/* graph.h */
/*
###################################################################
#                                                                 #
#    MAXFLOW - software for computing mincut/maxflow in a graph   #
#                        Version 3.0                              #
#    http://www.cs.adastral.ucl.ac.uk/~vnk/software.html          #
#                                                                 #
#    Yuri Boykov (yuri@csd.uwo.ca)                                #
#    Vladimir Kolmogorov (vnk@adastral.ucl.ac.uk)                 #
#    2001-2006                                                    #
#                                                                 #
###################################################################

1. Introduction.

This software library implements the maxflow algorithm described in

        "An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision."
        Yuri Boykov and Vladimir Kolmogorov.
        In IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI),
        September 2004

This algorithm was developed by Yuri Boykov and Vladimir Kolmogorov
at Siemens Corporate Research. To make it available for public use,
it was later reimplemented by Vladimir Kolmogorov based on open publications.

If you use this software for research purposes, you should cite
the aforementioned paper in any resulting publication.

----------------------------------------------------------------------

REUSING TREES:

Starting with version 3.0, there is a also an option of reusing search
trees from one maxflow computation to the next, as described in

        "Efficiently Solving Dynamic Markov Random Fields Using Graph Cuts."
        Pushmeet Kohli and Philip H.S. Torr
        International Conference on Computer Vision (ICCV), 2005

If you use this option, you should cite
the aforementioned paper in any resulting publication.

Tested under windows, Visual C++ 6.0 compiler and unix (SunOS 5.8
and RedHat Linux 7.0, GNU c++ compiler).

##################################################################

2. License & disclaimer.

    Copyright 2001 Vladimir Kolmogorov (vnk@adastral.ucl.ac.uk), Yuri Boykov (yuri@csd.uwo.ca).

    This software can be used for research purposes only.

    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
    A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
    OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
    LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
    DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
    THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
    (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
    OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

##################################################################
*/


#pragma once

#include <string.h>
#include "animaBlock.h"

#include <assert.h>
// NOTE: in UNIX you need to use -DNDEBUG preprocessor option to supress assert's!!!



// captype: type of edge capacities (excluding t-links)
// tcaptype: type of t-links (edges between nodes and terminals)
// flowtype: type of total flow
//
// Current instantiations are in instances.inc


namespace anima {

template <typename captype, typename tcaptype, typename flowtype> class Graph
{
public:
    typedef enum
    {
        SOURCE	= 0,
        SINK	= 1
              } termtype; // terminals
    typedef int node_id;

    /////////////////////////////////////////////////////////////////////////
    //                     BASIC INTERFACE FUNCTIONS                       //
    //              (should be enough for most applications)               //
    /////////////////////////////////////////////////////////////////////////

    // Constructor.
    // The first argument gives an estimate of the maximum number of nodes that can be added
    // to the graph, and the second argument is an estimate of the maximum number of edges.
    // The last (optional) argument is the pointer to the function which will be called
    // if an error occurs; an error message is passed to this function.
    // If this argument is omitted, exit(1) will be called.
    //
    // IMPORTANT: It is possible to add more nodes to the graph than node_num_max
    // (and node_num_max can be zero). However, if the count is exceeded, then
    // the internal memory is reallocated (increased by 50%) which is expensive.
    // Also, temporarily the amount of allocated memory would be more than twice than needed.
    // Similarly for edges.
    // If you wish to avoid this overhead, you can download version 2.2, where nodes and edges are stored in blocks.
    Graph(int node_num_max, int edge_num_max, void (*err_function)(char *) = NULL);

    // Destructor
    ~Graph();

    // Adds node(s) to the graph. By default, one node is added (num=1); then first call returns 0, second call returns 1, and so on.
    // If num>1, then several nodes are added, and node_id of the first one is returned.
    // IMPORTANT: see note about the constructor
    node_id add_node(int num = 1);

    // Adds a bidirectional edge between 'i' and 'j' with the weights 'cap' and 'rev_cap'.
    // IMPORTANT: see note about the constructor
    void add_edge(node_id i, node_id j, captype cap, captype rev_cap);

    // Adds new edges 'SOURCE->i' and 'i->SINK' with corresponding weights.
    // Can be called multiple times for each node.
    // Weights can be negative.
    // NOTE: the number of such edges is not counted in edge_num_max.
    //       No internal memory is allocated by this call.
    void add_tweights(node_id i, tcaptype cap_source, tcaptype cap_sink);


    // Computes the maxflow. Can be called several times.
    // FOR DESCRIPTION OF reuse_trees, SEE mark_node().
    // FOR DESCRIPTION OF changed_list, SEE remove_from_changed_list().
    flowtype maxflow(bool reuse_trees = false, Block<node_id>* changed_list = NULL);

