// Dijkstra's shortest paths algorithm, implemented
// with priority queue. Running time: O(M * log M)
// Learn more at: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#Using_a_priority_queue
public static void DijkstraAlgorithm(
Dictionary<Node, List<Edge>> graph,
Node sourceNode)
{
var queue = new PriorityQueue<Node>();
foreach (var node in graph)
{
node.Key.Distance = double.PositiveInfinity;
}
sourceNode.Distance = 0.0d;
queue.Enqueue(sourceNode);
while (queue.Count != 0)
{
var currentNode = queue.Dequeue();
if (double.IsPositiveInfinity(currentNode.Distance))
{
// All nodes processed --> algorithm finished
break;
}
foreach (var childEdge in graph[currentNode])
{
var newDistance = currentNode.Distance + childEdge.Distance;
if (newDistance < childEdge.Node.Distance)
{
childEdge.Node.Distance = newDistance;
childEdge.Node.PreviousNode = currentNode;
queue.Enqueue(childEdge.Node);
}
}
}
}
public static void DijkstraAlgorithm(Dictionary<Node, List<Connection>> graph, Node source)
{
var queue = new PriorityQueue<Node>();
foreach (var node in graph)
{
node.Key.DijkstraDistance = double.PositiveInfinity;
}
source.DijkstraDistance = 0.0d;
queue.Enqueue(source);
while (queue.Count != 0)
{
var currentNode = queue.Dequeue();
if (double.IsPositiveInfinity(currentNode.DijkstraDistance))
{
break;
}
foreach (var neighbor in graph[currentNode])
{
var potDistance = currentNode.DijkstraDistance + neighbor.Distance;
if (potDistance < neighbor.Node.DijkstraDistance)
{
neighbor.Node.DijkstraDistance = potDistance;
queue.Enqueue(neighbor.Node);
}
}
}
}
static void Main()
{
Node node1 = new Node(1);
Node node2 = new Node(2);
Node node3 = new Node(3);
Node node4 = new Node(4);
Node node5 = new Node(5);
Node node6 = new Node(6);
Node node7 = new Node(7);
Node node8 = new Node(8);
Node node9 = new Node(9);
Node node10 = new Node(10);
List<Node> nodes = new List<Node>();
nodes.Add(node1);
nodes.Add(node2);
nodes.Add(node3);
nodes.Add(node4);
nodes.Add(node5);
nodes.Add(node6);
nodes.Add(node7);
nodes.Add(node8);
nodes.Add(node9);
nodes.Add(node10);
Dictionary<Node, List<Connection>> graph = new Dictionary<Node, List<Connection>>()
{
{node1, new List<Connection> {new Connection(node2, 23), new Connection(node8, 8)} },
{node2, new List<Connection> {new Connection(node1, 23), new Connection(node4, 3), new Connection(node7, 34)} },
{node3, new List<Connection> {new Connection(node4, 6), new Connection(node8, 25), new Connection(node10, 7)} },
{node4, new List<Connection> {new Connection(node2, 3), new Connection(node3, 6)} },
{node5, new List<Connection> {new Connection(node6, 10)} },
{node6, new List<Connection> {new Connection(node5, 10)} },
{node7, new List<Connection> {new Connection(node2, 34)} },
{node8, new List<Connection> {new Connection(node1, 8), new Connection(node3, 25), new Connection(node10, 30)} },
{node9, new List<Connection> {} },
{node10, new List<Connection> {new Connection(node3, 7), new Connection(node8, 30)} },
};
Node source = node1;
DijkstraAlgorithm(graph, source);
for (int i = 0; i < nodes.Count; i++)
{
Console.Write("Distance from {0} to {1} ", source.ID, i);
Console.WriteLine(nodes[i].DijkstraDistance);
}
}
static void DijkstraAlgorithm(Dictionary<Node, List<Connection>> graph, Node source)
{
PriorityQueue<Node> queue = new PriorityQueue<Node>();
