/usr/include/ignition/math4/ignition/math/graph/GraphAlgorithms.hh is in libignition-math4-dev 4.0.0+dfsg1-4.
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* Copyright (C) 2017 Open Source Robotics Foundation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*/
#ifndef IGNITION_MATH_GRAPH_GRAPHALGORITHMS_HH_
#define IGNITION_MATH_GRAPH_GRAPHALGORITHMS_HH_
#include <functional>
#include <list>
#include <map>
#include <queue>
#include <stack>
#include <utility>
#include <vector>
#include <ignition/math/config.hh>
#include "ignition/math/graph/Graph.hh"
#include "ignition/math/Helpers.hh"
namespace ignition
{
namespace math
{
inline namespace IGNITION_MATH_VERSION_NAMESPACE
{
namespace graph
{
/// \def CostInfo.
/// \brief Used in Dijkstra. For a given source vertex, this pair represents
/// the cost (first element) to reach a destination vertex (second element).
using CostInfo = std::pair<double, VertexId>;
/// \brief Breadth first sort (BFS).
/// Starting from the vertex == _from, it traverses the graph exploring the
/// neighbors first, before moving to the next level neighbors.
/// \param[in] _graph A graph.
/// \param[in] _from The starting vertex.
/// \return The vector of vertices Ids traversed in a breadth first manner.
template<typename V, typename E, typename EdgeType>
std::vector<VertexId> BreadthFirstSort(const Graph<V, E, EdgeType> &_graph,
const VertexId &_from)
{
// Create an auxiliary graph, where the data is just a boolean value that
// stores whether the vertex has been visited or not.
Graph<bool, E, EdgeType> visitorGraph;
// Copy the vertices (just the Id).
for (auto const &v : _graph.Vertices())
visitorGraph.AddVertex("", false, v.first);
// Copy the edges (without data).
for (auto const &e : _graph.Edges())
visitorGraph.AddEdge(e.second.get().Vertices(), E());
std::vector<VertexId> visited;
std::list<VertexId> pending = {_from};
while (!pending.empty())
{
auto vId = pending.front();
pending.pop_front();
// If the vertex has been visited, skip.
auto &vertex = visitorGraph.VertexFromId(vId);
if (vertex.Data())
continue;
visited.push_back(vId);
vertex.Data() = true;
// Add more vertices to visit if they haven't been visited yet.
auto adjacents = visitorGraph.AdjacentsFrom(vId);
for (auto const &adj : adjacents)
{
vId = adj.first;
auto &v = adj.second.get();
if (!v.Data())
pending.push_back(vId);
}
}
return visited;
}
/// \brief Depth first sort (DFS).
/// Starting from the vertex == _from, it visits the graph as far as
/// possible along each branch before backtracking.
/// \param[in] _graph A graph.
/// \param[in] _from The starting vertex.
/// \return The vector of vertices Ids visited in a depth first manner.
template<typename V, typename E, typename EdgeType>
std::vector<VertexId> DepthFirstSort(const Graph<V, E, EdgeType> &_graph,
const VertexId &_from)
{
// Create an auxiliary graph, where the data is just a boolean value that
// stores whether the vertex has been visited or not.
Graph<bool, E, EdgeType> visitorGraph;
// Copy the vertices (just the Id).
for (auto const &v : _graph.Vertices())
visitorGraph.AddVertex("", false, v.first);
// Copy the edges (without data).
for (auto const &e : _graph.Edges())
visitorGraph.AddEdge(e.second.get().Vertices(), E());
std::vector<VertexId> visited;
std::stack<VertexId> pending({_from});
while (!pending.empty())
{
auto vId = pending.top();
pending.pop();
// If the vertex has been visited, skip.
auto &vertex = visitorGraph.VertexFromId(vId);
if (vertex.Data())
continue;
visited.push_back(vId);
vertex.Data() = true;
// Add more vertices to visit if they haven't been visited yet.
auto adjacents = visitorGraph.AdjacentsFrom(vId);
for (auto const &adj : adjacents)
{
vId = adj.first;
auto &v = adj.second.get();
if (!v.Data())
pending.push(vId);
}
}
return visited;
}
/// \brief Dijkstra algorithm.
/// Find the shortest path between the vertices in a graph.
/// If only a graph and a source vertex is provided, the algorithm will
/// find shortest paths from the source vertex to all other vertices in the
/// graph. If an additional destination vertex is provided, the algorithm
/// will stop when the shortest path is found between the source and
/// destination vertex.
/// \param[in] _graph A graph.
/// \param[in] _from The starting vertex.
/// \param[in] _to Optional destination vertex.
/// \return A map where the keys are the destination vertices. For each
/// destination, the value is another pair, where the key is the shortest
/// cost from the origin vertex. The value is the previous neighbor Id in the
/// shortest path.