    // After the maxflow is computed, this function returns to which
    // segment the node 'i' belongs (Graph<captype,tcaptype,flowtype>::SOURCE or Graph<captype,tcaptype,flowtype>::SINK).
    //
    // Occasionally there may be several minimum cuts. If a node can be assigned
    // to both the source and the sink, then default_segm is returned.
    termtype what_segment(node_id i, termtype default_segm = SOURCE);



    //////////////////////////////////////////////
    //       ADVANCED INTERFACE FUNCTIONS       //
    //      (provide access to the graph)       //
    //////////////////////////////////////////////

    //private:
public:
    struct node;
    struct arc;

public:

    ////////////////////////////
    // 1. Reallocating graph. //
    ////////////////////////////

    // Removes all nodes and edges.
    // After that functions add_node() and add_edge() must be called again.
    //
    // Advantage compared to deleting Graph and allocating it again:
    // no calls to delete/new (which could be quite slow).
    //
    // If the graph structure stays the same, then an alternative
    // is to go through all nodes/edges and set new residual capacities
    // (see functions below).
    void reset();

    ////////////////////////////////////////////////////////////////////////////////
    // 2. Functions for getting pointers to arcs and for reading graph structure. //
    //    NOTE: adding new arcs may invalidate these pointers (if reallocation    //
    //    happens). So it's best not to add arcs while reading graph structure.   //
    ////////////////////////////////////////////////////////////////////////////////

    // The following two functions return arcs in the same order that they
    // were added to the graph. NOTE: for each call add_edge(i,j,cap,cap_rev)
    // the first arc returned will be i->j, and the second j->i.
    // If there are no more arcs, then the function can still be called, but
    // the returned arc_id is undetermined.
    typedef arc* arc_id;
    arc_id get_first_arc();
    arc_id get_next_arc(arc_id a);

    // other functions for reading graph structure
    int get_node_num() { return node_num; }
    int get_arc_num() { return (int)(arc_last - arcs); }
    void get_arc_ends(arc_id a, node_id& i, node_id& j); // returns i,j to that a = i->j

    ///////////////////////////////////////////////////
    // 3. Functions for reading residual capacities. //
    ///////////////////////////////////////////////////

    // returns residual capacity of SOURCE->i minus residual capacity of i->SINK
    tcaptype get_trcap(node_id i);
    // returns residual capacity of arc a
    captype get_rcap(arc* a);

    /////////////////////////////////////////////////////////////////
    // 4. Functions for setting residual capacities.               //
    //    NOTE: If these functions are used, the value of the flow //
    //    returned by maxflow() will not be valid!                 //
    /////////////////////////////////////////////////////////////////

    void set_trcap(node_id i, tcaptype trcap);
    void set_rcap(arc* a, captype rcap);

    ////////////////////////////////////////////////////////////////////
    // 5. Functions related to reusing trees & list of changed nodes. //
    ////////////////////////////////////////////////////////////////////

    // If flag reuse_trees is true while calling maxflow(), then search trees
    // are reused from previous maxflow computation.
    // In this case before calling maxflow() the user must
    // specify which parts of the graph have changed by calling mark_node():
    //   add_tweights(i),set_trcap(i)    => call mark_node(i)
    //   add_edge(i,j),set_rcap(a)       => call mark_node(i); mark_node(j)
    //
    // This option makes sense only if a small part of the graph is changed.
    // The initialization procedure goes only through marked nodes then.
    //
    // mark_node(i) can either be called before or after graph modification.
    // Can be called more than once per node, but calls after the first one
    // do not have any effect.
    //
    // NOTE:
    //   - This option cannot be used in the first call to maxflow().
    //   - It is not necessary to call mark_node() if the change is ``not essential'',
    //     i.e. sign(trcap) is preserved for a node and zero/nonzero status is preserved for an arc.
    //   - To check that you marked all necessary nodes, you can call maxflow(false) after calling maxflow(true).
    //     If everything is correct, the two calls must return the same value of flow. (Useful for debugging).
    void mark_node(node_id i);

