// DFS
static bool TryMatching(int left,
BipartiteGraph G,
IDictionary <int, int> toMatchedRight,
IDictionary <int, int> toMatchedLeft,
IDictionary <int, long> distances)
{
if (left == 0)
{
return(true);
}
foreach (var right in G.Edge(left))
{
var nextLeft = toMatchedLeft[right];
if (distances[nextLeft] == distances[left] + 1)
{
if (TryMatching(nextLeft, G, toMatchedRight, toMatchedLeft, distances))
{
toMatchedLeft[right] = left;
toMatchedRight[left] = right;
return(true);
}
}
}
// The left could not match any right.
distances[left] = long.MaxValue;
return(false);
}
//static void Main()
//{
// var lefts = new HashSet<int> { 1, 2, 3, 4, 5 };
// var rights = new HashSet<int> { 6, 7, 8, 9, 10 };
// var edges = new Dictionary<int, HashSet<int>>
// {
// [1] = new HashSet<int> { 6, 7 },
// [2] = new HashSet<int> { 6, 10 },
// [3] = new HashSet<int> { 8, 9 },
// [4] = new HashSet<int> { 6, 10 },
// [5] = new HashSet<int> { 7, 9 }
// };
// var matches = HopcroftKarpFunction(lefts, rights, edges);
// Console.WriteLine($"# of matches: {matches.Count}\n");
// foreach (var match in matches)
// {
// Console.WriteLine($"Match: {match.Key} -> {match.Value}");
// }
//}
//public static Func<int, HashSet<int>> EdgeDelegate = BipartiteGraph.Edge;
// BFS
static bool HasAugmentingPath(IEnumerable <int> lefts,
BipartiteGraph G,
IReadOnlyDictionary <int, int> toMatchedRight,
IReadOnlyDictionary <int, int> toMatchedLeft,
IDictionary <int, long> distances,
Queue <int> q)
{
foreach (var left in lefts)
{
if (toMatchedRight[left] == 0)
{
distances[left] = 0;
q.Enqueue(left);
}
else
{
distances[left] = long.MaxValue;
}
}
distances[0] = long.MaxValue;
while (0 < q.Count)
{
var left = q.Dequeue();
if (distances[left] < distances[0])
{
foreach (var right in G.Edge(left))
{
var nextLeft = toMatchedLeft[right];
if (distances[nextLeft] == long.MaxValue)
{
// The nextLeft has not been visited and is being visited.
distances[nextLeft] = distances[left] + 1;
q.Enqueue(nextLeft);
}
}
}
}
return(distances[0] != long.MaxValue);
}