// TODO: This method should be private and should be called from the bottom of the constructor
        /// <summary>
        /// check optimality conditions:
        /// </summary>
        /// <param name="graph">The edge-weighted directed graph</param>
        /// <param name="sourceVertex">The source vertex to check optimality conditions from</param>
        private bool Check(EdgeWeightedDigraph graph, int sourceVertex)
        {
            if (graph == null)
            {
                if (LogFilter.logError)
                {
                    Debug.LogErrorFormat("EdgeWeightedDigraph cannot be null");
                }
            }

            if (_distanceTo[sourceVertex] != 0.0 || _edgeTo[sourceVertex] != null)
            {
                return(false);
            }
            for (int v = 0; v < graph.NumberOfVertices; v++)
            {
                if (v == sourceVertex)
                {
                    continue;
                }
                if (_edgeTo[v] == null && _distanceTo[v] != double.PositiveInfinity)
                {
                    return(false);
                }
            }
            for (int v = 0; v < graph.NumberOfVertices; v++)
            {
                foreach (DirectedEdge edge in graph.Adjacent(v))
                {
                    int w = edge.To;
                    if (_distanceTo[v] + edge.Weight < _distanceTo[w])
                    {
                        return(false);
                    }
                }
            }
            for (int w = 0; w < graph.NumberOfVertices; w++)
            {
                if (_edgeTo[w] == null)
                {
                    continue;
                }
                DirectedEdge edge = _edgeTo[w];
                int          v    = edge.From;
                if (w != edge.To)
                {
                    return(false);
                }
                if (_distanceTo[v] + edge.Weight != _distanceTo[w])
                {
                    return(false);
                }
            }
            return(true);
        }
        private DijkstraShortestPath(EdgeWeightedDigraph graph, int sourceVertex, int?destinationVertex)
        {
            if (graph == null)
            {
                if (LogFilter.logError)
                {
                    Debug.LogErrorFormat("EdgeWeightedDigraph cannot be null");
                }
            }

            foreach (DirectedEdge edge in graph.Edges())
            {
                if (edge.Weight < 0)
                {
                    if (LogFilter.logError)
                    {
                        Debug.LogErrorFormat("Edge: '{0}' has negative weight", edge);
                    }
                }
            }

            _distanceTo = new double[graph.NumberOfVertices];
            _edgeTo     = new DirectedEdge[graph.NumberOfVertices];
            for (int v = 0; v < graph.NumberOfVertices; v++)
            {
                _distanceTo[v] = Double.PositiveInfinity;
            }
            _distanceTo[sourceVertex] = 0.0;

            _priorityQueue = new IndexMinPriorityQueue <double>(graph.NumberOfVertices);
            _priorityQueue.Insert(sourceVertex, _distanceTo[sourceVertex]);
            while (!_priorityQueue.IsEmpty())
            {
                int v = _priorityQueue.DeleteMin();

                if (destinationVertex.HasValue && v == destinationVertex.Value)
                {
                    return;
                }

                foreach (DirectedEdge edge in graph.Adjacent(v))
                {
                    Relax(edge);
                }
            }
            Check(graph, sourceVertex);
        }