    // If changed_list is not NULL while calling maxflow(), then the algorithm
    // keeps a list of nodes which could potentially have changed their segmentation label.
    // Nodes which are not in the list are guaranteed to keep their old segmentation label (SOURCE or SINK).
    // Example usage:
    //
    //		typedef Graph<int,int,int> G;
    //		G* g = new Graph(nodeNum, edgeNum);
    //		Block<G::node_id>* changed_list = new Block<G::node_id>(128);
    //
    //		... // add nodes and edges
    //
    //		g->maxflow(); // first call should be without arguments
    //		for (int iter=0; iter<10; iter++)
    //		{
    //			... // change graph, call mark_node() accordingly
    //
    //			g->maxflow(true, changed_list);
    //			G::node_id* ptr;
    //			for (ptr=changed_list->ScanFirst(); ptr; ptr=changed_list->ScanNext())
    //			{
    //				G::node_id i = *ptr; assert(i>=0 && i<nodeNum);
    //				g->remove_from_changed_list(i);
    //				// do something with node i...
    //				if (g->what_segment(i) == G::SOURCE) { ... }
    //			}
    //			changed_list->Reset();
    //		}
    //		delete changed_list;
    //
    // NOTE:
    //  - If changed_list option is used, then reuse_trees must be used as well.
    //  - In the example above, the user may omit calls g->remove_from_changed_list(i) and changed_list->Reset() in a given iteration.
    //    Then during the next call to maxflow(true, &changed_list) new nodes will be added to changed_list.
    //  - If the next call to maxflow() does not use option reuse_trees, then calling remove_from_changed_list()
    //    is not necessary. ("changed_list->Reset()" or "delete changed_list" should still be called, though).
    void remove_from_changed_list(node_id i)
    {
        assert(i>=0 && i<node_num && nodes[i].is_in_changed_list);
        nodes[i].is_in_changed_list = 0;
    }






    /////////////////////////////////////////////////////////////////////////
    /////////////////////////////////////////////////////////////////////////
    /////////////////////////////////////////////////////////////////////////

    //private:
public:
    // internal variables and functions

    struct node
    {
        arc			*first;		// first outcoming arc

        arc			*parent;	// node's parent
        node		*next;		// pointer to the next active node
        //   (or to itself if it is the last node in the list)
        int			TS;			// timestamp showing when DIST was computed
        int			DIST;		// distance to the terminal
        int			is_sink : 1;	// flag showing whether the node is in the source or in the sink tree (if parent!=NULL)
        int			is_marked : 1;	// set by mark_node()
        int			is_in_changed_list : 1; // set by maxflow if

        tcaptype	tr_cap;		// if tr_cap > 0 then tr_cap is residual capacity of the arc SOURCE->node
        // otherwise         -tr_cap is residual capacity of the arc node->SINK

    };

    struct arc
    {
        node		*head;		// node the arc points to
        arc			*next;		// next arc with the same originating node
        arc			*sister;	// reverse arc

        captype		r_cap;		// residual capacity
    };

    struct nodeptr
    {
        node    	*ptr;
        nodeptr		*next;
    };
    static const int NODEPTR_BLOCK_SIZE = 128;

    node				*nodes, *node_last, *node_max; // node_last = nodes+node_num, node_max = nodes+node_num_max;
    arc					*arcs, *arc_last, *arc_max; // arc_last = arcs+2*edge_num, arc_max = arcs+2*edge_num_max;

    int					node_num;

    DBlock<nodeptr>		*nodeptr_block;

    void	(*error_function)(char *);	// this function is called if a error occurs,
    // with a corresponding error message
    // (or exit(1) is called if it's NULL)

    flowtype			flow;		// total flow

    // reusing trees & list of changed pixels
    int					maxflow_iteration; // counter
    Block<node_id>		*changed_list;

    /////////////////////////////////////////////////////////////////////////

    node				*queue_first[2], *queue_last[2];	// list of active nodes
    nodeptr				*orphan_first, *orphan_last;		// list of pointers to orphans
    int					TIME;								// monotonically increasing global counter

    /////////////////////////////////////////////////////////////////////////

    void reallocate_nodes(int num); // num is the number of new nodes
    void reallocate_arcs();

    // functions for processing active list
    void set_active(node *i);
    node *next_active();

    // functions for processing orphans list
    void set_orphan_front(node* i); // add to the beginning of the list
    void set_orphan_rear(node* i);  // add to the end of the list

    void add_to_changed_list(node* i);

    void maxflow_init();             // called if reuse_trees == false
    void maxflow_reuse_trees_init(); // called if reuse_trees == true
    void augment(arc *middle_arc);
    void process_source_orphan(node *i);
    void process_sink_orphan(node *i);

    void test_consistency(node* current_node=NULL); // debug function
};











///////////////////////////////////////
// Implementation - inline functions //
///////////////////////////////////////

template <typename captype, typename tcaptype, typename flowtype>
        inline Graph<captype, tcaptype, flowtype>::Graph(int node_num_max, int edge_num_max, void (*err_function)(char *))
            : node_num(0),
            nodeptr_block(NULL),
            error_function(err_function)
{
    if (node_num_max < 16) node_num_max = 16;
    if (edge_num_max < 16) edge_num_max = 16;
    arcs = (arc*) malloc(2*edge_num_max*sizeof(arc));
    nodes = (node*) malloc(node_num_max*sizeof(node));
    if (!nodes || !arcs) {
        free(arcs);
        throw std::bad_alloc();
    }
    node_last = nodes;
    node_max = nodes + node_num_max;
    arc_last = arcs;
    arc_max = arcs + 2*edge_num_max;

