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- <Head>
- <Title>Boost Graph Library: Find Flow Cost</Title>
- <BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
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- <BR Clear>
- <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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