private static List <Node> GetInterchangingChain(this Bigraph graph, HashSet <Edge> matching)
{
foreach (var xNode in graph.XPart.Where(x => !graph.DarkNodes.Contains(x)))
{
var chain = graph.GetChainFromNode(xNode, matching);
if (chain != null)
{
return(chain);
}
}
return(null);
}
public new Bigraph ParseGraph()
{
var input = File.ReadAllLines(fileName);
var counts = input[0].Split().Select(int.Parse).ToArray();
var k = counts[0];
var l = counts[1];
var graph = new Bigraph(k, l);
for (var i = 1; i < input.Length; i++)
{
var incidents = input[i].Split().Select(int.Parse).ToArray();
for (var j = 0; j < incidents.Length - 1; j++)
graph.Connect(i, incidents[j]);
}
return graph;
}
private static List <Node> GetChainFromNode(this Bigraph graph, Node start, HashSet <Edge> matching)
{
var visited = new HashSet <Node>();
var stack = new Stack <Node>();
var previous = new Dictionary <Node, Node>();
visited.Add(start);
foreach (var yNode in start.IncidentNodes)
{
previous[yNode] = start;
if (!graph.DarkNodes.Contains(yNode))
{
return(graph.BuildChain(start, yNode, previous));
}
stack.Push(yNode);
}
while (stack.Any())
{
var current = stack.Pop();
if (graph.YPart.Contains(current))
{
var xNodes = current.Edges
.Where(edge => matching.Contains(edge))
.Select(edge => edge.AnotherNode(current));
foreach (var xNode in xNodes)
{
stack.Push(xNode);
previous[xNode] = current;
}
}
else
{
var yNodes = current.Edges
.Where(edge => !matching.Contains(edge))
.Select(edge => edge.AnotherNode(current));
foreach (var yNode in yNodes)
{
previous[yNode] = current;
if (!graph.DarkNodes.Contains(yNode))
{
return(graph.BuildChain(start, yNode, previous));
}
stack.Push(yNode);
}
}
}
return(null);
}
private static List <Node> BuildChain(this Bigraph graph, Node start, Node end, Dictionary <Node, Node> previous)
{
var chain = new List <Node> {
end
};
previous.TryGetValue(end, out var parent);
while (parent != null)
{
chain.Add(parent);
previous.TryGetValue(parent, out parent);
}
//chain.Add(start);
chain.Reverse();
return(chain);
}
public static HashSet <Edge> GetBiggestMatching(this Bigraph graph)
{
var matching = new HashSet <Edge>();
while (true)
{
var chain = graph.GetInterchangingChain(matching);
if (chain == null)
{
return(matching);
}
var chainSet = GetEdgesFromChain(chain);
matching.SymmetricExceptWith(chainSet);
graph.DarkNodes.Add(chain[0]);
graph.DarkNodes.Add(chain[chain.Count - 1]);
}
}