/// <summary>
/// Get all exiting edges from startNode
/// </summary>
/// <param name="startNode"> Start node to find all edges from </param>
/// <returns> an array of edges which are adjacent to the startNode</returns>
public Edge[] GetAdjacentNodes(Node startNode)
{
return
(from edge in Edges
where edge.Start.NodeName == startNode.NodeName
select edge).ToArray<Edge>();
}
/// <summary>
/// Finds all cycles starting (and ending) at Node start, with a maxLength over the cycle
/// Because this does a very brute force approach, be smart about how large of a graph and maxLength given
/// Runtime will be something like (big "O") O(NumEdges ^ (maxLength/MinLength))
/// </summary>
/// <param name="start"> Node start (and end) of the cycle. </param>
/// <param name="maxLength"> int maximum length of the cycles to find </param>
/// <returns> The number of cycles found </returns>
public int CyclesShorterThan(Node start, int maxLength)
{
// This should use the bellman ford algorithm
// But, given all edges are atleast 1 unit long, we can just get all 30/Min(Edge Lengths) step routes,
// filtering out the ones which are longer thand 30 cost and those which dont end on the start node (non-cycles)
// inefficient computationally, but saves coding time :)
// Find the smallest edge
var minEdge =
(from edge in RouteMap.Edges
orderby edge.Distance
select edge.Distance).First();
// Find all routes with a number of edges of maxLength/minEdge
// ie, MaxLength = 25 and MinEdge = 5, we can find upto 5 stop routes.
var routes = getSteps(start, maxLength / minEdge, false);
// filter out the ones which dont end on our start (non-cycles)
var cycles =
(from route in routes
where route[route.Length - 1] == start.NodeName
where route.Length > 2 // Must have more than just the starting location
where RouteDistance(route) <= maxLength
select route).Distinct().ToList(); ;
return cycles.Count;
}
///<summary>
/// Takes a string to convert to a graph according to instructions
/// Utilizes fluent interface
///</summary>
///<param name="input"> the source string to build the graph from</param>
public GraphBuilder BuildFromString(string input)
{
// General pattern expected.
string pattern = "([A-E][A-E][0-9]{1,9}(( )?,( )?)?)+";
// Disregard Malformed input, you wiley recruiters you...
Match match = Regex.Match(input, pattern);
// If you're not being tricksy
if (!match.Success)
{
Console.WriteLine("Malformed input detected. Aborting.");
return null;
}
// Split on the comma
pattern = "[\\s]*[,][\\s]*";
String[] tokens = Regex.Split(input, pattern);
Dictionary<char, Node> nodeDictionary = new Dictionary<char, Node>(tokens.Count());
foreach (String token in tokens)
{
Node node1 = new Node(token[0]);
Node node2 = new Node(token[1]);
// Ensure we dont add nodes more than once.
if (!nodeDictionary.ContainsKey(token[0]))
{
nodeDictionary.Add(token[0], node1);
}
if (!nodeDictionary.ContainsKey(token[1]))
{
nodeDictionary.Add(token[1], node2);
}
nodes = nodeDictionary.Values.ToList();
// Dont have to check edges so stringently
// Email said: "For a given route will never appear more than once, and Node1 will != Node2"
edges.Add(new Edge(node1, node2, int.Parse(token.Substring(2))));
}
//Save the source of this graph.
source = input;
return this;
}
/// <summary>
/// Returns a path starting at start, a maximum depth (number of stops) of maxDepth
/// will only return strings of exactly maxDepth if exactLentgh is true
///</summary>
///
/// <param name="start"> The starting node for the route </param>
/// <param name="maxDepth"> The maximum length (number of stops) of the route </param>
/// <param name="exactLength"> return only exaclt maxDepth sized routes? </param>
/// <returns> A list of routes that match the invoked criteria </returns>
public List<string> getSteps(Node start, int maxDepth, bool exactLength)
{
// So far returning nothing.
