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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+
+#ifndef CERES_INTERNAL_GRAPH_H_
+#define CERES_INTERNAL_GRAPH_H_
+
+#include <limits>
+#include <glog/logging.h>
+#include "ceres/integral_types.h"
+#include "ceres/map_util.h"
+#include "ceres/collections_port.h"
+#include "ceres/internal/macros.h"
+#include "ceres/types.h"
+
+namespace ceres {
+namespace internal {
+
+// A weighted undirected graph templated over the vertex ids. Vertex
+// should be hashable and comparable.
+template <typename Vertex>
+class Graph {
+ public:
+  Graph() {}
+
+  // Add a weighted vertex. If the vertex already exists in the graph,
+  // its weight is set to the new weight.
+  void AddVertex(const Vertex& vertex, double weight) {
+    if (vertices_.find(vertex) == vertices_.end()) {
+      vertices_.insert(vertex);
+      edges_[vertex] = HashSet<Vertex>();
+    }
+    vertex_weights_[vertex] = weight;
+  }
+
+  // Uses weight = 1.0. If vertex already exists, its weight is set to
+  // 1.0.
+  void AddVertex(const Vertex& vertex) {
+    AddVertex(vertex, 1.0);
+  }
+
+  bool RemoveVertex(const Vertex& vertex) {
+    if (vertices_.find(vertex) == vertices_.end()) {
+      return false;
+    }
+
+    vertices_.erase(vertex);
+    vertex_weights_.erase(vertex);
+    const HashSet<Vertex>& sinks = edges_[vertex];
+    for (typename HashSet<Vertex>::const_iterator it = sinks.begin();
+         it != sinks.end(); ++it) {
+      if (vertex < *it) {
+        edge_weights_.erase(make_pair(vertex, *it));
+      } else {
+        edge_weights_.erase(make_pair(*it, vertex));
+      }
+      edges_[*it].erase(vertex);
+    }
+
+    edges_.erase(vertex);
+    return true;
+  }
+
+  // Add a weighted edge between the vertex1 and vertex2. Calling
+  // AddEdge on a pair of vertices which do not exist in the graph yet
+  // will result in undefined behavior.
+  //
+  // It is legal to call this method repeatedly for the same set of
+  // vertices.
+  void AddEdge(const Vertex& vertex1, const Vertex& vertex2, double weight) {
+    DCHECK(vertices_.find(vertex1) != vertices_.end());
+    DCHECK(vertices_.find(vertex2) != vertices_.end());
+
+    if (edges_[vertex1].insert(vertex2).second) {
+      edges_[vertex2].insert(vertex1);
+    }
+
+    if (vertex1 < vertex2) {
+      edge_weights_[make_pair(vertex1, vertex2)] = weight;
+    } else {
+      edge_weights_[make_pair(vertex2, vertex1)] = weight;
+    }
+  }
+
+  // Uses weight = 1.0.
+  void AddEdge(const Vertex& vertex1, const Vertex& vertex2) {
+    AddEdge(vertex1, vertex2, 1.0);
+  }
+
+  // Calling VertexWeight on a vertex not in the graph will result in
+  // undefined behavior.
+  double VertexWeight(const Vertex& vertex) const {
+    return FindOrDie(vertex_weights_, vertex);
+  }
+
+  // Calling EdgeWeight on a pair of vertices where either one of the
+  // vertices is not present in the graph will result in undefined
+  // behaviour. If there is no edge connecting vertex1 and vertex2,
+  // the edge weight is zero.
+  double EdgeWeight(const Vertex& vertex1, const Vertex& vertex2) const {
+    if (vertex1 < vertex2) {
+      return FindWithDefault(edge_weights_, make_pair(vertex1, vertex2), 0.0);
+    } else {
+      return FindWithDefault(edge_weights_, make_pair(vertex2, vertex1), 0.0);
+    }
+  }
+
+  // Calling Neighbors on a vertex not in the graph will result in
+  // undefined behaviour.
+  const HashSet<Vertex>& Neighbors(const Vertex& vertex) const {
+    return FindOrDie(edges_, vertex);
+  }
+
+  const HashSet<Vertex>& vertices() const {
+    return vertices_;
+  }
+
+  static double InvalidWeight() {
+    return std::numeric_limits<double>::quiet_NaN();
+  };
+
+ private:
+  HashSet<Vertex> vertices_;
+  HashMap<Vertex, double> vertex_weights_;
+  HashMap<Vertex, HashSet<Vertex> > edges_;
+  HashMap<pair<Vertex, Vertex>, double> edge_weights_;
+
+  CERES_DISALLOW_COPY_AND_ASSIGN(Graph);
+};
+
+}  // namespace internal
+}  // namespace ceres
+
+#endif  // CERES_INTERNAL_GRAPH_H_