//
// Performs Dijkstra's shortest path algorithm on the the constructed PathGraph object
//
// @param path -- Returns the actual shortest path in the List parameter
// @return the length of the shortest path via the return value
//
public int Dijkstra(List <int> path)
{
// Initialize all shortest paths to a node to be large and the shortest path to a start node to be 0
InitializeSingleSource(int.MaxValue - 100000); // -100000 prevents issues with arithmetic overflow
//
// Create the min-Fibonacci Heap by pushing all vertices onto the Heap
//
int numV = graph.NumVertices();
//FibonacciHeap<int> vertices = new FibonacciHeap<int>();
MinHeap vertices = new MinHeap(numV);
for (int i = 0; i < numV; i++) // VertexValues node : shortPathEst)
{
// Insert the weight, d, which is the short path to node i
HeapNode <int> node = new HeapNode <int>(i);
vertices.Insert(node, shortPathEst[i].d);
shortPathEst[i].heapNode = node; // maintain a pointer to the object for DecreaseKey
}
//
// Visit all vertices in the PathGraph (always visiting the shortest distance from the start node first)
// Do so by using a Fibonacci Heap
//
while (!vertices.IsEmpty())
{
//
// Acquire the minimum: min will contain a pair <shortest distance to node n, node n>
//
HeapNode <int> min = vertices.ExtractMin(); // Now, extract the node
//
// For each adjacent vertex, relax
//
int nodeIndex = min.data;
List <int> adjNodes = graph.AdjacentNodes(nodeIndex);
foreach (int neighbor in adjNodes)
{
Relax(nodeIndex, neighbor, graph.GetWeight(nodeIndex, neighbor), vertices);
}
}
//
// Look at predecessors to acquire the actual shortest path
//
path.Add(goalNode); // Add the last node
// Predecessor node
int predNode = shortPathEst[goalNode].pi;
// Loop while we have not yet reached the start node
// If we hit a NIL, a path does not exist
while (predNode != startNode && predNode != NIL)
{
path.Insert(0, predNode); // Insert at the beginning of the List; index 0
predNode = shortPathEst[predNode].pi;
}
// Check if the goal node was even reachable
if (predNode == NIL)
{
path.Clear();
return(NIL);
}
// Insert the first node at the beginning
path.Insert(0, predNode);
return(shortPathEst[goalNode].d); // recall .d contains the shortest path length to the goalNode
}