public void Test(BipartieGraph bg)
{
var matching = new BipartieGraphMaxMatching().FindMaxMatching(bg);
IsMatching(matching);
}
public static bool Lemma19(CspInstance instance)
{
Dictionary <Pair, bool> alreadyInACompontent = new();
List <(Pair, Pair, Pair)> Small2Components = new();
List <(Pair, Pair, Pair, Pair)> Good3Components = new();
foreach (Variable var in instance.Variables)
{
foreach (Color col in var.AvalibleColors)
{
if (!alreadyInACompontent.ContainsKey(new Pair(var, col)))
{
alreadyInACompontent[new Pair(var, col)] = true;
var tempTab = col.Restrictions.ToArray();
if (col.Restrictions.Count == 2)
{
Small2Components.Add(new(new Pair(var, col), tempTab[0], tempTab[1]));
alreadyInACompontent[tempTab[0]] = true;
alreadyInACompontent[tempTab[1]] = true;
}
else if (col.Restrictions.Count == 3)
{
Good3Components.Add(new(new Pair(var, col), tempTab[0], tempTab[1], tempTab[2]));
alreadyInACompontent[tempTab[0]] = true;
alreadyInACompontent[tempTab[1]] = true;
alreadyInACompontent[tempTab[2]] = true;
}
//else throw new Exception($"restriction count was {col.Restrictions.Count}");
}
}
}
Dictionary <int, int> idsToIndex = new();
Dictionary <int, int> indexToId = new();
int index = 0;
foreach (Variable var in instance.Variables)
{
idsToIndex.Add(var.Id, index);
indexToId.Add(index, var.Id);
index++;
}
BipartieGraph g = new(instance.Variables.Count, Small2Components.Count + Good3Components.Count);
for (int i = 0; i < Small2Components.Count; i++)
{
g.AddEdge(idsToIndex[Small2Components[i].Item1.Variable.Id], i);
g.AddEdge(idsToIndex[Small2Components[i].Item2.Variable.Id], i);
g.AddEdge(idsToIndex[Small2Components[i].Item3.Variable.Id], i);
}
for (int i = 0; i < Good3Components.Count; i++)
{
g.AddEdge(idsToIndex[Good3Components[i].Item1.Variable.Id], i + Small2Components.Count);
g.AddEdge(idsToIndex[Good3Components[i].Item2.Variable.Id], i + Small2Components.Count);
g.AddEdge(idsToIndex[Good3Components[i].Item3.Variable.Id], i + Small2Components.Count);
g.AddEdge(idsToIndex[Good3Components[i].Item4.Variable.Id], i + Small2Components.Count);
}
int[] result = new BipartieGraphMaxMatching().FindMaxMatching(g); //partA to są variables a partB to są komponenty
for (int i = 0; i < Small2Components.Count; i++)
{
if (result[i] == -1)
{
return(false);
}
int currId = indexToId[result[i]]; // id zmiennej ktora została przyznana do small2componentu i
if (Small2Components[i].Item1.Variable.Id == currId)
{
instance.AddToResult(Small2Components[i].Item1);
}
else if (Small2Components[i].Item2.Variable.Id == currId)
{
instance.AddToResult(Small2Components[i].Item2);
}
else
{
instance.AddToResult(Small2Components[i].Item3);
}
}
for (int i = 0; i < Good3Components.Count; i++)
{
if (result[i] == -1)
{
return(false);
}
int currId = indexToId[result[i + Small2Components.Count]]; // id zmiennej ktora została przyznana do good3component i
if (Good3Components[i].Item1.Variable.Id == currId)
{
instance.AddToResult(Good3Components[i].Item1);
}
else if (Good3Components[i].Item2.Variable.Id == currId)
{
instance.AddToResult(Good3Components[i].Item2);
}
else if (Good3Components[i].Item3.Variable.Id == currId)
{
instance.AddToResult(Good3Components[i].Item3);
}
else
{
instance.AddToResult(Good3Components[i].Item4);
}
}
return(true);
}