    maxflow_iteration = 0;
    flow = 0;
}

template <typename captype, typename tcaptype, typename flowtype>
        inline Graph<captype,tcaptype,flowtype>::~Graph()
{
    if (nodeptr_block)
    {
        delete nodeptr_block;
        nodeptr_block = NULL;
    }
    free(nodes);
    free(arcs);
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::reset()
{
    node_last = nodes;
    arc_last = arcs;
    node_num = 0;

    if (nodeptr_block)
    {
        delete nodeptr_block;
        nodeptr_block = NULL;
    }

    maxflow_iteration = 0;
    flow = 0;
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::reallocate_nodes(int num)
{
    int node_num_max = (int)(node_max - nodes);
    node* nodes_old = nodes;

    node_num_max += node_num_max / 2;
    if (node_num_max < node_num + num) node_num_max = node_num + num;
    nodes = (node*) realloc(nodes_old, node_num_max*sizeof(node));
    if (!nodes) { /*if (error_function) (*error_function)("Not enough memory!");*/ exit(1); }

    node_last = nodes + node_num;
    node_max = nodes + node_num_max;

    if (nodes != nodes_old)
    {
        arc* a;
        for (a=arcs; a<arc_last; a++)
        {
            a->head = (node*) ((char*)a->head + (((char*) nodes) - ((char*) nodes_old)));
        }
    }
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::reallocate_arcs()
{

    int arc_num_max = (int)(arc_max - arcs);
    int arc_num = (int)(arc_last - arcs);
    arc* arcs_old = arcs;

    arc_num_max += arc_num_max / 2; if (arc_num_max & 1) arc_num_max ++;
    arcs = (arc*) realloc(arcs_old, arc_num_max*sizeof(arc));
    if (!arcs) { /*if (error_function) (*error_function)("Not enough memory!"); */ exit(1); }

    arc_last = arcs + arc_num;
    arc_max = arcs + arc_num_max;

    if (arcs != arcs_old)
    {
        node* i;
        arc* a;
        for (i=nodes; i<node_last; i++)
        {
            if (i->first) i->first = (arc*) ((char*)i->first + (((char*) arcs) - ((char*) arcs_old)));
        }
        for (a=arcs; a<arc_last; a++)
        {
            if (a->next) a->next = (arc*) ((char*)a->next + (((char*) arcs) - ((char*) arcs_old)));
            a->sister = (arc*) ((char*)a->sister + (((char*) arcs) - ((char*) arcs_old)));
        }
    }
}

template <typename captype, typename tcaptype, typename flowtype>
        inline typename Graph<captype,tcaptype,flowtype>::node_id Graph<captype,tcaptype,flowtype>::add_node(int num)
{
    assert(num > 0);

    if (node_last + num > node_max) reallocate_nodes(num);

    if (num == 1)
    {
        node_last -> first = NULL;
        node_last -> tr_cap = 0;
        node_last -> is_marked = 0;
        node_last -> is_in_changed_list = 0;

        node_last ++;
        return node_num ++;
    }
    else
    {
        memset(node_last, 0, num*sizeof(node));

        node_id i = node_num;
        node_num += num;
        node_last += num;
        return i;
    }
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::add_tweights(node_id i, tcaptype cap_source, tcaptype cap_sink)
{
    assert(i >= 0 && i < node_num);

    tcaptype delta = nodes[i].tr_cap;
    if (delta > 0) cap_source += delta;
    else           cap_sink   -= delta;
    flow += (cap_source < cap_sink) ? cap_source : cap_sink;
    nodes[i].tr_cap = cap_source - cap_sink;
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::add_edge(node_id _i, node_id _j, captype cap, captype rev_cap)
{
    assert(_i >= 0 && _i < node_num);
    assert(_j >= 0 && _j < node_num);
    assert(_i != _j);
    assert(cap >= 0);
    assert(rev_cap >= 0);

    if (arc_last == arc_max) reallocate_arcs();

    arc *a = arc_last ++;
    arc *a_rev = arc_last ++;

    node* i = nodes + _i;
    node* j = nodes + _j;

    a -> sister = a_rev;
    a_rev -> sister = a;
    a -> next = i -> first;
    i -> first = a;
    a_rev -> next = j -> first;
    j -> first = a_rev;
    a -> head = j;
    a_rev -> head = i;
    a -> r_cap = cap;
    a_rev -> r_cap = rev_cap;
}

template <typename captype, typename tcaptype, typename flowtype>
        inline typename Graph<captype,tcaptype,flowtype>::arc* Graph<captype,tcaptype,flowtype>::get_first_arc()
{
    return arcs;
}

