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| <Head> |
| <Title>Boost Graph Library: Find Flow Cost</Title> |
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| <H1><A NAME="sec:find_flow_cost"> |
| <TT>find_flow_cost</TT> |
| </H1> |
| |
| <PRE> |
| <i>// named parameter version</i> |
| template <class <a href="./Graph.html">Graph</a>> |
| typename property_traits<typename property_map < Graph, edge_capacity_t >::type>::value_type |
| find_flow_cost(const Graph & g, |
| const bgl_named_params<P, T, R> & params = <i>all defaults</i>) |
| |
| <i>// non-named parameter version</i> |
| template<class <a href="./Graph.html">Graph</a>, class Capacity, class ResidualCapacity, class Weight> |
| typename property_traits<typename property_map < Graph, edge_capacity_t >::type>::value_type |
| find_flow_cost(const Graph & g, Capacity capacity, ResidualCapacity residual_capacity, Weight weight) |
| </PRE> |
| |
| <P> |
| The <tt>find_flow_cost()</tt> function calculates the minimum cost maximum flow value of a network and given flow. See Section <a |
| href="./graph_theory_review.html#sec:network-flow-algorithms">Network |
| Flow Algorithms</a> for a description of maximum flow. |
| The function calculates the cost from the flow values <i>f(u,v)</i> for <i>(u,v)</i> in |
| <i>E</i>, which are passed in the form of the residual capacity |
| <i>r(u,v) = c(u,v) - f(u,v)</i>. |
| |
| <p> |
| In order to compute the min cost max flow use : |
| <a href="./successive_shortest_path_nonnegative_weights.html"><tt>successive_shortest_path_nonnegative_weights()</tt></a> or |
| <a href="./cycle_canceling.html"><tt>cycle_canceling()</tt></a>. |
| |
| <H3>Where Defined</H3> |
| |
| <P> |
| <a href="../../../boost/graph/successive_shortest_path_nonnegative_weights.hpp"><TT>boost/graph/successive_shortest_path_nonnegative_weights.hpp</TT></a> |
| |
| <P> |
| |
| <h3>Parameters</h3> |
| |
| IN: <tt>const Graph& g</tt> |
| <blockquote> |
| A directed graph. The |
| graph's type must be a model of <a |
| href="./VertexListGraph.html">VertexListGraph</a> and <a href="./IncidenceGraph.html">IncidenceGraph</a> For each edge |
| <i>(u,v)</i> in the graph, the reverse edge <i>(v,u)</i> must also |
| be in the graph. |
| </blockquote> |
| <h3>Named Parameters</h3> |
| |
| |
| IN: <tt>capacity_map(CapacityEdgeMap cap)</tt> |
| <blockquote> |
| The edge capacity property map. The type must be a model of a |
| constant <a |
| href="../../property_map/doc/LvaluePropertyMap.html">Lvalue Property Map</a>. The |
| key type of the map must be the graph's edge descriptor type.<br> |
| <b>Default:</b> <tt>get(edge_capacity, g)</tt> |
| </blockquote> |
| |
| IN: <tt>residual_capacity_map(ResidualCapacityEdgeMap res)</tt> |
| <blockquote> |
| This maps edges to their residual capacity. The type must be a model |
| of a mutable <a |
| href="../../property_map/doc/LvaluePropertyMap.html">Lvalue Property |
| Map</a>. The key type of the map must be the graph's edge descriptor |
| type.<br> |
| <b>Default:</b> <tt>get(edge_residual_capacity, g)</tt> |
| </blockquote> |
| |
| |
| IN: <tt>weight_map(WeightMap w_map)</tt> |
| <blockquote> |
| The weight or ``cost'' of each edge in the graph. |
| The type <tt>WeightMap</tt> must be a model of |
| <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>. The edge descriptor type of |
| the graph needs to be usable as the key type for the weight |
| map. The value type for this map must be |
| the same as the value type of the distance map.<br> |
| <b>Default:</b> <tt>get(edge_weight, g)</tt><br> |
| |
| </blockquote> |
| |
| <h3>Complexity</h3> |
| The complexity is <i> O(|E|)</i>, |
| |
| <h3>Example</h3> |
| |
| The function is used in the successive_shortest_path_nonnegative_weights example. The program in <a |
| href="../example/successive_shortest_path_nonnegative_weights_example.cpp"><tt>example/successive_shortest_path_nonnegative_weights_example.cpp</tt></a>. |
| |
| <h3>See Also</h3> |
| |
| <a href="./cycle_canceling.html"><tt>cycle_canceling()</tt></a><br> |
| <a href="./successive_shortest_path_nonnegative_weights.html"><tt>successive_shortest_path_nonnegative_weights()</tt></a>. |
| |
| <br> |
| <HR> |
| <TABLE> |
| <TR valign=top> |
| <TD nowrap>Copyright © 2013</TD><TD> |
| Piotr Wygocki, University of Warsaw (<A HREF="mailto:wygos@mimuw.edu.pl">wygos at mimuw.edu.pl</A>) |
| </TD></TR></TABLE> |
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