path: root/ot/lp/network_simplex_simple.h

/* -*- mode: C++; indent-tabs-mode: nil; -*-
 *
 *
 * This file has been adapted by Nicolas Bonneel (2013),
 * from network_simplex.h from LEMON, a generic C++ optimization library,
 * to implement a lightweight network simplex for mass transport, more
 * memory efficient that the original file. A previous version of this file
 * is used as part of the Displacement Interpolation project,
 * Web: http://www.cs.ubc.ca/labs/imager/tr/2011/DisplacementInterpolation/
 *
 *
 **** Original file Copyright Notice :
 *
 * Copyright (C) 2003-2010
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
 *
 * Permission to use, modify and distribute this software is granted
 * provided that this copyright notice appears in all copies. For
 * precise terms see the accompanying LICENSE file.
 *
 * This software is provided "AS IS" with no warranty of any kind,
 * express or implied, and with no claim as to its suitability for any
 * purpose.
 *
 */

#ifndef LEMON_NETWORK_SIMPLEX_SIMPLE_H
#define LEMON_NETWORK_SIMPLEX_SIMPLE_H
#define DEBUG_LVL 0

#if DEBUG_LVL>0
#include <iomanip>
#endif


#define EPSILON 2.2204460492503131e-15
#define _EPSILON 1e-8
#define MAX_DEBUG_ITER 100000


/// \ingroup min_cost_flow_algs
///
/// \file
/// \brief Network Simplex algorithm for finding a minimum cost flow.

// if your compiler has troubles with stdext or hashmaps, just comment the following line to use a slower std::map instead
//#define HASHMAP

#include <vector>
#include <limits>
#include <algorithm>
#include <cstdio>
#ifdef HASHMAP
#include <hash_map>
#else
#include <map>
#endif
#include <cmath>
//#include "core.h"
//#include "lmath.h"

//#include "sparse_array_n.h"
#include "full_bipartitegraph.h"

#define INVALIDNODE -1
#define INVALID (-1)

namespace lemon {


    template <typename T>
	class ProxyObject;

	template<typename T>
	class SparseValueVector
	{
	public:
		SparseValueVector(int n=0)
		{
		}
		void resize(int n=0){};
		T operator[](const int id) const
		{
#ifdef HASHMAP
			typename stdext::hash_map<int,T>::const_iterator it = data.find(id);
#else
			typename std::map<int,T>::const_iterator it = data.find(id);
#endif
			if (it==data.end())
				return 0;
			else
				return it->second;
		}

		ProxyObject<T> operator[](const int id)
		{
			return ProxyObject<T>( this, id );
		}

        //private:
#ifdef HASHMAP
		stdext::hash_map<int,T> data;
#else
		std::map<int,T> data;
#endif

	};

	template <typename T>
	class ProxyObject {
	public:
		ProxyObject( SparseValueVector<T> *v, int idx ){_v=v; _idx=idx;};
		ProxyObject<T> & operator=( const T &v ) {
			// If we get here, we know that operator[] was called to perform a write access,
			// so we can insert an item in the vector if needed
			if (v!=0)
				_v->data[_idx]=v;
			return *this;
		}

		operator T() {
			// If we get here, we know that operator[] was called to perform a read access,
			// so we can simply return the existing object
#ifdef HASHMAP
			typename stdext::hash_map<int,T>::iterator it = _v->data.find(_idx);
#else
			typename std::map<int,T>::iterator it = _v->data.find(_idx);
#endif
			if (it==_v->data.end())
				return 0;
			else
				return it->second;
		}

		void operator+=(T val)
		{
			if (val==0) return;
#ifdef HASHMAP
			typename stdext::hash_map<int,T>::iterator it = _v->data.find(_idx);
#else
			typename std::map<int,T>::iterator it = _v->data.find(_idx);
#endif
			if (it==_v->data.end())
				_v->data[_idx] = val;
			else
			{
				T sum = it->second + val;
				if (sum==0)
					_v->data.erase(it);
				else
					it->second = sum;
			}
		}
		void operator-=(T val)
		{
			if (val==0) return;
#ifdef HASHMAP
			typename stdext::hash_map<int,T>::iterator it = _v->data.find(_idx);
#else
			typename std::map<int,T>::iterator it = _v->data.find(_idx);
#endif
			if (it==_v->data.end())
				_v->data[_idx] = -val;
			else
			{
				T sum = it->second - val;
				if (sum==0)
					_v->data.erase(it);
				else
					it->second = sum;
			}
		}

		SparseValueVector<T> *_v;
		int _idx;
	};



    /// \addtogroup min_cost_flow_algs
    /// @{

    /// \brief Implementation of the primal Network Simplex algorithm
    /// for finding a \ref min_cost_flow "minimum cost flow".
    ///
    /// \ref NetworkSimplexSimple implements the primal Network Simplex algorithm
    /// for finding a \ref min_cost_flow "minimum cost flow"
    /// \ref amo93networkflows, \ref dantzig63linearprog,
    /// \ref kellyoneill91netsimplex.
    /// This algorithm is a highly efficient specialized version of the
    /// linear programming simplex method directly for the minimum cost
    /// flow problem.
    ///
    /// In general, %NetworkSimplexSimple is the fastest implementation available
    /// in LEMON for this problem.
    /// Moreover, it supports both directions of the supply/demand inequality
    /// constraints. For more information, see \ref SupplyType.
    ///
    /// Most of the parameters of the problem (except for the digraph)
    /// can be given using separate functions, and the algorithm can be
    /// executed using the \ref run() function. If some parameters are not
    /// specified, then default values will be used.
    ///
    /// \tparam GR The digraph type the algorithm runs on.
    /// \tparam V The number type used for flow amounts, capacity bounds
    /// and supply values in the algorithm. By default, it is \c int.
    /// \tparam C The number type used for costs and potentials in the
    /// algorithm. By default, it is the same as \c V.
    ///
    /// \warning Both number types must be signed and all input data must
    /// be integer.
    ///
    /// \note %NetworkSimplexSimple provides five different pivot rule
    /// implementations, from which the most efficient one is used
    /// by default. For more information, see \ref PivotRule.
    template <typename GR, typename V = int, typename C = V, typename NodesType = unsigned short int>
    class NetworkSimplexSimple
    {
    public:

