public static bool DetectCycleinUndirectedGraphUsingDisjointSets <T>(this Graph <T> g, out long v1, out long v2)
{
DisjointSets ds = new DisjointSets();
v1 = Int32.MaxValue;
v2 = Int32.MaxValue;
//Step 1: Make a set for all nodes in graph
foreach (var v in g.AllVertex.Values)
{
ds.MakeSet(v.Id);
}
//For all edges, findset each vertex.
// If the findset does not match, do union else you have found a cycle
foreach (var edge in g.AllEdges)
{
var n1 = ds.FindSet(edge.V1.Id);
var n2 = ds.FindSet(edge.V2.Id);
if (n1 == n2)
{
v1 = edge.V1.Id;
v2 = edge.V2.Id;
return(true);
}
ds.Union(edge.V1.Id, edge.V2.Id);
}
return(false);
}
/// <summary>
/// Compute comparability for a method's parameters based on the types of the parameters. Two parameters
/// are considered comparable if one can be assigned to the other.
/// </summary>
/// <param name="parameters">the parameters</param>
/// <seealso cref="TypeHelper.TypesAreAssignmentCompatible"/>
/// <returns>comparability sets for the parameters</returns>
public static HashSet <HashSet <string> > ParameterTypeComparability(IEnumerable <IParameterDefinition> parameters)
{
Contract.Requires(parameters != null);
Contract.Ensures(Contract.Result <HashSet <HashSet <string> > >() != null);
Dictionary <IParameterDefinition, int> ids = new Dictionary <IParameterDefinition, int>();
DisjointSets cmp = new DisjointSets();
foreach (var p in parameters)
{
ids.Add(p, cmp.AddElement());
}
foreach (var lhs in parameters)
{
Contract.Assume(ids.ContainsKey(lhs), "Error tracking parameter " + lhs.Name);
foreach (var rhs in parameters)
{
Contract.Assume(ids.ContainsKey(rhs), "Error tracking parameter " + rhs.Name);
if (TypeHelper.TypesAreAssignmentCompatible(lhs.Type.ResolvedType, rhs.Type.ResolvedType, true))
{
cmp.Union(cmp.FindSet(ids[lhs]), cmp.FindSet(ids[rhs]));
}
}
}
var result = new HashSet <HashSet <string> >(ids.Keys.GroupBy(p => cmp.FindSet(ids[p])).Select(g => new HashSet <string>(g.Select(p => p.Name.Value))));
return(result);
}
public KruskalMST(Graph g)
{
BinaryHeapPQ <Edge> pq = new BinaryHeapPQ <Edge>();
for (int v = 0; v < g.V; v++)
{
for (int i = 0; i < g.Deg(v); i++)
{
pq.Insert(new Edge()
{
U = v, V = g.AdjV(v, i), W = g.AdjW(v, i)
});
}
}
DisjointSets ds = new DisjointSets(g.V);
while (pq.Count > 0 && mst.Count < g.V - 1)
{
Edge e = pq.ExtractMin();
int v = e.U;
int w = e.V;
if (ds.FindSet(v) != ds.FindSet(w))
{
ds.Union(v, w);
mst.Add(e);
}
}
}
public void RunTest()
{
DisjointSets ds = new DisjointSets(_numElements);
int[] e2set = new int[_numElements];
HashSet <int>[] sets = new HashSet <int> [_numSets];
for (int i = 0; i < _numSets; i++)
{
sets[i] = new HashSet <int>();
}
Random rnd = new Random();
for (int i = 0; i < _numElements; i++)
{
int nset = rnd.Next(_numSets);
e2set[i] = nset;
sets[nset].Add(i);
}
foreach (HashSet <int> set in sets)
{
Queue <int> q = new Queue <int>(set);
if (q.Count == 0)
{
continue;
}
int last = q.Dequeue();
while (q.Count > 0)
{
int cur = q.Dequeue();
ds.Union(ds.FindSet(last), ds.FindSet(cur));
last = cur;
}
}
int[] reps = new int[_numSets];
for (int i = 0; i < _numSets; i++)
{
reps[i] = -1;
}
for (int i = 0; i < _numElements; i++)
{
int rep = ds.FindSet(i);
int nset = e2set[i];
if (reps[nset] == -1)
{
reps[nset] = rep;
}
else if (reps[nset] != rep)
{
throw new TestFailedException("Test with " + _numElements + " elements and " + _numSets + " sets: wrong representant");
}
}
}
public void Union()
{
var sets = new DisjointSets <int>(new int[] { 1, 2, 3, 4, 5, 6 });
sets.Union(1, 2);
Assert.That(sets.FindSet(1), Is.EqualTo(1).Or.EqualTo(2));
Assert.That(sets.FindSet(2), Is.EqualTo(1).Or.EqualTo(2));
foreach (int i in new int[] { 3, 4, 5, 6 })
{
Assert.That(sets.FindSet(i), Is.EqualTo(i));
}
}
public int GetComparability(string name)
{
Contract.Requires(!string.IsNullOrWhiteSpace(name));
Contract.Ensures(Contract.Result <int>() >= 0);
return(comparability.FindSet(GetId(name)));
}
/// <summary>
/// Returns the names in the same comparability set as <code>name</code>. This set includes <code>name</code>.
