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// //======================================================================= // Copyright 1997, 1998, 1999, 2000 University of Notre Dame. // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek // // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) //======================================================================= // #ifndef BOOST_DISJOINT_SETS_HPP #define BOOST_DISJOINT_SETS_HPP #include #include #include namespace boost { struct find_with_path_halving { template < class ParentPA, class Vertex > Vertex operator()(ParentPA p, Vertex v) { return detail::find_representative_with_path_halving(p, v); } }; struct find_with_full_path_compression { template < class ParentPA, class Vertex > Vertex operator()(ParentPA p, Vertex v) { return detail::find_representative_with_full_compression(p, v); } }; // This is a generalized functor to provide disjoint sets operations // with "union by rank" and "path compression". A disjoint-set data // structure maintains a collection S={S1, S2, ..., Sk} of disjoint // sets. Each set is identified by a representative, which is some // member of of the set. Sets are represented by rooted trees. Two // heuristics: "union by rank" and "path compression" are used to // speed up the operations. // Disjoint Set requires two vertex properties for internal use. A // RankPA and a ParentPA. The RankPA must map Vertex to some Integral type // (preferably the size_type associated with Vertex). The ParentPA // must map Vertex to Vertex. template < class RankPA, class ParentPA, class FindCompress = find_with_full_path_compression > class disjoint_sets { typedef disjoint_sets self; inline disjoint_sets() {} public: inline disjoint_sets(RankPA r, ParentPA p) : rank(r), parent(p) {} inline disjoint_sets(const self& c) : rank(c.rank), parent(c.parent) {} // Make Set -- Create a singleton set containing vertex x template < class Element > inline void make_set(Element x) { put(parent, x, x); typedef typename property_traits< RankPA >::value_type R; put(rank, x, R()); } // Link - union the two sets represented by vertex x and y template < class Element > inline void link(Element x, Element y) { detail::link_sets(parent, rank, x, y); } // Union-Set - union the two sets containing vertex x and y template < class Element > inline void union_set(Element x, Element y) { link(find_set(x), find_set(y)); } // Find-Set - returns the Element representative of the set // containing Element x and applies path compression. template < class Element > inline Element find_set(Element x) { return rep(parent, x); } template < class ElementIterator > inline std::size_t count_sets(ElementIterator first, ElementIterator last) { std::size_t count = 0; for (; first != last; ++first) if (get(parent, *first) == *first) ++count; return count; } template < class ElementIterator > inline void normalize_sets(ElementIterator first, ElementIterator last) { for (; first != last; ++first) detail::normalize_node(parent, *first); } template < class ElementIterator > inline void compress_sets(ElementIterator first, ElementIterator last) { for (; first != last; ++first) detail::find_representative_with_full_compression(parent, *first); } protected: RankPA rank; ParentPA parent; FindCompress rep; }; template < class ID = identity_property_map, class InverseID = identity_property_map, class FindCompress = find_with_full_path_compression > class disjoint_sets_with_storage { typedef typename property_traits< ID >::value_type Index; typedef std::vector< Index > ParentContainer; typedef std::vector< unsigned char > RankContainer; public: typedef typename ParentContainer::size_type size_type; disjoint_sets_with_storage( size_type n = 0, ID id_ = ID(), InverseID inv = InverseID()) : id(id_), id_to_vertex(inv), rank(n, 0), parent(n) { for (Index i = 0; i < n; ++i) parent[i] = i; } // note this is not normally needed template < class Element > inline void make_set(Element x) { parent[x] = x; rank[x] = 0; } template < class Element > inline void link(Element x, Element y) { extend_sets(x, y); detail::link_sets(&parent[0], &rank[0], get(id, x), get(id, y)); } template < class Element > inline void union_set(Element x, Element y) { Element rx = find_set(x); Element ry = find_set(y); link(rx, ry); } template < class Element > inline Element find_set(Element x) { return id_to_vertex[rep(&parent[0], get(id, x))]; } template < class ElementIterator > inline std::size_t count_sets(ElementIterator first, ElementIterator last) { std::size_t count = 0; for (; first != last; ++first) if (parent[*first] == *first) ++count; return count; } template < class ElementIterator > inline void normalize_sets(ElementIterator first, ElementIterator last) { for (; first != last; ++first) detail::normalize_node(&parent[0], *first); } template < class ElementIterator > inline void compress_sets(ElementIterator first, ElementIterator last) { for (; first != last; ++first) detail::find_representative_with_full_compression( &parent[0], *first); } const ParentContainer& parents() { return parent; } protected: template < class Element > inline void extend_sets(Element x, Element y) { Index needed = get(id, x) > get(id, y) ? get(id, x) + 1 : get(id, y) + 1; if (needed > parent.size()) { rank.insert(rank.end(), needed - rank.size(), 0); for (Index k = parent.size(); k < needed; ++k) parent.push_back(k); } } ID id; InverseID id_to_vertex; RankContainer rank; ParentContainer parent; FindCompress rep; }; } // namespace boost #endif // BOOST_DISJOINT_SETS_HPP