template <typename captype, typename tcaptype, typename flowtype>
        inline typename Graph<captype,tcaptype,flowtype>::arc* Graph<captype,tcaptype,flowtype>::get_next_arc(arc* a)
{
    return a + 1;
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::get_arc_ends(arc* a, node_id& i, node_id& j)
{
    assert(a >= arcs && a < arc_last);
    i = (node_id) (a->sister->head - nodes);
    j = (node_id) (a->head - nodes);
}

template <typename captype, typename tcaptype, typename flowtype>
        inline tcaptype Graph<captype,tcaptype,flowtype>::get_trcap(node_id i)
{
    assert(i>=0 && i<node_num);
    return nodes[i].tr_cap;
}

template <typename captype, typename tcaptype, typename flowtype>
        inline captype Graph<captype,tcaptype,flowtype>::get_rcap(arc* a)
{
    assert(a >= arcs && a < arc_last);
    return a->r_cap;
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::set_trcap(node_id i, tcaptype trcap)
{
    assert(i>=0 && i<node_num);
    nodes[i].tr_cap = trcap;
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::set_rcap(arc* a, captype rcap)
{
    assert(a >= arcs && a < arc_last);
    a->r_cap = rcap;
}


template <typename captype, typename tcaptype, typename flowtype>
        inline typename Graph<captype,tcaptype,flowtype>::termtype Graph<captype,tcaptype,flowtype>::what_segment(node_id i, termtype default_segm)
{
    if (nodes[i].parent)
    {
        return (nodes[i].is_sink) ? SINK : SOURCE;
    }
    else
    {
        return default_segm;
    }
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::mark_node(node_id _i)
{
    node* i = nodes + _i;
    if (!i->next)
    {
        /* it's not in the list yet */
        if (queue_last[1]) queue_last[1] -> next = i;
        else               queue_first[1]        = i;
        queue_last[1] = i;
        i -> next = i;
    }
    i->is_marked = 1;
}

/*
        special constants for node->parent
*/
#define TERMINAL ( (arc *) 1 )		/* to terminal */
#define ORPHAN   ( (arc *) 2 )		/* orphan */


#define INFINITE_D ((int)(((unsigned)-1)/2))		/* infinite distance to the terminal */

/***********************************************************************/

/*
        Functions for processing active list.
        i->next points to the next node in the list
        (or to i, if i is the last node in the list).
        If i->next is NULL iff i is not in the list.

        There are two queues. Active nodes are added
        to the end of the second queue and read from
        the front of the first queue. If the first queue
        is empty, it is replaced by the second queue
        (and the second queue becomes empty).
*/


template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::set_active(node *i)
{
    if (!i->next)
    {
        /* it's not in the list yet */
        if (queue_last[1]) queue_last[1] -> next = i;
        else               queue_first[1]        = i;
        queue_last[1] = i;
        i -> next = i;
    }
}

/*
        Returns the next active node.
        If it is connected to the sink, it stays in the list,
        otherwise it is removed from the list
*/
template <typename captype, typename tcaptype, typename flowtype>
        inline typename Graph<captype,tcaptype,flowtype>::node* Graph<captype,tcaptype,flowtype>::next_active()
{
    node *i;

    while ( 1 )
    {
        if (!(i=queue_first[0]))
        {
            queue_first[0] = i = queue_first[1];
            queue_last[0]  = queue_last[1];
            queue_first[1] = NULL;
            queue_last[1]  = NULL;
            if (!i) return NULL;
        }

        /* remove it from the active list */
        if (i->next == i) queue_first[0] = queue_last[0] = NULL;
        else              queue_first[0] = i -> next;
        i -> next = NULL;

        /* a node in the list is active iff it has a parent */
        if (i->parent) return i;
    }
}

/***********************************************************************/

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::set_orphan_front(node *i)
{
    nodeptr *np;
    i -> parent = ORPHAN;
    np = nodeptr_block -> New();
    np -> ptr = i;
    np -> next = orphan_first;
    orphan_first = np;
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::set_orphan_rear(node *i)
{
    nodeptr *np;
    i -> parent = ORPHAN;
    np = nodeptr_block -> New();
    np -> ptr = i;
    if (orphan_last) orphan_last -> next = np;
    else             orphan_first        = np;
    orphan_last = np;
    np -> next = NULL;
}

/***********************************************************************/

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::add_to_changed_list(node *i)
{
    if (changed_list && !i->is_in_changed_list)
    {
        node_id* ptr = changed_list->New();
        *ptr = (node_id)(i - nodes);
        i->is_in_changed_list = true;
    }
}

/***********************************************************************/

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::maxflow_init()
{
    node *i;

    queue_first[0] = queue_last[0] = NULL;
    queue_first[1] = queue_last[1] = NULL;
    orphan_first = NULL;