/// </summary>
/// <param name="name"></param>
/// <returns></returns>
public HashSet <string> ComparabilitySet(string name)
{
Contract.Requires(!string.IsNullOrWhiteSpace(name));
Contract.Ensures(Contract.Result <HashSet <string> >() != null);
Contract.Ensures(Contract.Result <HashSet <string> >().Contains(name));
if (ids.ContainsKey(name))
{
var groupId = comparability.FindSet(ids[name]);
return(new HashSet <string>(Comparability.Where(x => x.Value == groupId).Select(x => x.Key)));
}
else
{
return(new HashSet <string>(new[] { name }));
}
}
static void Main(string[] args)
{
DisjointSets ds = new DisjointSets();
ds.MakeSet(1);
ds.MakeSet(2);
ds.MakeSet(3);
ds.MakeSet(4);
ds.MakeSet(5);
ds.MakeSet(6);
ds.MakeSet(7);
ds.Union(1, 2);
ds.Union(2, 3);
ds.Union(4, 5);
ds.Union(6, 7);
ds.Union(5, 6);
ds.Union(3, 7);
Console.WriteLine(ds.FindSet(1).Data);
Console.WriteLine(ds.FindSet(2).Data);
Console.WriteLine(ds.FindSet(3).Data);
Console.WriteLine(ds.FindSet(4).Data);
Console.WriteLine(ds.FindSet(5).Data);
Console.WriteLine(ds.FindSet(6).Data);
Console.WriteLine(ds.FindSet(7).Data);
}
public void FindSet_WithoutPreExistingElements()
{
var sets = new DisjointSets <int>();
foreach (int i in Enumerable.Range(1, 10))
{
sets.MakeSet(i);
foreach (int j in Enumerable.Range(1, i))
{
Assert.That(sets.FindSet(j), Is.EqualTo(j));
}
}
foreach (int i in Enumerable.Range(1, 10))
{
Assert.That(sets.FindSet(i), Is.EqualTo(i));
}
}
public void Union_TypicalCase()
{
var sets = new DisjointSets <int>(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 });
sets.Union(1, 2);
sets.Union(2, 3);
sets.Union(3, 4);
sets.Union(5, 6);
sets.Union(3, 7);
foreach (int i in new int[] { 1, 2, 3, 4, 5, 6, 7 })
{
Assert.That(new int[] { sets.FindSet(i) }, Is.SubsetOf(new int[] { 1, 2, 3, 4, 5, 6, 7 })); // Sort of hacky; Is.MemberOf would be better
}
foreach (int i in new int[] { 8, 9, 10 })
{
Assert.That(sets.FindSet(i), Is.EqualTo(i));
}
}
/// <summary>
///
/**https://en.wikipedia.org/wiki/Kruskal%27s_algorithm
* KRUSKAL(G):
* 1 A = ∅
* 2 foreach v ∈ G.V:
* 3 MAKE-SET(v)
* 4 foreach (u, v) in G.E ordered by weight(u, v), increasing:
* 5 if FIND-SET(u) ≠ FIND-SET(v):
* 6 A = A ∪ {(u, v)}
* 7 UNION(u, v)
* 8 return A
* **/
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="g"></param>
/// <returns></returns>
public static List <Edge <T> > GetMSTUsingKruskal <T>(this Graph <T> g)
{
EdgeComparer <T> comparer = new EdgeComparer <T>();
List <Edge <T> > result = new List <Edge <T> >();
//First sort the edges
g.AllEdges.Sort(comparer);
Console.WriteLine("Edes in Sorted Order");
foreach (var e in g.AllEdges)
{
Console.WriteLine(e.ToString());
}
DisjointSets disjointSet = new DisjointSets();
//Create Set for each vertex
foreach (var v in g.AllVertex.Values)
{
disjointSet.MakeSet(v.Id);
}
//For each edge, check if vertex is already in SET.
