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diff --git a/extern/quadriflow/3rd/lemon-1.3.1/lemon/capacity_scaling.h b/extern/quadriflow/3rd/lemon-1.3.1/lemon/capacity_scaling.h new file mode 100644 index 00000000000..ca64b56d3b3 --- /dev/null +++ b/extern/quadriflow/3rd/lemon-1.3.1/lemon/capacity_scaling.h @@ -0,0 +1,1014 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2013 + * 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_CAPACITY_SCALING_H +#define LEMON_CAPACITY_SCALING_H + +/// \ingroup min_cost_flow_algs +/// +/// \file +/// \brief Capacity Scaling algorithm for finding a minimum cost flow. + +#include <vector> +#include <limits> +#include <lemon/core.h> +#include <lemon/bin_heap.h> + +namespace lemon { + + /// \brief Default traits class of CapacityScaling algorithm. + /// + /// Default traits class of CapacityScaling algorithm. + /// \tparam GR Digraph type. + /// \tparam V The number type used for flow amounts, capacity bounds + /// and supply values. By default it is \c int. + /// \tparam C The number type used for costs and potentials. + /// By default it is the same as \c V. + template <typename GR, typename V = int, typename C = V> + struct CapacityScalingDefaultTraits + { + /// The type of the digraph + typedef GR Digraph; + /// The type of the flow amounts, capacity bounds and supply values + typedef V Value; + /// The type of the arc costs + typedef C Cost; + + /// \brief The type of the heap used for internal Dijkstra computations. + /// + /// The type of the heap used for internal Dijkstra computations. + /// It must conform to the \ref lemon::concepts::Heap "Heap" concept, + /// its priority type must be \c Cost and its cross reference type + /// must be \ref RangeMap "RangeMap<int>". + typedef BinHeap<Cost, RangeMap<int> > Heap; + }; + + /// \addtogroup min_cost_flow_algs + /// @{ + + /// \brief Implementation of the Capacity Scaling algorithm for + /// finding a \ref min_cost_flow "minimum cost flow". + /// + /// \ref CapacityScaling implements the capacity scaling version + /// of the successive shortest path algorithm for finding a + /// \ref min_cost_flow "minimum cost flow" \cite amo93networkflows, + /// \cite edmondskarp72theoretical. It is an efficient dual + /// solution method, which runs in polynomial time + /// \f$O(m\log U (n+m)\log n)\f$, where <i>U</i> denotes the maximum + /// of node supply and arc capacity values. + /// + /// This algorithm is typically slower than \ref CostScaling and + /// \ref NetworkSimplex, but in special cases, it can be more + /// efficient than them. + /// (For more information, see \ref min_cost_flow_algs "the module page".) + /// + /// 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. + /// \tparam TR The traits class that defines various types used by the + /// algorithm. By default, it is \ref CapacityScalingDefaultTraits + /// "CapacityScalingDefaultTraits<GR, V, C>". + /// In most cases, this parameter should not be set directly, + /// consider to use the named template parameters instead. + /// + /// \warning Both \c V and \c C must be signed number types. + /// \warning Capacity bounds and supply values must be integer, but + /// arc costs can be arbitrary real numbers. + /// \warning This algorithm does not support negative costs for + /// arcs having infinite upper bound. +#ifdef DOXYGEN + template <typename GR, typename V, typename C, typename TR> +#else + template < typename GR, typename V = int, typename C = V, + typename TR = CapacityScalingDefaultTraits<GR, V, C> > +#endif + class CapacityScaling + { + public: + + /// The type of the digraph + typedef typename TR::Digraph Digraph; + /// The type of the flow amounts, capacity bounds and supply values + typedef typename TR::Value Value; + /// The type of the arc costs + typedef typename TR::Cost Cost; + + /// The type of the heap used for internal Dijkstra computations + typedef typename TR::Heap Heap; + + /// \brief The \ref lemon::CapacityScalingDefaultTraits "traits class" + /// of the algorithm + typedef TR Traits; + + 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 digraph contains an arc of negative cost and infinite + /// upper bound. It means that the objective function is unbounded + /// on that arc, however, note that it could actually be bounded + /// over the feasible flows, but this algroithm cannot handle + /// these