    TIME = 0;

    for (i=nodes; i<node_last; i++)
    {
        i -> next = NULL;
        i -> is_marked = 0;
        i -> is_in_changed_list = 0;
        i -> TS = TIME;
        if (i->tr_cap > 0)
        {
            /* i is connected to the source */
            i -> is_sink = 0;
            i -> parent = TERMINAL;
            set_active(i);
            i -> DIST = 1;
        }
        else if (i->tr_cap < 0)
        {
            /* i is connected to the sink */
            i -> is_sink = 1;
            i -> parent = TERMINAL;
            set_active(i);
            i -> DIST = 1;
        }
        else
        {
            i -> parent = NULL;
        }
    }
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::maxflow_reuse_trees_init()
{
    node* i;
    node* j;
    node* queue = queue_first[1];
    arc* a;
    nodeptr* np;

    queue_first[0] = queue_last[0] = NULL;
    queue_first[1] = queue_last[1] = NULL;
    orphan_first = orphan_last = NULL;

    TIME ++;

    while ((i=queue))
    {
        queue = i->next;
        if (queue == i) queue = NULL;
        i->next = NULL;
        i->is_marked = 0;
        set_active(i);

        if (i->tr_cap == 0)
        {
            if (i->parent) set_orphan_rear(i);
            continue;
        }

        if (i->tr_cap > 0)
        {
            if (!i->parent || i->is_sink)
            {
                i->is_sink = 0;
                for (a=i->first; a; a=a->next)
                {
                    j = a->head;
                    if (!j->is_marked)
                    {
                        if (j->parent == a->sister) set_orphan_rear(j);
                        if (j->parent && j->is_sink && a->r_cap > 0) set_active(j);
                    }
                }
                add_to_changed_list(i);
            }
        }
        else
        {
            if (!i->parent || !i->is_sink)
            {
                i->is_sink = 1;
                for (a=i->first; a; a=a->next)
                {
                    j = a->head;
                    if (!j->is_marked)
                    {
                        if (j->parent == a->sister) set_orphan_rear(j);
                        if (j->parent && !j->is_sink && a->sister->r_cap > 0) set_active(j);
                    }
                }
                add_to_changed_list(i);
            }
        }
        i->parent = TERMINAL;
        i -> TS = TIME;
        i -> DIST = 1;
    }

    //test_consistency();

    /* adoption */
    while ((np=orphan_first))
    {
        orphan_first = np -> next;
        i = np -> ptr;
        nodeptr_block -> Delete(np);
        if (!orphan_first) orphan_last = NULL;
        if (i->is_sink) process_sink_orphan(i);
        else            process_source_orphan(i);
    }
    /* adoption end */

    //test_consistency();
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::augment(arc *middle_arc)
{
    node *i;
    arc *a;
    tcaptype bottleneck;


    /* 1. Finding bottleneck capacity */
    /* 1a - the source tree */
    bottleneck = middle_arc -> r_cap;
    for (i=middle_arc->sister->head; ; i=a->head)
    {
        a = i -> parent;
        if (a == TERMINAL) break;
        if (bottleneck > a->sister->r_cap) bottleneck = a -> sister -> r_cap;
    }
    if (bottleneck > i->tr_cap) bottleneck = i -> tr_cap;
    /* 1b - the sink tree */
    for (i=middle_arc->head; ; i=a->head)
    {
        a = i -> parent;
        if (a == TERMINAL) break;
        if (bottleneck > a->r_cap) bottleneck = a -> r_cap;
    }
    if (bottleneck > - i->tr_cap) bottleneck = - i -> tr_cap;


    /* 2. Augmenting */
    /* 2a - the source tree */
    middle_arc -> sister -> r_cap += bottleneck;
    middle_arc -> r_cap -= bottleneck;
    for (i=middle_arc->sister->head; ; i=a->head)
    {
        a = i -> parent;
        if (a == TERMINAL) break;
        a -> r_cap += bottleneck;
        a -> sister -> r_cap -= bottleneck;
        if (!a->sister->r_cap)
        {
            set_orphan_front(i); // add i to the beginning of the adoption list
        }
    }
    i -> tr_cap -= bottleneck;
    if (!i->tr_cap)
    {
        set_orphan_front(i); // add i to the beginning of the adoption list
    }
    /* 2b - the sink tree */
    for (i=middle_arc->head; ; i=a->head)
    {
        a = i -> parent;
        if (a == TERMINAL) break;
        a -> sister -> r_cap += bottleneck;
        a -> r_cap -= bottleneck;
        if (!a->r_cap)
        {
            set_orphan_front(i); // add i to the beginning of the adoption list
        }
    }
    i -> tr_cap += bottleneck;
    if (!i->tr_cap)
    {
        set_orphan_front(i); // add i to the beginning of the adoption list
    }


    flow += bottleneck;
}

/***********************************************************************/

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::process_source_orphan(node *i)
{
    node *j;
    arc *a0, *a0_min = NULL, *a;
    int d, d_min = INFINITE_D;