//1. If yes, ignore
//2. If not, Union and add it to result of edge
foreach (var e in g.AllEdges)
{
var n1 = disjointSet.FindSet(e.V1.Id);
var n2 = disjointSet.FindSet(e.V2.Id);
if (n1 == n2)
{
continue;
}
else
{
result.Add(e);
disjointSet.Union(e.V1.Id, e.V2.Id);
}
}
return(result);
}
public void RunTest()
{
DisjointSets ds = new DisjointSets(_numElements);
int[] e2set = new int[_numElements];
HashSet<int>[] sets = new HashSet<int>[_numSets];
for (int i = 0; i < _numSets; i++)
{
sets[i] = new HashSet<int>();
}
Random rnd = new Random();
for (int i = 0; i < _numElements; i++)
{
int nset = rnd.Next(_numSets);
e2set[i] = nset;
sets[nset].Add(i);
}
foreach (HashSet<int> set in sets)
{
Queue<int> q = new Queue<int>(set);
if (q.Count == 0)
continue;
int last = q.Dequeue();
while (q.Count > 0)
{
int cur = q.Dequeue();
ds.Union(ds.FindSet(last), ds.FindSet(cur));
last = cur;
}
}
int[] reps = new int[_numSets];
for (int i = 0; i < _numSets; i++)
reps[i] = -1;
for (int i = 0; i < _numElements; i++)
{
int rep = ds.FindSet(i);
int nset = e2set[i];
if (reps[nset] == -1)
reps[nset] = rep;
else if (reps[nset] != rep)
throw new TestFailedException("Test with " + _numElements + " elements and " + _numSets + " sets: wrong representant");
}
}
public void FindSet_WithPreExistingElements()
{
var elements = new int[] { 1, 2, 3, 4 };
var sets = new DisjointSets <int>(elements);
foreach (var element in elements)
{
Assert.That(sets.FindSet(element), Is.EqualTo(element));
}
}
public void Constructor_TypicalCase()
{
var elements = new int[] { 1, 2, 3, 4, 5 };
var sets = new DisjointSets <int>(elements);
foreach (var element in elements)
{
Assert.That(sets.FindSet(element), Is.EqualTo(element));
}
}
public TypeSummary(string assemblyQualifiedName, NameBuilder names, IEnumerable <MethodVisitor> methods)
{
Contract.Requires(!string.IsNullOrEmpty(assemblyQualifiedName));
Contract.Requires(names != null);
Contract.Requires(methods != null);
Contract.Ensures(ids.Keys.SetEquals(names.ThisNames()));
this.AssemblyQualifiedName = assemblyQualifiedName;
// give a union-find id to each instance expression name
foreach (var name in names.ThisNames())
{
ids.Add(name, comparability.AddElement());
}
// union the sets, according to each method's opinion
foreach (var name in names.ThisNames())
{
HashSet <string> indexOpinion = new HashSet <string>();
foreach (var method in methods)
{
var opinion = method.ComparabilitySet(name).Intersect(ids.Keys);
string last = null;
foreach (var other in opinion)
{
if (last != null)
{
comparability.Union(comparability.FindSet(ids[last]), comparability.FindSet(ids[name]));
}
last = other;
}
indexOpinion.UnionWith(method.IndexComparabilityOpinion(name).Intersect(names.ThisNames()));
}
if (indexOpinion.Count > 0)
{
arrayIndexes.Add(name, indexOpinion);
}
}
}
public void FindSet_ThrowsOnNonExistentElement()
{
var sets = new DisjointSets <int>(new int[] { 1, 2, 3 });
Assert.That(() => sets.FindSet(4), Throws.ArgumentException);
}
/// <summary>
/// Finds the representant of a set element.
/// </summary>
/// <param name="elem">set element</param>
/// <returns>representant</returns>
public T Find(T elem)
{
int fidx = _impl.FindSet(_index[elem]);
return(_elems[_repShuffle[fidx]]);
}