List<string> retVal = new List<string>();
if (maxDepth == 0)
{
// Stop here and Return.
retVal.Add(start.ToString());
return retVal;
}
// Need to go deeper! get Adjacencies
Edge[] adjacent = RouteMap.GetAdjacentNodes(start);
foreach (Edge edge in adjacent)
{
// Step deeper to build the path
List<string> subGraphs = getSteps(edge.End, maxDepth - 1, exactLength);
// For each Subgraph, mark that we were "here"
foreach (string graph in subGraphs)
{
retVal.Add(start.NodeName + "-" + graph);
}
// Add this < maxDepth length path
if (!exactLength)
{
retVal.Add(edge.Start.NodeName.ToString());
}
}
return retVal;
}
/// <summary>
/// Implements a modified Djikstra's Algorithm to find Min routes from Node start
/// Also has the ability to search for a Cycle if bool findCycle is true
/// </summary>
/// <param name="start">Node to start search from, also the end node if finding cycles</param>
/// <param name="findCycle"> Should we find cycles or just find all other nodes?</param>
/// <returns> Returns a dictionary giving the distance and route from Start to the key in the dictionary</returns>
public Dictionary<char, Tuple<int, string>> GetMinRoutes(Node start, bool findCycle)
{
// So that we dont count it a million times
var count = graph.Nodes.Count;
// We want to keep track of distances, which we've visited, routes. And eventually return a formated value
Dictionary<char, int> distances = new Dictionary<char, int>(count);
Dictionary<char, bool> visited = new Dictionary<char, bool>(count);
Dictionary<char, string> routes = new Dictionary<char, string>(count);
Dictionary<char, Tuple<int, string>> retVal = new Dictionary<char, Tuple<int, string>>(count);
// Initialize to default values
foreach (Node n in graph.Nodes)
{
distances.Add(n.NodeName, Int32.MaxValue);
routes.Add(n.NodeName, start.NodeName.ToString());
}
// We're not coming back here, so assume distance of 0
if (!findCycle)
{
distances[start.NodeName] = 0;
}
// Copy the Edges list so this function doesnt have side-effects
var edges = graph.Edges.ToList();
// Start from our start position.
var current = start;
// We want to visit every node if possible (see "break;" below)
while (visited.Keys.Count < count)
{
// Skip adding the start node once, so that we'll return to it again.
if (findCycle)
{
// But from now on, track which we've visited
findCycle = false;
}
else
{
visited.Add(current.NodeName, true);
}
// Check each edge for a better route
foreach (Edge edge in graph.GetAdjacentNodes(current))
{
// Never check this edge again.
edges.Remove(edge);
// If we dont have a route, or if we've found a better route
if (distances[edge.End.NodeName] == Int32.MaxValue
|| distances[current.NodeName] + edge.Distance < distances[edge.End.NodeName])
{
if (current.NodeName == start.NodeName)
{
distances[edge.End.NodeName] = edge.Distance;
}
else
{
distances[edge.End.NodeName] = distances[current.NodeName] + edge.Distance;
}
routes[edge.End.NodeName] = routes[current.NodeName] + "-" + edge.End;
}
}
// Figure out all nodes which are adjacent to the currently visited nodes
List<char> adjacencies = new List<char>();
adjacencies = adjacencies.Union(
graph.GetAdjacentNodes(current)
.Select(edge => edge.End.NodeName)).ToList();
foreach (char n in visited.Keys)
{
adjacencies = adjacencies.Union(
graph.GetAdjacentNodes(new Node(n))
.Select(edge => edge.End.NodeName)).ToList();
}
// Select the node with the lowest distance, and hasnt been visited
current =
(from KeyValuePair<char, int> pair in distances
where pair.Key != current.NodeName
where !visited.Keys.Contains(pair.Key)
where adjacencies.Contains(pair.Key)
orderby pair.Value
select new Node(pair.Key)).DefaultIfEmpty(null).First();
// There are maybe nodes left, but they're not accessible
if (current == null)
{
break;
}
}
// Build our return value.
foreach (KeyValuePair<char, string> pair in routes)
{
retVal.Add(pair.Key, new Tuple<int, string>(distances[pair.Key], pair.Value));
}
return retVal;
}
/// <summary>
/// Constructor
/// </summary>
/// <param name="start">starting point of this directed edge</param>
/// <param name="end">end point</param>
/// <param name="distance">Distance or cost of this edge</param>
public Edge(Node start, Node end, int distance)
{
Start = start;
End = end;
Distance = distance;
}