        /// \brief Constructor.
        ///
        /// The constructor of the class.
        ///
        /// \param graph The digraph the algorithm runs on.
        /// \param arc_mixing Indicate if the arcs have to be stored in a
        /// mixed order in the internal data structure.
        /// In special cases, it could lead to better overall performance,
        /// but it is usually slower. Therefore it is disabled by default.
        NetworkSimplexSimple(const GR& graph, bool arc_mixing, int nbnodes, long long nb_arcs,int maxiters) :
        _graph(graph),  //_arc_id(graph),
        _arc_mixing(arc_mixing), _init_nb_nodes(nbnodes), _init_nb_arcs(nb_arcs),
        MAX(std::numeric_limits<Value>::max()),
        INF(std::numeric_limits<Value>::has_infinity ?
            std::numeric_limits<Value>::infinity() : MAX)
        {
            // Reset data structures
            reset();
            max_iter=maxiters;
        }

        /// The type of the flow amounts, capacity bounds and supply values
        typedef V Value;
        /// The type of the arc costs
        typedef C Cost;

    public:

        /// \brief Problem type constants for the \c run() function.
        ///
        /// Enum type containing the problem type constants that can be
        /// returned by the \ref run() function of the algorithm.
        enum ProblemType {
            /// The problem has no feasible solution (flow).
            INFEASIBLE,
            /// The problem has optimal solution (i.e. it is feasible and
            /// bounded), and the algorithm has found optimal flow and node
            /// potentials (primal and dual solutions).
            OPTIMAL,
            /// The objective function of the problem is unbounded, i.e.
            /// there is a directed cycle having negative total cost and
            /// infinite upper bound.
            UNBOUNDED,
			/// The maximum number of iteration has been reached
			MAX_ITER_REACHED
        };

        /// \brief Constants for selecting the type of the supply constraints.
        ///
        /// Enum type containing constants for selecting the supply type,
        /// i.e. the direction of the inequalities in the supply/demand
        /// constraints of the \ref min_cost_flow "minimum cost flow problem".
        ///
        /// The default supply type is \c GEQ, the \c LEQ type can be
        /// selected using \ref supplyType().
        /// The equality form is a special case of both supply types.
        enum SupplyType {
            /// This option means that there are <em>"greater or equal"</em>
            /// supply/demand constraints in the definition of the problem.
            GEQ,
            /// This option means that there are <em>"less or equal"</em>
            /// supply/demand constraints in the definition of the problem.
            LEQ
        };



    private:

        int max_iter;
        TEMPLATE_DIGRAPH_TYPEDEFS(GR);

        typedef std::vector<int> IntVector;
        typedef std::vector<NodesType> UHalfIntVector;
        typedef std::vector<Value> ValueVector;
        typedef std::vector<Cost> CostVector;
        //	typedef SparseValueVector<Cost> CostVector;
        typedef std::vector<char> BoolVector;
        // Note: vector<char> is used instead of vector<bool> for efficiency reasons

        // State constants for arcs
        enum ArcState {
            STATE_UPPER = -1,
            STATE_TREE  =  0,
            STATE_LOWER =  1
        };

        typedef std::vector<signed char> StateVector;
        // Note: vector<signed char> is used instead of vector<ArcState> for
        // efficiency reasons

    private:

        // Data related to the underlying digraph
        const GR &_graph;
        int _node_num;
        int _arc_num;
        int _all_arc_num;
        int _search_arc_num;

        // Parameters of the problem
        SupplyType _stype;
        Value _sum_supply;

        inline int _node_id(int n) const {return _node_num-n-1;} ;

	    //IntArcMap _arc_id;
        UHalfIntVector _source;
        UHalfIntVector _target;
        bool _arc_mixing;
    public:
        // Node and arc data
        CostVector _cost;
        ValueVector _supply;
        ValueVector _flow;
        //SparseValueVector<Value> _flow;
        CostVector _pi;


    private:
        // Data for storing the spanning tree structure
        IntVector _parent;
        IntVector _pred;
        IntVector _thread;
        IntVector _rev_thread;
        IntVector _succ_num;
        IntVector _last_succ;
        IntVector _dirty_revs;
        BoolVector _forward;
        StateVector _state;
        int _root;

        // Temporary data used in the current pivot iteration
        int in_arc, join, u_in, v_in, u_out, v_out;
        int first, second, right, last;
        int stem, par_stem, new_stem;
        Value delta;

        const Value MAX;

        int mixingCoeff;

    public:

        /// \brief Constant for infinite upper bounds (capacities).
        ///
        /// Constant for infinite upper bounds (capacities).
        /// It is \c std::numeric_limits<Value>::infinity() if available,
        /// \c std::numeric_limits<Value>::max() otherwise.
        const Value INF;

    private:

        // thank you to DVK and MizardX from StackOverflow for this function!
        inline int sequence(int k) const {
            int smallv = (k > num_total_big_subsequence_numbers) & 1;

            k -= num_total_big_subsequence_numbers * smallv;
            int subsequence_length2 = subsequence_length- smallv;
            int subsequence_num = (k / subsequence_length2) + num_big_subseqiences * smallv;
            int subsequence_offset = (k % subsequence_length2) * mixingCoeff;

            return subsequence_offset + subsequence_num;
        }
        int subsequence_length;
        int num_big_subseqiences;
        int num_total_big_subsequence_numbers;

        inline int getArcID(const Arc &arc) const
        {
            //int n = _arc_num-arc._id-1;
            int n = _arc_num-GR::id(arc)-1;

            //int a = mixingCoeff*(n%mixingCoeff) + n/mixingCoeff;
            //int b = _arc_id[arc];
            if (_arc_mixing)
                return sequence(n);
            else
                return n;
        }

