public static List <GraphNode <TValue> > GetShortestDistancesFromRoot <TValue>(GraphNode <TValue> startNode)
{
//1- Get the list of all vertexes in the graph .
List <GraphNode <TValue> > bfsOrdering = BFS.BFS_Iterative(startNode); /* Extra space usage O(V) for bfsOrdering. */
//2- Set the distance of all the nodes from the root node to infinite.
foreach (GraphNode <TValue> node in bfsOrdering)
{
node.DistanceFromStartNode = int.MaxValue; // aka. Infinite.
}
//3- Set the distance of the root node from the root node to zero.
startNode.DistanceFromStartNode = 0;
//4- Build a MinHeap over all the nodes in the array.
var minHeap = new MinBinaryHeap <GraphNode <TValue>, TValue>(bfsOrdering.Select(o => new KeyValuePair <GraphNode <TValue>, TValue>(o, o.Value)).ToList()); /* Extra space usage O(V) for heapArray. */
var shortestDistanceFromRoot = new List <GraphNode <TValue> >(); /* Extra space usage O(V) for tracking shortest distances of all the nodes from the root node. */
while (true) // Repeat until minHeap is empty.
{
//5- Update the distance of all the adjacent nodes of the current minimum node.
if (minHeap.TryFindRoot(out KeyValuePair <GraphNode <TValue>, TValue> currentMinNode, minHeap.HeapArray.Count))
{
foreach (GraphEdge <TValue> edge in currentMinNode.Key.Adjacents)
{
if (!shortestDistanceFromRoot.Contains(edge.Node))
{
if (edge.Node.DistanceFromStartNode > currentMinNode.Key.DistanceFromStartNode + edge.Weight)
{
edge.Node.DistanceFromStartNode = currentMinNode.Key.DistanceFromStartNode + edge.Weight;
int index = minHeap.FindIndex(edge.Node); /* Can be O(1) if the index of each element is stored with the element. */
if (index >= 0)
{
minHeap.BubbleUp_Iteratively(index, minHeap.HeapArray.Count);
}
}
}
}
if (minHeap.TryRemoveRoot(out currentMinNode, minHeap.HeapArray.Count))
{
shortestDistanceFromRoot.Add(currentMinNode.Key);
}
else
{
break;
}
}
else
{
break;
}
}
return(shortestDistanceFromRoot);
}