cases. + UNBOUNDED + }; + + private: + + TEMPLATE_DIGRAPH_TYPEDEFS(GR); + + typedef std::vector<int> IntVector; + typedef std::vector<Value> ValueVector; + typedef std::vector<Cost> CostVector; + typedef std::vector<char> BoolVector; + // Note: vector<char> is used instead of vector<bool> for efficiency reasons + + private: + + // Data related to the underlying digraph + const GR &_graph; + int _node_num; + int _arc_num; + int _res_arc_num; + int _root; + + // Parameters of the problem + bool _has_lower; + Value _sum_supply; + + // Data structures for storing the digraph + IntNodeMap _node_id; + IntArcMap _arc_idf; + IntArcMap _arc_idb; + IntVector _first_out; + BoolVector _forward; + IntVector _source; + IntVector _target; + IntVector _reverse; + + // Node and arc data + ValueVector _lower; + ValueVector _upper; + CostVector _cost; + ValueVector _supply; + + ValueVector _res_cap; + CostVector _pi; + ValueVector _excess; + IntVector _excess_nodes; + IntVector _deficit_nodes; + + Value _delta; + int _factor; + IntVector _pred; + + 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: + + // Special implementation of the Dijkstra algorithm for finding + // shortest paths in the residual network of the digraph with + // respect to the reduced arc costs and modifying the node + // potentials according to the found distance labels. + class ResidualDijkstra + { + private: + + int _node_num; + bool _geq; + const IntVector &_first_out; + const IntVector &_target; + const CostVector &_cost; + const ValueVector &_res_cap; + const ValueVector &_excess; + CostVector &_pi; + IntVector &_pred; + + IntVector _proc_nodes; + CostVector _dist; + + public: + + ResidualDijkstra(CapacityScaling& cs) : + _node_num(cs._node_num), _geq(cs._sum_supply < 0), + _first_out(cs._first_out), _target(cs._target), _cost(cs._cost), + _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi), + _pred(cs._pred), _dist(cs._node_num) + {} + + int run(int s, Value delta = 1) { + RangeMap<int> heap_cross_ref(_node_num, Heap::PRE_HEAP); + Heap heap(heap_cross_ref); + heap.push(s, 0); + _pred[s] = -1; + _proc_nodes.clear(); + + // Process nodes + while (!heap.empty() && _excess[heap.top()] > -delta) { + int u = heap.top(), v; + Cost d = heap.prio() + _pi[u], dn; + _dist[u] = heap.prio(); + _proc_nodes.push_back(u); + heap.pop(); + + // Traverse outgoing residual arcs + int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1; + for (int a = _first_out[u]; a != last_out; ++a) { + if (_res_cap[a] < delta) continue; + v = _target[a]; + switch (heap.state(v)) { + case Heap::PRE_HEAP: + heap.push(v, d + _cost[a] - _pi[v]); + _pred[v] = a; + break; + case Heap::IN_HEAP: + dn = d + _cost[a] - _pi[v]; + if (dn < heap[v]) { + heap.decrease(v, dn); + _pred[v] = a; + } + break; + case Heap::POST_HEAP: + break; + } + } + } + if (heap.empty()) return -1; + + // Update potentials of processed nodes + int t = heap.top(); + Cost dt = heap.prio(); + for (int i = 0; i < int(_proc_nodes.size()); ++i) { + _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt; + } + + return t; + } + + }; //class ResidualDijkstra + + public: + + /// \name Named Template Parameters + /// @{ + + template <typename T> + struct SetHeapTraits : public Traits { + typedef T Heap; + }; + + /// \brief \ref named-templ-param "Named parameter" for setting + /// \c Heap type. + /// + /// \ref named-templ-param "Named parameter" for setting \c Heap + /// type, which is used for internal Dijkstra computations. + /// It must conform to the \ref lemon::concepts::Heap "Heap" concept, + /// its priority type must be \c Cost and its cross reference type + /// must be \ref RangeMap "RangeMap<int>". + template <typename T> + struct SetHeap + : public CapacityScaling<GR, V, C, SetHeapTraits<T> > { + typedef CapacityScaling<GR, V, C, SetHeapTraits<T> > Create; + }; + + /// @} + + protected: + + CapacityScaling() {} + + public: + + /// \brief Constructor. + /// + /// The constructor of the class. + /// + /// \param graph The digraph the algorithm runs on. + CapacityScaling(const GR& graph) : + _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), + INF(std::numeric_limits<Value>::has_infinity ? + std::numeric_limits<Value>::infinity() : + std::numeric_limits<Value>::max()) + { + // Check the number types + LEMON_ASSERT(std::numeric_limits<Value>::is_signed, + "The flow type of