        // finally unused because too slow
        inline int getSource(const int arc) const
        {
            //int a = _source[arc];
            //return a;

            int n = _arc_num-arc-1;
            if (_arc_mixing)
                n = mixingCoeff*(n%mixingCoeff) + n/mixingCoeff;

            int b;
            if (n>=0)
                b = _node_id(_graph.source(GR::arcFromId( n ) ));
            else
            {
                n = arc+1-_arc_num;
                if ( n<=_node_num)
                    b = _node_num;
                else
                    if ( n>=_graph._n1)
                        b = _graph._n1;
                    else
                        b = _graph._n1-n;
            }

            return b;
        }



        // Implementation of the Block Search pivot rule
        class BlockSearchPivotRule
        {
        private:

            // References to the NetworkSimplexSimple class
            const UHalfIntVector  &_source;
            const UHalfIntVector  &_target;
            const CostVector &_cost;
            const StateVector &_state;
            const CostVector &_pi;
            int &_in_arc;
            int _search_arc_num;

            // Pivot rule data
            int _block_size;
            int _next_arc;
            NetworkSimplexSimple &_ns;

        public:

            // Constructor
            BlockSearchPivotRule(NetworkSimplexSimple &ns) :
            _source(ns._source), _target(ns._target),
            _cost(ns._cost), _state(ns._state), _pi(ns._pi),
            _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
            _next_arc(0),_ns(ns)
            {
                // The main parameters of the pivot rule
                const double BLOCK_SIZE_FACTOR = 1.0;
                const int MIN_BLOCK_SIZE = 10;

                _block_size = std::max( int(BLOCK_SIZE_FACTOR *
                                            std::sqrt(double(_search_arc_num))),
                                       MIN_BLOCK_SIZE );
            }
            // Find next entering arc
            bool findEnteringArc() {
                Cost c, min = 0;
                int e;
                int cnt = _block_size;
                double a;
                    for (e = _next_arc; e != _search_arc_num; ++e) {
                        c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
                        if (c < min) {
                            min = c;
                            _in_arc = e;
                        }
                        if (--cnt == 0) {
                            a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]);
                            a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]);
                            if (min <  -EPSILON*a) goto search_end;
                            cnt = _block_size;
                        }
                    }
                    for (e = 0; e != _next_arc; ++e) {
                        c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
                        if (c < min) {
                            min = c;
                            _in_arc = e;
                        }
                        if (--cnt == 0) {
                            a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]);
                            a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]);
                            if (min <  -EPSILON*a) goto search_end;
                            cnt = _block_size;
                        }
                    }
                    a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]);
                    a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]);
                    if (min >=  -EPSILON*a) return false;

            search_end:
                _next_arc = e;
                return true;
            }

        }; //class BlockSearchPivotRule



    public:



        int _init_nb_nodes;
        long long _init_nb_arcs;

        /// \name Parameters
        /// The parameters of the algorithm can be specified using these
        /// functions.

        /// @{


        /// \brief Set the costs of the arcs.
        ///
        /// This function sets the costs of the arcs.
        /// If it is not used before calling \ref run(), the costs
        /// will be set to \c 1 on all arcs.
        ///
        /// \param map An arc map storing the costs.
        /// Its \c Value type must be convertible to the \c Cost type
        /// of the algorithm.
        ///
        /// \return <tt>(*this)</tt>
        template<typename CostMap>
        NetworkSimplexSimple& costMap(const CostMap& map) {
            Arc a; _graph.first(a);
            for (; a != INVALID; _graph.next(a)) {
                _cost[getArcID(a)] = map[a];
            }
            return *this;
        }


        /// \brief Set the costs of one arc.
        ///
        /// This function sets the costs of one arcs.
        /// Done for memory reasons
        ///
        /// \param arc An arc.
        /// \param arc A cost
        ///
        /// \return <tt>(*this)</tt>
        template<typename Value>
        NetworkSimplexSimple& setCost(const Arc& arc, const Value cost) {
            _cost[getArcID(arc)] = cost;
            return *this;
        }


        /// \brief Set the supply values of the nodes.
        ///
        /// This function sets the supply values of the nodes.
        /// If neither this function nor \ref stSupply() is used before
        /// calling \ref run(), the supply of each node will be set to zero.
        ///
        /// \param map A node map storing the supply values.
        /// Its \c Value type must be convertible to the \c Value type
        /// of the algorithm.
        ///
        /// \return <tt>(*this)</tt>
        template<typename SupplyMap>
        NetworkSimplexSimple& supplyMap(const SupplyMap& map) {
            Node n; _graph.first(n);
            for (; n != INVALIDNODE; _graph.next(n)) {
                _supply[_node_id(n)] = map[n];
            }
            return *this;
        }
        template<typename SupplyMap>
        NetworkSimplexSimple& supplyMap(const SupplyMap* map1, int n1, const SupplyMap* map2, int n2) {
            Node n; _graph.first(n);
            for (; n != INVALIDNODE; _graph.next(n)) {
                if (n<n1)
                    _supply[_node_id(n)] = map1[n];
                else
                    _supply[_node_id(n)] = map2[n-n1];
            }
            return *this;
        }
        template<typename SupplyMap>
        NetworkSimplexSimple& supplyMapAll(SupplyMap val1, int n1, SupplyMap val2, int n2) {
            Node n; _graph.first(n);
            for (; n != INVALIDNODE; _graph.next(n)) {
                if (n<n1)
                    _supply[_node_id(n)] = val1;
                else
                    _supply[_node_id(n)] = val2;
            }
            return *this;
        }

        /// \brief Set single source and target nodes and a supply value.
        ///
        /// This function sets a single source node and a single target node
        /// and the required flow value.
        /// If neither this function nor \ref supplyMap() is used before
        /// calling \ref run(), the supply of each node will be set to zero.
        ///
        /// Using this function has the same effect as using \ref supplyMap()
        /// with such a map in which \c k is assigned to \c s, \c -k is
        /// assigned to \c t and all other nodes have zero supply value.
        ///
        /// \param s The source node.
        /// \param t The target node.
        /// \param k The required amount of flow from node \c s to node \c t
        /// (i.e. the supply of \c s and the demand of \c t).
        ///
        /// \return <tt>(*this)</tt>
        NetworkSimplexSimple& stSupply(const Node& s, const Node& t, Value k) {
            for (int i = 0; i != _node_num; ++i) {
                _supply[i] = 0;
            }
            _supply[_node_id(s)] =  k;
            _supply[_node_id(t)] = -k;
            return *this;
        }

        /// \brief Set the type of the supply constraints.
        ///
        /// This function sets the type of the supply/demand constraints.
        /// If it is not used before calling \ref run(), the \ref GEQ supply
        /// type will be used.
        ///
        /// For more information, see \ref SupplyType.
        ///
        /// \return <tt>(*this)</tt>
        NetworkSimplexSimple& supplyType(SupplyType supply_type) {
            _stype = supply_type;
            return *this;
        }

        /// @}

        /// \name Execution Control
        /// The algorithm can be executed using \ref run().

