private void Relax(Edge edge)
{
//get the source and target vertex of the edge
int v = edge.Source, w = edge.Target;
/*
* _distTo[w] contains the shortest path so far to the
* vertex w so we can compare it to the weight of of going through
* v, if it is less use the new path instead
* */
if (_distanceTo[w] > _distanceTo[v] + edge.Weight)
{
//set the distance to w to the new(lower) weight
_distanceTo[w] = _distanceTo[v] + edge.Weight;
//add the edge to the list of edges in our shortest paths
_edgeTo[w] = edge;
if (_priorityQueue.Contains(w))
{
/*
* if w is already in the priority que update its minimum path and re-order the que
* */
_priorityQueue.DecreaseKey(w, _distanceTo[w]);
}
else
{
_priorityQueue.Insert(w, _distanceTo[w]);
}
}
}