    /* trying to find a new parent */
    for (a0=i->first; a0; a0=a0->next)
        if (a0->sister->r_cap)
        {
        j = a0 -> head;
        if (!j->is_sink && (a=j->parent))
        {
            /* checking the origin of j */
            d = 0;
            while ( 1 )
            {
                if (j->TS == TIME)
                {
                    d += j -> DIST;
                    break;
                }
                a = j -> parent;
                d ++;
                if (a==TERMINAL)
                {
                    j -> TS = TIME;
                    j -> DIST = 1;
                    break;
                }
                if (a==ORPHAN) { d = INFINITE_D; break; }
                j = a -> head;
            }
            if (d<INFINITE_D) /* j originates from the source - done */
            {
                if (d<d_min)
                {
                    a0_min = a0;
                    d_min = d;
                }
                /* set marks along the path */
                for (j=a0->head; j->TS!=TIME; j=j->parent->head)
                {
                    j -> TS = TIME;
                    j -> DIST = d --;
                }
            }
        }
    }

    if ((i->parent = a0_min))
    {
        i -> TS = TIME;
        i -> DIST = d_min + 1;
    }
    else
    {
        /* no parent is found */
        add_to_changed_list(i);

        /* process neighbors */
        for (a0=i->first; a0; a0=a0->next)
        {
            j = a0 -> head;
            if (!j->is_sink && (a=j->parent))
            {
                if (a0->sister->r_cap) set_active(j);
                if (a!=TERMINAL && a!=ORPHAN && a->head==i)
                {
                    set_orphan_rear(j); // add j to the end of the adoption list
                }
            }
        }
    }
}

template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::process_sink_orphan(node *i)
{
    node *j;
    arc *a0, *a0_min = NULL, *a;
    int d, d_min = INFINITE_D;

    /* trying to find a new parent */
    for (a0=i->first; a0; a0=a0->next)
        if (a0->r_cap)
        {
        j = a0 -> head;
        if (j->is_sink && (a=j->parent))
        {
            /* checking the origin of j */
            d = 0;
            while ( 1 )
            {
                if (j->TS == TIME)
                {
                    d += j -> DIST;
                    break;
                }
                a = j -> parent;
                d ++;
                if (a==TERMINAL)
                {
                    j -> TS = TIME;
                    j -> DIST = 1;
                    break;
                }
                if (a==ORPHAN) { d = INFINITE_D; break; }
                j = a -> head;
            }
            if (d<INFINITE_D) /* j originates from the sink - done */
            {
                if (d<d_min)
                {
                    a0_min = a0;
                    d_min = d;
                }
                /* set marks along the path */
                for (j=a0->head; j->TS!=TIME; j=j->parent->head)
                {
                    j -> TS = TIME;
                    j -> DIST = d --;
                }
            }
        }
    }

    if ((i->parent = a0_min))
    {
        i -> TS = TIME;
        i -> DIST = d_min + 1;
    }
    else
    {
        /* no parent is found */
        add_to_changed_list(i);

        /* process neighbors */
        for (a0=i->first; a0; a0=a0->next)
        {
            j = a0 -> head;
            if (j->is_sink && (a=j->parent))
            {
                if (a0->r_cap) set_active(j);
                if (a!=TERMINAL && a!=ORPHAN && a->head==i)
                {
                    set_orphan_rear(j); // add j to the end of the adoption list
                }
            }
        }
    }
}

/***********************************************************************/

template <typename captype, typename tcaptype, typename flowtype>
        inline flowtype Graph<captype,tcaptype,flowtype>::maxflow(bool reuse_trees, Block<node_id>* _changed_list)
{
    node *i, *j, *current_node = NULL;
    arc *a;
    nodeptr *np, *np_next;

    if (!nodeptr_block)
    {
        nodeptr_block = new DBlock<nodeptr>(NODEPTR_BLOCK_SIZE, error_function);
    }

    changed_list = _changed_list;
    if (maxflow_iteration == 0 && reuse_trees) { /*if (error_function) (*error_function)("reuse_trees cannot be used in the first call to maxflow()!");*/ exit(1); }
    if (changed_list && !reuse_trees) { /*if (error_function) (*error_function)("changed_list cannot be used without reuse_trees!");*/ exit(1); }

    if (reuse_trees) maxflow_reuse_trees_init();
    else             maxflow_init();

    // main loop
    while ( 1 )
    {
        // test_consistency(current_node);

        if ((i=current_node))
        {
            i -> next = NULL; /* remove active flag */
            if (!i->parent) i = NULL;
        }
        if (!i)
        {
            if (!(i = next_active())) break;
        }

