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212 lines
6.3 KiB
HTML
<HTML>
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<!--
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-- Copyright (c) Jeremy Siek 2000
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--
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-- Permission to use, copy, modify, distribute and sell this software
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-- and its documentation for any purpose is hereby granted without fee,
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-- provided that the above copyright notice appears in all copies and
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-- that both that copyright notice and this permission notice appear
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-- in supporting documentation. Jeremy Siek makes no
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-- representations about the suitability of this software for any
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-- purpose. It is provided "as is" without express or implied warranty.
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-->
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<Head>
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<Title>Boost Graph Library: Prim Minimum Spanning Tree</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="../../../c++boost.gif"
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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:prim"></A>
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<TT>prim_minimum_spanning_tree</TT>
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</H1>
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<P>
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<DIV ALIGN="left">
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<TABLE CELLPADDING=3 border>
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<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
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<TD ALIGN="LEFT">undirected</TD>
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</TR>
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<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
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<TD ALIGN="LEFT">distance, weight, color, vertex id</TD>
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</TR>
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<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
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<TD ALIGN="LEFT"><i>O(E log V)</i></TD>
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</TR>
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</TABLE>
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</DIV>
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<P>
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<PRE>
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(1)
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template <class VertexListGraph, class Vertex>
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void prim_minimum_spanning_tree(VertexListGraph& G, Vertex s);
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(2)
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template <class VertexListGraph, class Vertex, class Distance>
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void prim_minimum_spanning_tree(VertexListGraph& G, Vertex s, Distance d);
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(3)
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template <class VertexListGraph, class Vertex,
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class Distance, class Visitor>
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void prim_minimum_spanning_tree(VertexListGraph& G, Vertex s,
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Distance d, Visitor visit);
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(4)
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template <class VertexListGraph, class Vertex, class Visitor,
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class Distance, class Weight, class Color, class ID>
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void prim_minimum_spanning_tree(VertexListGraph& G, Vertex s,
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Distance d, Weight w, Color c, ID id,
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Visitor visit);
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</PRE>
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<P>
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This is Prim's algorithm [<A
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HREF="bibliography.html#prim57:_short">25</A>,<A
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HREF="bibliography.html#clr90">8</A>,<A
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HREF="bibliography.html#tarjan83:_data_struct_network_algo">27</A>,<A
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HREF="bibliography.html#graham85">15</A>] for solving the minimum
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spanning tree problem for an undirected graph with weighted edges. See
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Section <A
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HREF="graph_theory_review.html#sec:minimum-spanning-tree">Minimum
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Spanning Tree Algorithms</A> for a definition of the minimum spanning
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tree problem. The implementation is simply a call to <a
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href="./uniform_cost_search.html"><TT>uniform_cost_search()</TT></a>
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with the appropriate choice of comparison and combine functors.
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<P>
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<H3>Where Defined</H3>
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<P>
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<a href="../../../boost/graph/prim_minimum_spanning_tree.hpp"><TT>boost/graph/prim_minimum_spanning_tree.hpp</TT></a>
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<P>
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<H3>Requirements on Types</H3>
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<P>
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<UL>
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<LI>The type <TT>VertexListGraph</TT> must be a model of <a href="./VertexListGraph.html">VertexListGraph</a>.
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</LI>
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<LI>The type <TT>Vertex</TT> must be convertible to type <TT>boost::graph_traits<VertexListGraph>::vertex_descriptor</TT>.
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</LI>
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<LI>The type <TT>Visitor</TT> must be a model of <I>Visitor</I>.
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</LI>
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<LI>The type <TT>Distance</TT> must be a model of
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<a href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>. The vertex descriptor type of
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the graph needs to be usable as the key type of the distance
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map. The value type of the distance map must be
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<I>LessThanComparable</I>.
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</LI>
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<LI>The type <TT>Weight</TT> must be a model of
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<a href="../../property_map/ReadablePropertyMap.html">ReadablePropertyMap</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 the map must be
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<I>Addable</I> with the value type of the distance map.
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</LI>
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<LI>The type <TT>Color</TT> must be a model of
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<a href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>. A vertex descriptor must be
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usable as the key type of the map, and the value type of the
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map must be a model of <I>ColorValue</I>.
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</LI>
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<LI>The type <TT>ID</TT> must be a model of
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<a href="../../property_map/ReadablePropertyMap.html">ReadablePropertyMap</a>. The value type of <TT>ID</TT>
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must be an integer type. The vertex descriptor type of the graph
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needs to be usable as the key type of the ID map.
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</LI>
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</UL>
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<P>
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<H3>Complexity</H3>
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<P>
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The time complexity is <i>O(E log V)</i>.
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<P>
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<H3>Example</H3>
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<P>
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The source code for this example is in <a
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href="../example/prim.cpp"><TT>examples/prim.cpp</TT></a>.
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<P>
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<PRE>
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int main(int , char* [])
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{
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using namespace boost;
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typedef adjacency_list<vecS, vecS, undirectedS,
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property<vertex_color_t, default_color_type,
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property<vertex_distance_t,int> >, property<edge_weight_t,int> >
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Graph;
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typedef graph_traits<Graph>::vertex_descriptor Vertex;
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typedef std::pair<int,int> E;
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const int num_nodes = 9;
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char name[] = "abcdefghi";
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enum { a, b, c, d, e, f, g, h, i };
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E edges[] = { E(a,b), E(a,h),
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E(b,h), E(b,c),
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E(c,d), E(c,f), E(c,i),
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E(d,e), E(d,f),
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E(e,f),
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E(f,g),
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E(g,i), E(g,h),
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E(h,i) };
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int weights[] = { 4, 8,
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11, 8,
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7, 4, 2,
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9, 14,
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10,
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2,
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6, 1,
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7 };
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Graph G(num_nodes, edges, edges + sizeof(edges)/sizeof(E), weights);
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std::vector<Vertex> p(num_vertices(G));
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Vertex src = *(vertices(G).first);
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p[src] = src;
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prim_minimum_spanning_tree
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(G, src, get(vertex_distance, G),
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make_ucs_visitor(record_predecessors(&p[0], on_edge_relaxed())));
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for ( std::vector<Vertex>::iterator vi = p.begin();
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vi != p.end(); ++vi)
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std::cout << "parent[" << name[vi - p.begin()]
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<< "] = " << name[*vi] << std::endl;
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return 0;
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}
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</PRE>
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The output is:
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<PRE>
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parent[a] = a
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parent[b] = a
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parent[c] = f
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parent[d] = c
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parent[e] = d
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parent[f] = g
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parent[g] = h
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parent[h] = a
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parent[i] = c
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</PRE>
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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 © 2000</TD><TD>
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<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
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</TD></TR></TABLE>
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</BODY>
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</HTML>
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