/// Note: In the case of providing a destination vertex, only the entry in the
/// map with key = _to should be used. The rest of the map may contain
/// incomplete information. If you want all shortest paths to all other
/// vertices, please remove the destination vertex.
/// If the source or destination vertex don't exist, the function will return
/// an empty map.
///
/// E.g.: Given the following undirected graph, g, with five vertices:
///
/// (6) |
/// 0-------1 |
/// | /|\ |
/// | / | \(5) |
/// | (2)/ | \ |
/// | / | 2 |
/// (1)| / (2)| / |
/// | / | /(5) |
/// |/ |/ |
/// 3-------4 |
/// (1) |
///
/// This is the resut of Dijkstra(g, 0):
///
/// ================================
/// | Dst | Cost | Previous vertex |
/// ================================
/// | 0 | 0 | 0 |
/// | 1 | 3 | 3 |
/// | 2 | 7 | 4 |
/// | 3 | 1 | 0 |
/// | 4 | 2 | 3 |
/// ================================
///
/// This is the result of Dijkstra(g, 0, 3):
///
/// ================================
/// | Dst | Cost | Previous vertex |
/// ================================
/// | 0 | 0 | 0 |
/// | 1 |ignore| ignore |
/// | 2 |ignore| ignore |
/// | 3 | 1 | 0 |
/// | 4 |ignore| ignore |
/// ================================
template<typename V, typename E, typename EdgeType>
std::map<VertexId, CostInfo> Dijkstra(const Graph<V, E, EdgeType> &_graph,
const VertexId &_from,
const VertexId &_to = kNullId)
{
auto allVertices = _graph.Vertices();
// Sanity check: The source vertex should exist.
if (allVertices.find(_from) == allVertices.end())
{
std::cerr << "Vertex [" << _from << "] Not found" << std::endl;
return {};
}
// Sanity check: The destination vertex should exist (if used).
if (_to != kNullId &&
allVertices.find(_to) == allVertices.end())
{
std::cerr << "Vertex [" << _from << "] Not found" << std::endl;
return {};
}
// Store vertices that are being preprocessed.
std::priority_queue<CostInfo,
std::vector<CostInfo>, std::greater<CostInfo>> pq;
// Create a map for distances and next neightbor and initialize all
// distances as infinite.
std::map<VertexId, CostInfo> dist;
for (auto const &v : allVertices)
{
auto id = v.first;
dist[id] = std::make_pair(MAX_D, kNullId);
}
// Insert _from in the priority queue and initialize its distance as 0.
pq.push(std::make_pair(0.0, _from));
dist[_from] = std::make_pair(0.0, _from);
while (!pq.empty())
{
// This is the minimum distance vertex.
VertexId u = pq.top().second;
// Shortcut: Destination vertex found, exiting.
if (_to != kNullId && _to == u)
break;
pq.pop();
for (auto const &edgePair : _graph.IncidentsFrom(u))
{
const auto &edge = edgePair.second.get();
const auto &v = edge.From(u);
double weight = edge.Weight();
// If there is shorted path to v through u.
if (dist[v].first > dist[u].first + weight)
{
// Updating distance of v.
dist[v] = std::make_pair(dist[u].first + weight, u);
pq.push(std::make_pair(dist[v].first, v));
}
}
}
return dist;
}
/// \brief Calculate the connected components of an undirected graph.
/// A connected component of an undirected graph is a subgraph in which any
/// two vertices are connected to each other by paths, and which is connected
/// to no additional vertices in the supergraph.
/// \ref https://en.wikipedia.org/wiki/Connected_component_(graph_theory)
/// \param[in] _graph A graph.
/// \return A vector of graphs. Each element of the graph is a component
/// (subgraph) of the original graph.
template<typename V, typename E>
std::vector<UndirectedGraph<V, E>> ConnectedComponents(
const UndirectedGraph<V, E> &_graph)
{
std::map<VertexId, unsigned int> visited;
unsigned int componentCount = 0;
for (auto const &v : _graph.Vertices())
{
if (visited.find(v.first) == visited.end())
{
auto component = BreadthFirstSort(_graph, v.first);
for (auto const &vId : component)
visited[vId] = componentCount;
++componentCount;
}
}
std::vector<UndirectedGraph<V, E>> res(componentCount);
// Create the vertices.
for (auto const &vPair : _graph.Vertices())
{
const auto &v = vPair.second.get();
const auto &componentId = visited[v.Id()];
res[componentId].AddVertex(v.Name(), v.Data(), v.Id());
}
// Create the edges.
for (auto const &ePair : _graph.Edges())
{
const auto &e = ePair.second.get();
const auto &vertices = e.Vertices();
const auto &componentId = visited[vertices.first];
res[componentId].AddEdge(vertices, e.Data(), e.Weight());
}
return res;
}
}
}
}
}
#endif
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