140 lines
5.0 KiB
HTML
140 lines
5.0 KiB
HTML
<HTML>
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<!--
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Copyright (c) Piotr Wygocki 2013
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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-->
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<Head>
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<Title>Boost Graph Library: Find Flow Cost</Title>
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<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
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ALINK="#ff0000">
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<IMG SRC="../../../boost.png"
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ALT="C++ Boost" width="277" height="86">
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<BR Clear>
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<H1><A NAME="sec:find_flow_cost">
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<TT>find_flow_cost</TT>
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</H1>
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<PRE>
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<i>// named parameter version</i>
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template <class <a href="./Graph.html">Graph</a>>
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typename property_traits<typename property_map < Graph, edge_capacity_t >::type>::value_type
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find_flow_cost(const Graph & g,
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const bgl_named_params<P, T, R> & params = <i>all defaults</i>)
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<i>// non-named parameter version</i>
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template<class <a href="./Graph.html">Graph</a>, class Capacity, class ResidualCapacity, class Weight>
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typename property_traits<typename property_map < Graph, edge_capacity_t >::type>::value_type
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find_flow_cost(const Graph & g, Capacity capacity, ResidualCapacity residual_capacity, Weight weight)
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</PRE>
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<P>
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The <tt>find_flow_cost()</tt> function calculates the minimum cost maximum flow value of a network and given flow. See Section <a
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href="./graph_theory_review.html#sec:network-flow-algorithms">Network
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Flow Algorithms</a> for a description of maximum flow.
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The function calculates the cost from the flow values <i>f(u,v)</i> for <i>(u,v)</i> in
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<i>E</i>, which are passed in the form of the residual capacity
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<i>r(u,v) = c(u,v) - f(u,v)</i>.
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<p>
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In order to compute the min cost max flow use :
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<a href="./successive_shortest_path_nonnegative_weights.html"><tt>successive_shortest_path_nonnegative_weights()</tt></a> or
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<a href="./cycle_canceling.html"><tt>cycle_canceling()</tt></a>.
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<H3>Where Defined</H3>
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<P>
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<a href="../../../boost/graph/successive_shortest_path_nonnegative_weights.hpp"><TT>boost/graph/successive_shortest_path_nonnegative_weights.hpp</TT></a>
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<P>
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<h3>Parameters</h3>
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IN: <tt>const Graph& g</tt>
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<blockquote>
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A directed graph. The
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graph's type must be a model of <a
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href="./VertexListGraph.html">VertexListGraph</a> and <a href="./IncidenceGraph.html">IncidenceGraph</a> For each edge
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<i>(u,v)</i> in the graph, the reverse edge <i>(v,u)</i> must also
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be in the graph.
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</blockquote>
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<h3>Named Parameters</h3>
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IN: <tt>capacity_map(CapacityEdgeMap cap)</tt>
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<blockquote>
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The edge capacity property map. The type must be a model of a
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constant <a
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href="../../property_map/doc/LvaluePropertyMap.html">Lvalue Property Map</a>. The
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key type of the map must be the graph's edge descriptor type.<br>
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<b>Default:</b> <tt>get(edge_capacity, g)</tt>
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</blockquote>
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IN: <tt>residual_capacity_map(ResidualCapacityEdgeMap res)</tt>
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<blockquote>
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This maps edges to their residual capacity. The type must be a model
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of a mutable <a
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href="../../property_map/doc/LvaluePropertyMap.html">Lvalue Property
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Map</a>. The key type of the map must be the graph's edge descriptor
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type.<br>
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<b>Default:</b> <tt>get(edge_residual_capacity, g)</tt>
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</blockquote>
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IN: <tt>weight_map(WeightMap w_map)</tt>
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<blockquote>
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The weight or ``cost'' of each edge in the graph.
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The type <tt>WeightMap</tt> must be a model of
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<a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>. The edge descriptor type of
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the graph needs to be usable as the key type for the weight
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map. The value type for this map must be
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the same as the value type of the distance map.<br>
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<b>Default:</b> <tt>get(edge_weight, g)</tt><br>
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</blockquote>
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<h3>Complexity</h3>
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The complexity is <i> O(|E|)</i>,
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<h3>Example</h3>
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The function is used in the successive_shortest_path_nonnegative_weights example. The program in <a
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href="../example/successive_shortest_path_nonnegative_weights_example.cpp"><tt>example/successive_shortest_path_nonnegative_weights_example.cpp</tt></a>.
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<h3>See Also</h3>
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<a href="./cycle_canceling.html"><tt>cycle_canceling()</tt></a><br>
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<a href="./successive_shortest_path_nonnegative_weights.html"><tt>successive_shortest_path_nonnegative_weights()</tt></a>.
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<br>
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<HR>
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<TABLE>
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<TR valign=top>
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<TD nowrap>Copyright © 2013</TD><TD>
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Piotr Wygocki, University of Warsaw (<A HREF="mailto:wygos@mimuw.edu.pl">wygos at mimuw.edu.pl</A>)
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</TD></TR></TABLE>
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</BODY>
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</HTML>
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