76 lines
2.5 KiB
C++
76 lines
2.5 KiB
C++
#include "edmonds.h"
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using namespace ED;
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namespace Edmonds {
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std::vector<NodeId> path_to_forest_root(Graph const & graph, NodeId id)
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{
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std::vector<NodeId> retval;
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retval.push_back(id);
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while (graph.matched_neighbor(id) != id)
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{
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id = graph.matched_neighbor(id);
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retval.push_back(id);
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// Note that it is guaranteed that this does not produce a loop:
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// We are traversing the path to a root of the forest,
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// but we know that each root is exposed by M, so after traversing
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// the matching edge, we cannot have reached a root.
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id = graph.ear_or_root_neighbor(id);
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retval.push_back(id);
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}
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return retval;
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}
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Graph maximum_matching(Graph & graph)
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{
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graph.reset_forest();
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for(NodeId id = 0; id < graph.num_nodes(); ++id) {
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if (graph.is_out_of_forest(id))
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{
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for(NodeId neighbor_id : graph.node(id).neighbors())
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{
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if (graph.is_out_of_forest(neighbor_id))
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{
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// Grow Forest
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graph.node(neighbor_id).ear_or_root_neighbor = id;
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}
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else if (graph.is_outer(neighbor_id) and \
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graph.root_of_ear_component(id) != graph.root_of_ear_component(neighbor_id))
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{
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std::vector<NodeId> x_path = path_to_forest_root(graph, id);
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std::vector<NodeId> y_path = path_to_forest_root(graph, neighbor_id);
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if (x_path.back() != y_path.back())
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{
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// Paths are disjoint -> augment
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graph.node(x_path.front()).matched_neighbor = y_path.front();
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graph.node(y_path.front()).matched_neighbor = x_path.front();
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// TODO: put this into own method?
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for(size_t i = 1; i < x_path.size(); i += 2)
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{
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graph.node(x_path[i]).matched_neighbor = x_path[i+1];
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graph.node(x_path[i+1]).matched_neighbor = x_path[i];
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}
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for(size_t i = 1; i < y_path.size(); i += 2)
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{
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graph.node(y_path[i]).matched_neighbor = y_path[i+1];
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graph.node(y_path[i+1]).matched_neighbor = y_path[i];
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}
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// Note that since this is tail-recursion, this will not generate
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// new stack frames in OPT mode
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return maximum_matching(graph);
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}
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else
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{
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// Paths are not disjoint -> shrink blossom
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}
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}
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}
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}
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}
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};
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} |