public string ShortestPath(Dictionary <string, Dictionary <string, int> > graph, string source, string destination)
{
// get all nodes of the graph
HashSet <string> allNodes = new HashSet <string>();
foreach (string u in graph.Keys)
{
allNodes.Add(u);
foreach (string v in graph[u].Keys)
{
allNodes.Add(v);
}
}
Dictionary <string, int> distances = new Dictionary <string, int>();
distances.Add(source, 0);
Dictionary <string, string> path = new Dictionary <string, string>();
List <Triple> tripleList = new List <Triple>();
// build heap with nodes that connected to source
// key is the min distance of the source to the node(headNode of the triple)
foreach (string u in graph[source].Keys)
{
int len = graph[source][u];
tripleList.Add(new Triple(u, source, len));
}
HeapForTriple heap = new HeapForTriple(tripleList);
heap.Heapsify();
// X stores nodes that being checked
HashSet <string> X = new HashSet <string>();
X.Add(source);
// loop until checking all nodes
while (!X.Equals(allNodes))
{
if (heap.HeapIsEmpty())
{
break;
}
// extract node with min distance from heap
Triple minTriple = heap.DeleteMin();
string minNode = minTriple.GetHeadNode();
X.Add(minNode);
distances.Add(minNode, minTriple.GetLength());
path.Add(minNode, minTriple.GetTailNode());
// update key value for nodes(headNodes) that form edge with minNode(tailNode)
if (graph.ContainsKey(minNode))
{
foreach (string v in graph[minNode].Keys)
{
int newLen = distances[minNode] + graph[minNode][v];
if (!heap.ContainsNode(v))
{
heap.Insert(new Triple(v, minNode, newLen));
}
else
{
int oldLen = heap.GetLength(v);
if (newLen < oldLen)
{
heap.Delete(v);
heap.Insert(new Triple(v, minNode, newLen));
}
}
}
}
}
if (!path.ContainsKey(destination))
{
return("Path not exist!");
}
StringBuilder sb = new StringBuilder();
string n = destination;
sb.Append(n);
while (path.ContainsKey(n))
{
string v = path[n];
int len = graph[v][n];
sb.Insert(0, " ->(" + len + ") ");
sb.Insert(0, v);
n = v;
}
return(sb.ToString());
}