        /// @{

        /// \brief Run the algorithm.
        ///
        /// This function runs the algorithm.
        /// The paramters can be specified using functions \ref lowerMap(),
        /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(),
        /// \ref supplyType().
        /// For example,
        /// \code
        ///   NetworkSimplexSimple<ListDigraph> ns(graph);
        ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
        ///     .supplyMap(sup).run();
        /// \endcode
        ///
        /// This function can be called more than once. All the given parameters
        /// are kept for the next call, unless \ref resetParams() or \ref reset()
        /// is used, thus only the modified parameters have to be set again.
        /// If the underlying digraph was also modified after the construction
        /// of the class (or the last \ref reset() call), then the \ref reset()
        /// function must be called.
        ///
        /// \param pivot_rule The pivot rule that will be used during the
        /// algorithm. For more information, see \ref PivotRule.
        ///
        /// \return \c INFEASIBLE if no feasible flow exists,
        /// \n \c OPTIMAL if the problem has optimal solution
        /// (i.e. it is feasible and bounded), and the algorithm has found
        /// optimal flow and node potentials (primal and dual solutions),
        /// \n \c UNBOUNDED if the objective function of the problem is
        /// unbounded, i.e. there is a directed cycle having negative total
        /// cost and infinite upper bound.
        ///
        /// \see ProblemType, PivotRule
        /// \see resetParams(), reset()
        ProblemType run() {
#if DEBUG_LVL>0
            std::cout << "OPTIMAL = " << OPTIMAL << "\nINFEASIBLE = " << INFEASIBLE << "\nUNBOUNDED = " << UNBOUNDED << "\nMAX_ITER_REACHED" << MAX_ITER_REACHED << "\n" ;
#endif

            if (!init()) return INFEASIBLE;
#if DEBUG_LVL>0
            std::cout << "Init done, starting iterations\n";
#endif
            return start();
        }

        /// \brief Reset all the parameters that have been given before.
        ///
        /// This function resets all the paramaters that have been given
        /// before using functions \ref lowerMap(), \ref upperMap(),
        /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType().
        ///
        /// It is useful for multiple \ref run() calls. Basically, all the given
        /// parameters are kept for the next \ref run() call, unless
        /// \ref resetParams() or \ref reset() is used.
        /// If the underlying digraph was also modified after the construction
        /// of the class or the last \ref reset() call, then the \ref reset()
        /// function must be used, otherwise \ref resetParams() is sufficient.
        ///
        /// For example,
        /// \code
        ///   NetworkSimplexSimple<ListDigraph> ns(graph);
        ///
        ///   // First run
        ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
        ///     .supplyMap(sup).run();
        ///
        ///   // Run again with modified cost map (resetParams() is not called,
        ///   // so only the cost map have to be set again)
        ///   cost[e] += 100;
        ///   ns.costMap(cost).run();
        ///
        ///   // Run again from scratch using resetParams()
        ///   // (the lower bounds will be set to zero on all arcs)
        ///   ns.resetParams();
        ///   ns.upperMap(capacity).costMap(cost)
        ///     .supplyMap(sup).run();
        /// \endcode
        ///
        /// \return <tt>(*this)</tt>
        ///
        /// \see reset(), run()
        NetworkSimplexSimple& resetParams() {
            for (int i = 0; i != _node_num; ++i) {
                _supply[i] = 0;
            }
            for (int i = 0; i != _arc_num; ++i) {
                _cost[i] = 1;
            }
            _stype = GEQ;
            return *this;
        }



        int divid (int x, int y)
        {
            return (x-x%y)/y;
        }

        /// \brief Reset the internal data structures and all the parameters
        /// that have been given before.
        ///
        /// This function resets the internal data structures and all the
        /// paramaters that have been given before using functions \ref lowerMap(),
        /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(),
        /// \ref supplyType().
        ///
        /// It is useful for multiple \ref run() calls. Basically, all the given
        /// parameters are kept for the next \ref run() call, unless
        /// \ref resetParams() or \ref reset() is used.
        /// If the underlying digraph was also modified after the construction
        /// of the class or the last \ref reset() call, then the \ref reset()
        /// function must be used, otherwise \ref resetParams() is sufficient.
        ///
        /// See \ref resetParams() for examples.
        ///
        /// \return <tt>(*this)</tt>
        ///
        /// \see resetParams(), run()
        NetworkSimplexSimple& reset() {
            // Resize vectors
            _node_num = _init_nb_nodes;
            _arc_num = _init_nb_arcs;
            int all_node_num = _node_num + 1;
            int max_arc_num = _arc_num + 2 * _node_num;

            _source.resize(max_arc_num);
            _target.resize(max_arc_num);

            _cost.resize(max_arc_num);
            _supply.resize(all_node_num);
            _flow.resize(max_arc_num);
            _pi.resize(all_node_num);

            _parent.resize(all_node_num);
            _pred.resize(all_node_num);
            _forward.resize(all_node_num);
            _thread.resize(all_node_num);
            _rev_thread.resize(all_node_num);
            _succ_num.resize(all_node_num);
            _last_succ.resize(all_node_num);
            _state.resize(max_arc_num);


            //_arc_mixing=false;
            if (_arc_mixing) {
                // Store the arcs in a mixed order
                int k = std::max(int(std::sqrt(double(_arc_num))), 10);
                mixingCoeff = k;
                subsequence_length = _arc_num / mixingCoeff + 1;
                num_big_subseqiences = _arc_num % mixingCoeff;
                num_total_big_subsequence_numbers = subsequence_length * num_big_subseqiences;

                int i = 0, j = 0;
                Arc a; _graph.first(a);
                for (; a != INVALID; _graph.next(a)) {
                    _source[i] = _node_id(_graph.source(a));
                    _target[i] = _node_id(_graph.target(a));
                    //_arc_id[a] = i;
                    if ((i += k) >= _arc_num) i = ++j;
                }
            } else {
                // Store the arcs in the original order
                int i = 0;
                Arc a; _graph.first(a);
                for (; a != INVALID; _graph.next(a), ++i) {
                    _source[i] = _node_id(_graph.source(a));
                    _target[i] = _node_id(_graph.target(a));
                    //_arc_id[a] = i;
                }
            }

            // Reset parameters
            resetParams();
            return *this;
        }

        /// @}

        /// \name Query Functions
        /// The results of the algorithm can be obtained using these
        /// functions.\n
        /// The \ref run() function must be called before using them.