        /* growth */
        if (!i->is_sink)
        {
            /* grow source tree */
            for (a=i->first; a; a=a->next)
                if (a->r_cap)
                {
                j = a -> head;
                if (!j->parent)
                {
                    j -> is_sink = 0;
                    j -> parent = a -> sister;
                    j -> TS = i -> TS;
                    j -> DIST = i -> DIST + 1;
                    set_active(j);
                    add_to_changed_list(j);
                }
                else if (j->is_sink) break;
                else if (j->TS <= i->TS &&
                         j->DIST > i->DIST)
                {
                    /* heuristic - trying to make the distance from j to the source shorter */
                    j -> parent = a -> sister;
                    j -> TS = i -> TS;
                    j -> DIST = i -> DIST + 1;
                }
            }
        }
        else
        {
            /* grow sink tree */
            for (a=i->first; a; a=a->next)
                if (a->sister->r_cap)
                {
                j = a -> head;
                if (!j->parent)
                {
                    j -> is_sink = 1;
                    j -> parent = a -> sister;
                    j -> TS = i -> TS;
                    j -> DIST = i -> DIST + 1;
                    set_active(j);
                    add_to_changed_list(j);
                }
                else if (!j->is_sink) { a = a -> sister; break; }
                else if (j->TS <= i->TS &&
                         j->DIST > i->DIST)
                {
                    /* heuristic - trying to make the distance from j to the sink shorter */
                    j -> parent = a -> sister;
                    j -> TS = i -> TS;
                    j -> DIST = i -> DIST + 1;
                }
            }
        }

        TIME ++;

        if (a)
        {
            i -> next = i; /* set active flag */
            current_node = i;

            /* augmentation */
            augment(a);
            /* augmentation end */

            /* adoption */
            while ((np=orphan_first))
            {
                np_next = np -> next;
                np -> next = NULL;

                while ((np=orphan_first))
                {
                    orphan_first = np -> next;
                    i = np -> ptr;
                    nodeptr_block -> Delete(np);
                    if (!orphan_first) orphan_last = NULL;
                    if (i->is_sink) process_sink_orphan(i);
                    else            process_source_orphan(i);
                }

                orphan_first = np_next;
            }
            /* adoption end */
        }
        else current_node = NULL;
    }
    // test_consistency();

    if (!reuse_trees || (maxflow_iteration % 64) == 0)
    {
        delete nodeptr_block;
        nodeptr_block = NULL;
    }

    maxflow_iteration ++;
    return flow;
}

/***********************************************************************/


template <typename captype, typename tcaptype, typename flowtype>
        inline void Graph<captype,tcaptype,flowtype>::test_consistency(node* current_node)
{
    node *i;
    arc *a;
    int r;
    int num1 = 0, num2 = 0;

    // test whether all nodes i with i->next!=NULL are indeed in the queue
    for (i=nodes; i<node_last; i++)
    {
        if (i->next || i==current_node) num1 ++;
    }
    for (r=0; r<3; r++)
    {
        i = (r == 2) ? current_node : queue_first[r];
        if (i)
            for ( ; ; i=i->next)
            {
            num2 ++;
            if (i->next == i)
            {
                if (r<2) assert(i == queue_last[r]);
                else     assert(i == current_node);
                break;
            }
        }
    }
    assert(num1 == num2);

    for (i=nodes; i<node_last; i++)
    {
        // test whether all edges in seach trees are non-saturated
        if (i->parent == NULL) {}
        else if (i->parent == ORPHAN) {}
        else if (i->parent == TERMINAL)
        {
            if (!i->is_sink) assert(i->tr_cap > 0);
            else             assert(i->tr_cap < 0);
        }
        else
        {
            if (!i->is_sink) assert (i->parent->sister->r_cap > 0);
            else             assert (i->parent->r_cap > 0);
        }
        // test whether passive nodes in search trees have neighbors in
        // a different tree through non-saturated edges
        if (i->parent && !i->next)
        {
            if (!i->is_sink)
            {
                assert(i->tr_cap >= 0);
                for (a=i->first; a; a=a->next)
                {
                    if (a->r_cap > 0) assert(a->head->parent && !a->head->is_sink);
                }
            }
            else
            {
                assert(i->tr_cap <= 0);
                for (a=i->first; a; a=a->next)
                {
                    if (a->sister->r_cap > 0) assert(a->head->parent && a->head->is_sink);
                }
            }
        }
        // test marking invariants
        if (i->parent && i->parent!=ORPHAN && i->parent!=TERMINAL)
        {
            assert(i->TS <= i->parent->head->TS);
            if (i->TS == i->parent->head->TS) assert(i->DIST > i->parent->head->DIST);
        }
    }
}

}