CapacityScaling must be signed"); + LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, + "The cost type of CapacityScaling must be signed"); + + // Reset data structures + reset(); + } + + /// \name Parameters + /// The parameters of the algorithm can be specified using these + /// functions. + + /// @{ + + /// \brief Set the lower bounds on the arcs. + /// + /// This function sets the lower bounds on the arcs. + /// If it is not used before calling \ref run(), the lower bounds + /// will be set to zero on all arcs. + /// + /// \param map An arc map storing the lower bounds. + /// Its \c Value type must be convertible to the \c Value type + /// of the algorithm. + /// + /// \return <tt>(*this)</tt> + template <typename LowerMap> + CapacityScaling& lowerMap(const LowerMap& map) { + _has_lower = true; + for (ArcIt a(_graph); a != INVALID; ++a) { + _lower[_arc_idf[a]] = map[a]; + } + return *this; + } + + /// \brief Set the upper bounds (capacities) on the arcs. + /// + /// This function sets the upper bounds (capacities) on the arcs. + /// If it is not used before calling \ref run(), the upper bounds + /// will be set to \ref INF on all arcs (i.e. the flow value will be + /// unbounded from above). + /// + /// \param map An arc map storing the upper bounds. + /// Its \c Value type must be convertible to the \c Value type + /// of the algorithm. + /// + /// \return <tt>(*this)</tt> + template<typename UpperMap> + CapacityScaling& upperMap(const UpperMap& map) { + for (ArcIt a(_graph); a != INVALID; ++a) { + _upper[_arc_idf[a]] = map[a]; + } + return *this; + } + + /// \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> + CapacityScaling& costMap(const CostMap& map) { + for (ArcIt a(_graph); a != INVALID; ++a) { + _cost[_arc_idf[a]] = map[a]; + _cost[_arc_idb[a]] = -map[a]; + } + 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> + CapacityScaling& supplyMap(const SupplyMap& map) { + for (NodeIt n(_graph); n != INVALID; ++n) { + _supply[_node_id[n]] = map[n]; + } + 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 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> + CapacityScaling& 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; + } + + /// @} + + /// \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(). + /// For example, + /// \code + /// CapacityScaling<ListDigraph> cs(graph); + /// cs.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 factor The capacity scaling factor. It must be larger than + /// one to use scaling. If it is less or equal to one, then scaling + /// will be disabled. + /// + /// \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 digraph contains an arc of negative cost + /// and infinite upper bound. It means that the objective function + /// is unbounded on that arc, however, note that it could actually be + /// bounded over the feasible flows, but this algroithm cannot handle + /// these cases. + /// + /// \see ProblemType + /// \see resetParams(), reset() + ProblemType run(int factor = 4) { + _factor = factor; + ProblemType pt = init(); + if (pt != OPTIMAL) return pt; + 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(). + /// + /// 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 + /// CapacityScaling<ListDigraph> cs(graph); + /// + /// // First run + /// cs.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; + /// cs.costMap(cost).run(); + /// + /// // Run again from scratch using resetParams() + /// // (the lower bounds will be set to zero on all arcs) + /// cs.resetParams(); + /// cs.upperMap(capacity).costMap(cost) + /// .supplyMap(sup).run(); + /// \endcode + /// + /// \return <tt>(*this)</tt> + /// + /// \see reset(), run() + CapacityScaling& resetParams() { + for (int i = 0; i != _node_num; ++i) { + _supply[i] = 0; + } + for (int j = 0; j != _res_arc_num; ++j) { + _lower[j] = 0; + _upper[j] = INF; + _cost[j] = _forward[j] ? 