foreach (var node in graph)
{
if (source.ID != node.Key.ID)
{
node.Key.DijkstraDistance = double.PositiveInfinity;
queue.Enqueue(node.Key);
}
}
source.DijkstraDistance = 0.0d;
queue.Enqueue(source);
while (queue.Count != 0)
{
Node currentNode = queue.Peek();
if (currentNode.DijkstraDistance == double.PositiveInfinity)
{
break;
}
foreach (var neighbour in graph[currentNode])
{
double potDistance = currentNode.DijkstraDistance + neighbour.Distance;
if (potDistance < neighbour.Node.DijkstraDistance)
{
neighbour.Node.DijkstraDistance = potDistance;
}
}
queue.Dequeue();
}
}
public static void DijkstraAlgorithm(Dictionary<Node, List<Edge>> graph, Node source)
{
var pQueue = new PriorityQueue<Node>();
source.MinDistance = 0.0;
pQueue.Enqueue(source);
while (pQueue.Count != 0)
{
Console.WriteLine(string.Join<Node>(", ", pQueue.heap));
Node currentNode = pQueue.Dequeue();
foreach (var neighbour in graph[currentNode])
{
double newDist = currentNode.MinDistance + neighbour.Distance;
if (newDist < neighbour.Node.MinDistance)
{
neighbour.Node.MinDistance = newDist;
pQueue.Enqueue(neighbour.Node);
}
}
}
}
public static void Main()
{
int n = 12;
var nodes = new Node[n];
for (int i = 0; i < n; i++)
{
nodes[i] = new Node(i);
}
var graph = new Dictionary<Node, List<Edge>>
{
{
nodes[0], new List<Edge>
{
new Edge(nodes[6], 10),
new Edge(nodes[8], 12),
}
},
{
nodes[1], new List<Edge>
{
new Edge(nodes[4], 20),
new Edge(nodes[7], 26),
new Edge(nodes[9], 5),
new Edge(nodes[11], 6),
}
},
{
nodes[2], new List<Edge>
{
new Edge(nodes[7], 15),
new Edge(nodes[8], 14),
new Edge(nodes[11], 9),
}
},
{
nodes[3], new List<Edge>
{
new Edge(nodes[10], 7),
}
},
{
nodes[4], new List<Edge>
{
new Edge(nodes[1], 20),
new Edge(nodes[5], 5),
new Edge(nodes[6], 17),
new Edge(nodes[11], 11),
}
},
{
nodes[5], new List<Edge>
{
new Edge(nodes[4], 5),
new Edge(nodes[6], 6),
new Edge(nodes[8], 3),
new Edge(nodes[11], 33),
}
},
{
nodes[6], new List<Edge>
{
new Edge(nodes[0], 10),
new Edge(nodes[4], 17),
new Edge(nodes[5], 6),
}
},
{
nodes[7], new List<Edge>
{
new Edge(nodes[1], 26),
new Edge(nodes[2], 15),
new Edge(nodes[9], 3),
new Edge(nodes[11], 20),
}
},
{
nodes[8], new List<Edge>
{
new Edge(nodes[0], 12),
new Edge(nodes[2], 14),
new Edge(nodes[5], 3),
}
},
{
nodes[9], new List<Edge>
{
new Edge(nodes[1], 5),
new Edge(nodes[7], 3),
}
},
{
nodes[10], new List<Edge>
{
new Edge(nodes[3], 7),
}
},
{
nodes[11], new List<Edge>
{
new Edge(nodes[1], 6),
new Edge(nodes[2], 9),
new Edge(nodes[4], 11),
new Edge(nodes[5], 33),
new Edge(nodes[7], 20),
}
}
};
Node source = nodes[0];
DijkstraAlgorithm(graph, source);
for (int i = 0; i < nodes.Length; i++)
{
Console.Write("Shortest distance [{0} -> {1}]: ", source.Id, i);
double distance = nodes[i].Distance;
if (double.IsPositiveInfinity(distance))
{
Console.WriteLine("no path");
}
else
{
var path = FindPath(graph, nodes[i]);
var pathStr = string.Join("->", path.Select(node => node.Id));
Console.WriteLine("{0} (Path = {1})", distance, pathStr);
}
}
}
private static List<Node> FindPath(
Dictionary<Node, List<Edge>> graph,
Node node)
{
var path = new List<Node>();
while (node != null)
{
path.Add(node);
node = node.PreviousNode;
}
path.Reverse();
return path;
}
public Connection(Node node, double distance)
{
this.Node = node;
this.Distance = distance;
}