        /// @{

        /// \brief Return the total cost of the found flow.
        ///
        /// This function returns the total cost of the found flow.
        /// Its complexity is O(e).
        ///
        /// \note The return type of the function can be specified as a
        /// template parameter. For example,
        /// \code
        ///   ns.totalCost<double>();
        /// \endcode
        /// It is useful if the total cost cannot be stored in the \c Cost
        /// type of the algorithm, which is the default return type of the
        /// function.
        ///
        /// \pre \ref run() must be called before using this function.
        /*template <typename Number>
         Number totalCost() const {
         Number c = 0;
         for (ArcIt a(_graph); a != INVALID; ++a) {
         int i = getArcID(a);
         c += Number(_flow[i]) * Number(_cost[i]);
         }
         return c;
         }*/

        template <typename Number>
        Number totalCost() const {
            Number c = 0;

            /*#ifdef HASHMAP
             typename stdext::hash_map<int, Value>::const_iterator it;
             #else
             typename std::map<int, Value>::const_iterator it;
             #endif
             for (it = _flow.data.begin(); it!=_flow.data.end(); ++it)
             c += Number(it->second) * Number(_cost[it->first]);
             return c;*/

            for (unsigned long i=0; i<_flow.size(); i++)
                c += _flow[i] * Number(_cost[i]);
            return c;

        }

#ifndef DOXYGEN
        Cost totalCost() const {
            return totalCost<Cost>();
        }
#endif

        /// \brief Return the flow on the given arc.
        ///
        /// This function returns the flow on the given arc.
        ///
        /// \pre \ref run() must be called before using this function.
        Value flow(const Arc& a) const {
            return _flow[getArcID(a)];
        }

        /// \brief Return the flow map (the primal solution).
        ///
        /// This function copies the flow value on each arc into the given
        /// map. The \c Value type of the algorithm must be convertible to
        /// the \c Value type of the map.
        ///
        /// \pre \ref run() must be called before using this function.
        template <typename FlowMap>
        void flowMap(FlowMap &map) const {
            Arc a; _graph.first(a);
            for (; a != INVALID; _graph.next(a)) {
                map.set(a, _flow[getArcID(a)]);
            }
        }

        /// \brief Return the potential (dual value) of the given node.
        ///
        /// This function returns the potential (dual value) of the
        /// given node.
        ///
        /// \pre \ref run() must be called before using this function.
        Cost potential(const Node& n) const {
            return _pi[_node_id(n)];
        }

        /// \brief Return the potential map (the dual solution).
        ///
        /// This function copies the potential (dual value) of each node
        /// into the given map.
        /// The \c Cost type of the algorithm must be convertible to the
        /// \c Value type of the map.
        ///
        /// \pre \ref run() must be called before using this function.
        template <typename PotentialMap>
        void potentialMap(PotentialMap &map) const {
            Node n; _graph.first(n);
            for (; n != INVALID; _graph.next(n)) {
                map.set(n, _pi[_node_id(n)]);
            }
        }

        /// @}

    private:

        // Initialize internal data structures
        bool init() {
            if (_node_num == 0) return false;
            
            // Check the sum of supply values
            _sum_supply = 0;
            for (int i = 0; i != _node_num; ++i) {
                _sum_supply += _supply[i];
            }
            if ( fabs(_sum_supply) > _EPSILON ) return false;
            
			_sum_supply = 0;

            // Initialize artifical cost
            Cost ART_COST;
            if (std::numeric_limits<Cost>::is_exact) {
                ART_COST = std::numeric_limits<Cost>::max() / 2 + 1;
            } else {
                ART_COST = 0;
                for (int i = 0; i != _arc_num; ++i) {
                    if (_cost[i] > ART_COST) ART_COST = _cost[i];
                }
                ART_COST = (ART_COST + 1) * _node_num;
            }

            // Initialize arc maps
            for (int i = 0; i != _arc_num; ++i) {
                //_flow[i] = 0; //by default, the sparse matrix is empty
                _state[i] = STATE_LOWER;
            }

            // Set data for the artificial root node
            _root = _node_num;
            _parent[_root] = -1;
            _pred[_root] = -1;
            _thread[_root] = 0;
            _rev_thread[0] = _root;
            _succ_num[_root] = _node_num + 1;
            _last_succ[_root] = _root - 1;
            _supply[_root] = -_sum_supply;
            _pi[_root] = 0;

