph& G, ListPure<node>* MAO, ListPure<ListPure<edge>>* F);

	/**
	 * @copydoc MaxAdjOrdering::calcForest
	 */
	void calcForest(const Graph& G, const ListPure<node>& MAO, ListPure<ListPure<edge>>* F);

	/**
	 * \brief Test if a given ordering is a MAO
	 * @param G is the graph to work on
	 * @param Ordering is a ListPure that contains a permutation of the nodes
	 */
	bool testIfMAO(const Graph* G, ListPure<node>* Ordering);

	/**
	 * \brief Test if a given ordering is a MAO that follows lex-bfs tie breaking
	 * @param G is the graph to work on
	 * @param Ordering is a ListPure that contains a permutation of the nodes
	 */
	bool testIfMAOBfs(const Graph* G, ListPure<node>* Ordering);


	/**
	 * @brief testIfAllMAOs checks all permutations (must be provided) if they are a MAO and if
	 * yes searches this ordering in the provided list. If one permutation is no MAO
	 * it still gets searched to rule out any false elements in \p Perms. So we make sure we generated
	 * all MAOs of \p G.
	 * @param G is the graph to work on
	 * @param Orderings contains Lists that are supposedly MAOs
	 * @param Perms contains all permutations of a graph with the same size as \p G
	 * @return
	 */
	bool testIfAllMAOs(const Graph* G, ListPure<ListPure<node>>* Orderings,
			ListPure<ListPure<node>>* Perms);
	/**
	 * \brief Convenient way to visualize a MAO with the LinearLayout class.
	 * @param GA Graphattributes of the Graph to paint
	 * @param MAO Mao to use for ordering the nodes
	 */
	void visualize(GraphAttributes* GA, ListPure<node>* MAO);

	/**
	 * @copydoc MaxAdjOrdering::visualize(GraphAttributes*, ListPure<node>*)
	 * @param F A forest decomposition that is also visualized
	 */
	void visualize(GraphAttributes* GA, ListPure<node>* MAO, ListPure<ListPure<edge>>* F);

	/**
	 * @copydoc MaxAdjOrdering::visualize(GraphAttributes*, ListPure<node>*, ListPure<ListPure<edge>>*)
	 */
	void visualize(GraphAttributes* GA, const ListPure<node>& MAO, ListPure<ListPure<edge>>* F);
};

}