1 : -1; + } + _has_lower = false; + return *this; + } + + /// \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(). + /// + /// 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() + CapacityScaling& reset() { + // Resize vectors + _node_num = countNodes(_graph); + _arc_num = countArcs(_graph); + _res_arc_num = 2 * (_arc_num + _node_num); + _root = _node_num; + ++_node_num; + + _first_out.resize(_node_num + 1); + _forward.resize(_res_arc_num); + _source.resize(_res_arc_num); + _target.resize(_res_arc_num); + _reverse.resize(_res_arc_num); + + _lower.resize(_res_arc_num); + _upper.resize(_res_arc_num); + _cost.resize(_res_arc_num); + _supply.resize(_node_num); + + _res_cap.resize(_res_arc_num); + _pi.resize(_node_num); + _excess.resize(_node_num); + _pred.resize(_node_num); + + // Copy the graph + int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1; + for (NodeIt n(_graph); n != INVALID; ++n, ++i) { + _node_id[n] = i; + } + i = 0; + for (NodeIt n(_graph); n != INVALID; ++n, ++i) { + _first_out[i] = j; + for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { + _arc_idf[a] = j; + _forward[j] = true; + _source[j] = i; + _target[j] = _node_id[_graph.runningNode(a)]; + } + for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { + _arc_idb[a] = j; + _forward[j] = false; + _source[j] = i; + _target[j] = _node_id[_graph.runningNode(a)]; + } + _forward[j] = false; + _source[j] = i; + _target[j] = _root; + _reverse[j] = k; + _forward[k] = true; + _source[k] = _root; + _target[k] = i; + _reverse[k] = j; + ++j; ++k; + } + _first_out[i] = j; + _first_out[_node_num] = k; + for (ArcIt a(_graph); a != INVALID; ++a) { + int fi = _arc_idf[a]; + int bi = _arc_idb[a]; + _reverse[fi] = bi; + _reverse[bi] = fi; + } + + // 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(m). + /// + /// \note The return type of the function can be specified as a + /// template parameter. For example, + /// \code + /// cs.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 = _arc_idb[a]; + c += static_cast<Number>(_res_cap[i]) * + (-static_cast<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 _res_cap[_arc_idb[a]]; + } + + /// \brief Copy the flow values (the primal solution) into the + /// given map. + /// + /// 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 { + for (ArcIt a(_graph); a != INVALID; ++a) { + map.set(a, _res_cap[_arc_idb[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 Copy the potential values (the dual solution) into the + /// given map. + /// + /// 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 { + for (NodeIt n(_graph); n != INVALID; ++n) { + map.set(n, _pi[_node_id[n]]); + } + } + + /// @} + + private: + + // Initialize the algorithm + ProblemType init() { + if (_node_num <= 1) return INFEASIBLE; + + // Check the sum of supply values + _sum_supply = 0; + for (int i = 0; i != _root; ++i) { + _sum_supply += _supply[i]; + } + if (_sum_supply > 0) return INFEASIBLE; + + // Check lower and upper bounds + LEMON_DEBUG(checkBoundMaps(), + "Upper bounds must be greater or equal to the lower bounds"); + + + // Initialize vectors + for (int i = 0; i != _root; ++i) { + _pi[i] = 0; + _excess[i] = _supply[i]; + } + + // Remove non-zero lower bounds + const Value MAX = std::numeric_limits<Value>::max(); + int last_out; + if (_has_lower) { + for (int i = 0; i != _root; ++i) { + last_out = _first_out[i+1]; + for (int j = _first_out[i]; j != last_out; ++j) { + if (_forward[j]) { + Value c = _lower[j]; + if (c >= 0) { + _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF; + } else { + _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF; + } + _excess[i] -= c; + _excess[_target[j]] += c; + } else { + _res_cap[j] = 0; + } + } + } + } else { + for (int j = 0; j != _res_arc_num; ++j) { + _res_cap[j] = _forward[j] ? _upper[j] : 0; + } + } + + // Handle negative costs + for (int i = 0; i != _root; ++i) { + last_out = _first_out[i+1] - 1; + for (int j = _first_out[i]; j != last_out; ++j) { + Value rc = _res_cap[j]; + if (_cost[j] < 0 && rc > 0) { + if (rc >= MAX) return UNBOUNDED; + _excess[i] -= rc; + _excess[_target[j]] += rc; + _res_cap[j] = 0; + _res_cap[_reverse[j]] += rc; + } + } + } + + // Handle GEQ supply type + if (_sum_supply < 0) { + _pi[_root] = 0; + _excess[_root] = -_sum_supply; + for (int a = _first_out[_root]; a != _res_arc_num; ++a) { + int ra = _reverse[a]; + _res_cap[a] = -_sum_supply + 1; + _res_cap[ra] = 0; + _cost[a] = 0; + _cost[ra] = 0; + } + } else { + _pi[_root] = 0; + _excess[_root] = 0; + for (int a = _first_out[_root]; a != _res_arc_num; ++a) { + int ra = _reverse[a]; + _res_cap[a] = 1; + _res_cap[ra] = 0; + _cost[a] = 0; + _cost[ra] = 0; + } + } + + // Initialize delta value + if (_factor > 1) { + // With scaling + Value max_sup = 0, max_dem = 0, max_cap = 0; + for (int i = 0; i != _root; ++i) { + Value ex = _excess[i]; + if ( ex > max_sup) max_sup = ex; + if (-ex > max_dem) max_dem = -ex; + int last_out = _first_out[i+1] - 1; + for (int j = _first_out[i]; j != last_out; ++j) { + if (_res_cap[j] > max_cap) max_cap = _res_cap[j]; + } + } + max_sup = std::min(std::min(max_sup, max_dem), max_cap); + for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ; + } else { + // Without scaling + _delta = 1; + } + + return OPTIMAL; + } + + // Check if the upper bound is greater than or equal to the lower bound + // on each forward arc. + bool checkBoundMaps() { + for (int j = 0; j != _res_arc_num; ++j) { + if (_forward[j] && _upper[j] < _lower[j]) return false; + } + return true; + } + + ProblemType start() { + // Execute the algorithm + ProblemType pt; + if (_delta > 1) + pt = startWithScaling(); + else + pt = startWithoutScaling(); + + // Handle non-zero lower bounds + if (_has_lower) { + int limit = _first_out[_root]; + for (int j = 0; j != limit; ++j) { + if (_forward[j]) _res_cap[_reverse[j]] += _lower[j]; + } + } + + // Shift potentials if necessary + Cost pr = _pi[_root]; + if (_sum_supply < 0 || pr > 0) { + for (int i = 0; i != _node_num; ++i) { + _pi[i] -= pr; + } + } + + return pt; + } + + // Execute the capacity scaling algorithm + ProblemType startWithScaling() { + // Perform capacity scaling phases + int s, t; + ResidualDijkstra _dijkstra(*this); + while (true) { + // Saturate all arcs not satisfying the optimality condition + int last_out; + for (int u = 0; u != _node_num; ++u) { + last_out = _sum_supply < 0 ? + _first_out[u+1] : _first_out[u+1] - 1; + for (int a = _first_out[u]; a != last_out; ++a) { + int v = _target[a]; + Cost c = _cost[a] + _pi[u] - _pi[v]; + Value rc = _res_cap[a]; + if (c < 0 && rc >= _delta) { + _excess[u] -= rc; + _excess[v] += rc; + _res_cap[a] = 0; + _res_cap[_reverse[a]] += rc; + } + } + } + + // Find excess nodes and deficit nodes + _excess_nodes.clear(); + _deficit_nodes.clear(); + for (int u = 0; u != _node_num; ++u) { + Value ex = _excess[u]; + if (ex >= _delta) _excess_nodes.push_back(u); + if (ex <= -_delta) _deficit_nodes.push_back(u); + } + int next_node = 0, next_def_node = 0; + + // Find augmenting shortest paths + while (next_node < int(_excess_nodes.size())) { + // Check deficit nodes + if (_delta > 1) { + bool delta_deficit = false; + for ( ; next_def_node < int(_deficit_nodes.size()); + ++next_def_node ) { + if (_excess[_deficit_nodes[next_def_node]] <= -_delta) { + delta_deficit = true; + break; + } + } + if (!delta_deficit) break; + } + + // Run Dijkstra in the residual network + s = _excess_nodes[next_node]; + if ((t = _dijkstra.run(s, _delta)) == -1) { + if (_delta > 1) { + ++next_node; + continue; + } + return INFEASIBLE; + } + + // Augment along a shortest path from s to t + Value d = std::min(_excess[s], -_excess[t]); + int u = t; + int a; + if (d > _delta) { + while ((a = _pred[u]) != -1) { + if (_res_cap[a] < d) d = _res_cap[a]; + u = _source[a]; + } + } + u = t; + while ((a = _pred[u]) != -1) { + _res_cap[a] -= d; + _res_cap[_reverse[a]] += d; + u = _source[a]; + } + _excess[s] -= d; + _excess[t] += d; + + if (_excess[s] < _delta) ++next_node; + } + + if (_delta == 1) break; + _delta = _delta <= _factor ? 1 : _delta / _factor; + } + + return OPTIMAL; + } + + // Execute the successive shortest path algorithm + ProblemType startWithoutScaling() { + // Find excess nodes + _excess_nodes.clear(); + for (int i = 0; i != _node_num; ++i) { + if (_excess[i] > 0) _excess_nodes.push_back(i); + } + if (_excess_nodes.size() == 0) return OPTIMAL; + int next_node = 0; + + // Find shortest paths + int s, t; + ResidualDijkstra _dijkstra(*this); + while ( _excess[_excess_nodes[next_node]] > 0 || + ++next_node < int(_excess_nodes.size()) ) + { + // Run Dijkstra in the residual network + s = _excess_nodes[next_node]; + if ((t = _dijkstra.run(s)) == -1) return INFEASIBLE; + + // Augment along a shortest path from s to t + Value d = std::min(_excess[s], -_excess[t]); + int u = t; + int a; + if (d > 1) { + while ((a = _pred[u]) != -1) { + if (_res_cap[a] < d) d = _res_cap[a]; + u = _source[a]; + } + } + u = t; + while ((a = _pred[u]) != -1) { + _res_cap[a] -= d; + _res_cap[_reverse[a]] += d; + u = _source[a]; + } + _excess[s] -= d; + _excess[t] += d; + } + + return OPTIMAL; + } + + }; //class CapacityScaling + + ///@} + +} //namespace lemon + +#endif //LEMON_CAPACITY_SCALING_H |