            // Add artificial arcs and initialize the spanning tree data structure
            if (_sum_supply == 0) {
                // EQ supply constraints
                _search_arc_num = _arc_num;
                _all_arc_num = _arc_num + _node_num;
                for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
                    _parent[u] = _root;
                    _pred[u] = e;
                    _thread[u] = u + 1;
                    _rev_thread[u + 1] = u;
                    _succ_num[u] = 1;
                    _last_succ[u] = u;
                    _state[e] = STATE_TREE;
                    if (_supply[u] >= 0) {
                        _forward[u] = true;
                        _pi[u] = 0;
                        _source[e] = u;
                        _target[e] = _root;
                        _flow[e] = _supply[u];
                        _cost[e] = 0;
                    } else {
                        _forward[u] = false;
                        _pi[u] = ART_COST;
                        _source[e] = _root;
                        _target[e] = u;
                        _flow[e] = -_supply[u];
                        _cost[e] = ART_COST;
                    }
                }
            }
            else if (_sum_supply > 0) {
                // LEQ supply constraints
                _search_arc_num = _arc_num + _node_num;
                int f = _arc_num + _node_num;
                for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
                    _parent[u] = _root;
                    _thread[u] = u + 1;
                    _rev_thread[u + 1] = u;
                    _succ_num[u] = 1;
                    _last_succ[u] = u;
                    if (_supply[u] >= 0) {
                        _forward[u] = true;
                        _pi[u] = 0;
                        _pred[u] = e;
                        _source[e] = u;
                        _target[e] = _root;
                        _flow[e] = _supply[u];
                        _cost[e] = 0;
                        _state[e] = STATE_TREE;
                    } else {
                        _forward[u] = false;
                        _pi[u] = ART_COST;
                        _pred[u] = f;
                        _source[f] = _root;
                        _target[f] = u;
                        _flow[f] = -_supply[u];
                        _cost[f] = ART_COST;
                        _state[f] = STATE_TREE;
                        _source[e] = u;
                        _target[e] = _root;
                        //_flow[e] = 0;  //by default, the sparse matrix is empty
                        _cost[e] = 0;
                        _state[e] = STATE_LOWER;
                        ++f;
                    }
                }
                _all_arc_num = f;
            }
            else {
                // GEQ supply constraints
                _search_arc_num = _arc_num + _node_num;
                int f = _arc_num + _node_num;
                for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
                    _parent[u] = _root;
                    _thread[u] = u + 1;
                    _rev_thread[u + 1] = u;
                    _succ_num[u] = 1;
                    _last_succ[u] = u;
                    if (_supply[u] <= 0) {
                        _forward[u] = false;
                        _pi[u] = 0;
                        _pred[u] = e;
                        _source[e] = _root;
                        _target[e] = u;
                        _flow[e] = -_supply[u];
                        _cost[e] = 0;
                        _state[e] = STATE_TREE;
                    } else {
                        _forward[u] = true;
                        _pi[u] = -ART_COST;
                        _pred[u] = f;
                        _source[f] = u;
                        _target[f] = _root;
                        _flow[f] = _supply[u];
                        _state[f] = STATE_TREE;
                        _cost[f] = ART_COST;
                        _source[e] = _root;
                        _target[e] = u;
                        //_flow[e] = 0; //by default, the sparse matrix is empty
                        _cost[e] = 0;
                        _state[e] = STATE_LOWER;
                        ++f;
                    }
                }
                _all_arc_num = f;
            }

            return true;
        }

        // Find the join node
        void findJoinNode() {
            int u = _source[in_arc];
            int v = _target[in_arc];
            while (u != v) {
                if (_succ_num[u] < _succ_num[v]) {
                    u = _parent[u];
                } else {
                    v = _parent[v];
                }
            }
            join = u;
        }

        // Find the leaving arc of the cycle and returns true if the
        // leaving arc is not the same as the entering arc
        bool findLeavingArc() {
            // Initialize first and second nodes according to the direction
            // of the cycle
            if (_state[in_arc] == STATE_LOWER) {
                first  = _source[in_arc];
                second = _target[in_arc];
            } else {
                first  = _target[in_arc];
                second = _source[in_arc];
            }
            delta = INF;
            int result = 0;
            Value d;
            int e;

            // Search the cycle along the path form the first node to the root
            for (int u = first; u != join; u = _parent[u]) {
                e = _pred[u];
                d = _forward[u] ? _flow[e] : INF ;
                if (d < delta) {
                    delta = d;
                    u_out = u;
                    result = 1;
                }
            }
            // Search the cycle along the path form the second node to the root
            for (int u = second; u != join; u = _parent[u]) {
                e = _pred[u];
                d = _forward[u] ? INF  : _flow[e];
                if (d <= delta) {
                    delta = d;
                    u_out = u;
                    result = 2;
                }
            }

            if (result == 1) {
                u_in = first;
                v_in = second;
            } else {
                u_in = second;
                v_in = first;
            }
            return result != 0;
        }

        // Change _flow and _state vectors
        void changeFlow(bool change) {
            // Augment along the cycle
            if (delta > 0) {
                Value val = _state[in_arc] * delta;
                _flow[in_arc] += val;
                for (int u = _source[in_arc]; u != join; u = _parent[u]) {
                    _flow[_pred[u]] += _forward[u] ? -val : val;
                }
                for (int u = _target[in_arc]; u != join; u = _parent[u]) {
                    _flow[_pred[u]] += _forward[u] ? val : -val;
                }
            }
            // Update the state of the entering and leaving arcs
            if (change) {
                _state[in_arc] = STATE_TREE;
                _state[_pred[u_out]] =
                (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
            } else {
                _state[in_arc] = -_state[in_arc];
            }
        }

        // Update the tree structure
        void updateTreeStructure() {
            int u, w;
            int old_rev_thread = _rev_thread[u_out];
            int old_succ_num = _succ_num[u_out];
            int old_last_succ = _last_succ[u_out];
            v_out = _parent[u_out];

            u = _last_succ[u_in];  // the last successor of u_in
            right = _thread[u];    // the node after it

            // Handle the case when old_rev_thread equals to v_in
            // (it also means that join and v_out coincide)
            if (old_rev_thread == v_in) {
                last = _thread[_last_succ[u_out]];
            } else {
                last = _thread[v_in];
            }

            // Update _thread and _parent along the stem nodes (i.e. the nodes
            // between u_in and u_out, whose parent have to be changed)
            _thread[v_in] = stem = u_in;
            _dirty_revs.clear();
            _dirty_revs.push_back(v_in);
            par_stem = v_in;
            while (stem != u_out) {
                // Insert the next stem node into the thread list
                new_stem = _parent[stem];
                _thread[u] = new_stem;
                _dirty_revs.push_back(u);

                // Remove the subtree of stem from the thread list
                w = _rev_thread[stem];
                _thread[w] = right;
                _rev_thread[right] = w;

                // Change the parent node and shift stem nodes
                _parent[stem] = par_stem;
                par_stem = stem;
                stem = new_stem;

                // Update u and right
                u = _last_succ[stem] == _last_succ[par_stem] ?
                _rev_thread[par_stem] : _last_succ[stem];
                right = _thread[u];
            }
            _parent[u_out] = par_stem;
            _thread[u] = last;
            _rev_thread[last] = u;
            _last_succ[u_out] = u;

            // Remove the subtree of u_out from the thread list except for
            // the case when old_rev_thread equals to v_in
            // (it also means that join and v_out coincide)
            if (old_rev_thread != v_in) {
                _thread[old_rev_thread] = right;
                _rev_thread[right] = old_rev_thread;
            }

            // Update _rev_thread using the new _thread values
            for (int i = 0; i != int(_dirty_revs.size()); ++i) {
                u = _dirty_revs[i];
                _rev_thread[_thread[u]] = u;
            }

            // Update _pred, _forward, _last_succ and _succ_num for the
            // stem nodes from u_out to u_in
            int tmp_sc = 0, tmp_ls = _last_succ[u_out];
            u = u_out;
            while (u != u_in) {
                w = _parent[u];
                _pred[u] = _pred[w];
                _forward[u] = !_forward[w];
                tmp_sc += _succ_num[u] - _succ_num[w];
                _succ_num[u] = tmp_sc;
                _last_succ[w] = tmp_ls;
                u = w;
            }
            _pred[u_in] = in_arc;
            _forward[u_in] = ((unsigned int)u_in == _source[in_arc]);
            _succ_num[u_in] = old_succ_num;

            // Set limits for updating _last_succ form v_in and v_out
            // towards the root
            int up_limit_in = -1;
            int up_limit_out = -1;
            if (_last_succ[join] == v_in) {
                up_limit_out = join;
            } else {
                up_limit_in = join;
            }

            // Update _last_succ from v_in towards the root
            for (u = v_in; u != up_limit_in && _last_succ[u] == v_in;
                 u = _parent[u]) {
                _last_succ[u] = _last_succ[u_out];
            }
            // Update _last_succ from v_out towards the root
            if (join != old_rev_thread && v_in != old_rev_thread) {
                for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
                     u = _parent[u]) {
                    _last_succ[u] = old_rev_thread;
                }
            } else {
                for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
                     u = _parent[u]) {
                    _last_succ[u] = _last_succ[u_out];
                }
            }

            // Update _succ_num from v_in to join
            for (u = v_in; u != join; u = _parent[u]) {
                _succ_num[u] += old_succ_num;
            }
            // Update _succ_num from v_out to join
            for (u = v_out; u != join; u = _parent[u]) {
                _succ_num[u] -= old_succ_num;
            }
        }

        // Update potentials
        void updatePotential() {
            Cost sigma = _forward[u_in] ?
            _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
            _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
            // Update potentials in the subtree, which has been moved
            int end = _thread[_last_succ[u_in]];
            for (int u = u_in; u != end; u = _thread[u]) {
                _pi[u] += sigma;
            }
        }

        // Heuristic initial pivots
        bool initialPivots() {
            Value curr, total = 0;
            std::vector<Node> supply_nodes, demand_nodes;
            Node u; _graph.first(u);
            for (; u != INVALIDNODE; _graph.next(u)) {
                curr = _supply[_node_id(u)];
                if (curr > 0) {
                    total += curr;
                    supply_nodes.push_back(u);
                }
                else if (curr < 0) {
                    demand_nodes.push_back(u);
                }
            }
            if (_sum_supply > 0) total -= _sum_supply;
            if (total <= 0) return true;

            IntVector arc_vector;
            if (_sum_supply >= 0) {
                if (supply_nodes.size() == 1 && demand_nodes.size() == 1) {
                    // Perform a reverse graph search from the sink to the source
                    //typename GR::template NodeMap<bool> reached(_graph, false);
                    BoolVector reached(_node_num, false);
                    Node s = supply_nodes[0], t = demand_nodes[0];
                    std::vector<Node> stack;
                    reached[t] = true;
                    stack.push_back(t);
                    while (!stack.empty()) {
                        Node u, v = stack.back();
                        stack.pop_back();
                        if (v == s) break;
                        Arc a; _graph.firstIn(a, v);
                        for (; a != INVALID; _graph.nextIn(a)) {
                            if (reached[u = _graph.source(a)]) continue;
                            int j = getArcID(a);
                            if (INF >= total) {
                                arc_vector.push_back(j);
                                reached[u] = true;
                                stack.push_back(u);
                            }
                        }
                    }
                } else {
                    // Find the min. cost incomming arc for each demand node
                    for (int i = 0; i != int(demand_nodes.size()); ++i) {
                        Node v = demand_nodes[i];
                        Cost c, min_cost = std::numeric_limits<Cost>::max();
                        Arc min_arc = INVALID;
                        Arc a; _graph.firstIn(a, v);
                        for (; a != INVALID; _graph.nextIn(a)) {
                            c = _cost[getArcID(a)];
                            if (c < min_cost) {
                                min_cost = c;
                                min_arc = a;
                            }
                        }
                        if (min_arc != INVALID) {
                            arc_vector.push_back(getArcID(min_arc));
                        }
                    }
                }
            } else {
                // Find the min. cost outgoing arc for each supply node
                for (int i = 0; i != int(supply_nodes.size()); ++i) {
                    Node u = supply_nodes[i];
                    Cost c, min_cost = std::numeric_limits<Cost>::max();
                    Arc min_arc = INVALID;
                    Arc a; _graph.firstOut(a, u);
                    for (; a != INVALID; _graph.nextOut(a)) {
                        c = _cost[getArcID(a)];
                        if (c < min_cost) {
                            min_cost = c;
                            min_arc = a;
                        }
                    }
                    if (min_arc != INVALID) {
                        arc_vector.push_back(getArcID(min_arc));
                    }
                }
            }

            // Perform heuristic initial pivots
            for (int i = 0; i != int(arc_vector.size()); ++i) {
                in_arc = arc_vector[i];
                // l'erreur est probablement ici...
                if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -
                                      _pi[_target[in_arc]]) >= 0) continue;
                findJoinNode();
                bool change = findLeavingArc();
                if (delta >= MAX) return false;
                changeFlow(change);
                if (change) {
                    updateTreeStructure();
                    updatePotential();
                }
            }
            return true;
        }

        // Execute the algorithm
        ProblemType start() {
            return start<BlockSearchPivotRule>();
        }

        template <typename PivotRuleImpl>
        ProblemType start() {
            PivotRuleImpl pivot(*this);
			ProblemType retVal = OPTIMAL;

            // Perform heuristic initial pivots
            if (!initialPivots()) return UNBOUNDED;

            int iter_number=0;
            //pivot.setDantzig(true);
            // Execute the Network Simplex algorithm
            while (pivot.findEnteringArc()) {
                if(max_iter > 0 && ++iter_number>=max_iter&&max_iter>0){
                    char errMess[1000];
                    sprintf( errMess, "RESULT MIGHT BE INACURATE\nMax number of iteration reached, currently \%d. Sometimes iterations go on in cycle even though the solution has been reached, to check if it's the case here have a look at the minimal reduced cost. If it is very close to machine precision, you might actually have the correct solution, if not try setting the maximum number of iterations a bit higher\n",iter_number );
                    std::cerr << errMess;
					retVal = MAX_ITER_REACHED;
                    break;
                }
#if DEBUG_LVL>0
                if(iter_number>MAX_DEBUG_ITER)
                    break;
                if(iter_number%1000==0||iter_number%1000==1){
                    double curCost=totalCost();
                    double sumFlow=0;
                    double a;
                    a= (fabs(_pi[_source[in_arc]])>=fabs(_pi[_target[in_arc]])) ? fabs(_pi[_source[in_arc]]) : fabs(_pi[_target[in_arc]]);
                    a=a>=fabs(_cost[in_arc])?a:fabs(_cost[in_arc]);
                    for (int i=0; i<_flow.size(); i++) {
                        sumFlow+=_state[i]*_flow[i];
                    }
                    std::cout << "Sum of the flow " << std::setprecision(20) << sumFlow << "\n" << iter_number << " iterations, current cost=" << curCost << "\nReduced cost=" << _state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -_pi[_target[in_arc]]) << "\nPrecision = "<< -EPSILON*(a) << "\n";
                    std::cout << "Arc in = (" << _node_id(_source[in_arc]) << ", " << _node_id(_target[in_arc]) <<")\n";
                    std::cout << "Supplies = (" << _supply[_source[in_arc]] << ", " << _supply[_target[in_arc]] << ")\n";
                    std::cout << _cost[in_arc] << "\n";
                    std::cout << _pi[_source[in_arc]] << "\n";
                    std::cout << _pi[_target[in_arc]] << "\n";
                    std::cout << a << "\n";
                }
#endif

                findJoinNode();
                bool change = findLeavingArc();
                if (delta >= MAX) return UNBOUNDED;
                changeFlow(change);
                if (change) {
                    updateTreeStructure();
                    updatePotential();
                }
#if DEBUG_LVL>0
                else{
                    std::cout << "No change\n";
                }
#endif
#if DEBUG_LVL>1
                std::cout << "Arc in = (" << _source[in_arc] << ", " << _target[in_arc] << ")\n";
#endif

            }


#if DEBUG_LVL>0
                double curCost=totalCost();
                double sumFlow=0;
                double a;
                a= (fabs(_pi[_source[in_arc]])>=fabs(_pi[_target[in_arc]])) ? fabs(_pi[_source[in_arc]]) : fabs(_pi[_target[in_arc]]);
                a=a>=fabs(_cost[in_arc])?a:fabs(_cost[in_arc]);
                for (int i=0; i<_flow.size(); i++) {
                    sumFlow+=_state[i]*_flow[i];
                }
            
                std::cout << "Sum of the flow " << std::setprecision(20) << sumFlow << "\n" << niter << " iterations, current cost=" << curCost << "\nReduced cost=" << _state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -_pi[_target[in_arc]]) << "\nPrecision = "<< -EPSILON*(a) << "\n";
            
                std::cout << "Arc in = (" << _node_id(_source[in_arc]) << ", " << _node_id(_target[in_arc]) <<")\n";
                std::cout << "Supplies = (" << _supply[_source[in_arc]] << ", " << _supply[_target[in_arc]] << ")\n";

#endif

#if DEBUG_LVL>1
            sumFlow=0;
            for (int i=0; i<_flow.size(); i++) {
                sumFlow+=_state[i]*_flow[i];
                if (_state[i]==STATE_TREE) {
                    std::cout << "Non zero value at (" << _node_num+1-_source[i] << ", " << _node_num+1-_target[i] << ")\n";
                }
            }
            std::cout << "Sum of the flow " << sumFlow << "\n"<< niter <<" iterations, current cost=" << totalCost() << "\n";
#endif
            // Check feasibility
			if( retVal == OPTIMAL){
                for (int e = _search_arc_num; e != _all_arc_num; ++e) {
                    if (_flow[e] != 0){
                        if (abs(_flow[e]) > EPSILON)
                            return INFEASIBLE;
                        else
                            _flow[e]=0;

                    }
                }
			}

            // Shift potentials to meet the requirements of the GEQ/LEQ type
            // optimality conditions
            if (_sum_supply == 0) {
                if (_stype == GEQ) {
                    Cost max_pot = -std::numeric_limits<Cost>::max();
                    for (int i = 0; i != _node_num; ++i) {
                        if (_pi[i] > max_pot) max_pot = _pi[i];
                    }
                    if (max_pot > 0) {
                        for (int i = 0; i != _node_num; ++i)
                            _pi[i] -= max_pot;
                    }
                } else {
                    Cost min_pot = std::numeric_limits<Cost>::max();
                    for (int i = 0; i != _node_num; ++i) {
                        if (_pi[i] < min_pot) min_pot = _pi[i];
                    }
                    if (min_pot < 0) {
                        for (int i = 0; i != _node_num; ++i)
                            _pi[i] -= min_pot;
                    }
                }
            }

            return retVal;
        }

    }; //class NetworkSimplexSimple

    ///@}

} //namespace lemon

#endif //LEMON_NETWORK_SIMPLEX_H