private void GetPrimes()
{
SufficientCandidateKeys.Clear();
_prime = new BitArray(Keys.Count);
var leftBits = new BitArray(Keys.Count);
foreach (var key in Left)
{
_prime[key] = true;
leftBits[key] = true;
}
foreach (var key in Right)
{
_prime[key] = false;
}
foreach (var key in Middle)
{
_prime[key] = false;
}
var currentCover = Reachability(leftBits);
var candidates = new List <int>(Middle);
candidates.RemoveAll(key => currentCover[key]);
if (candidates.Count == 0)
{
SufficientCandidateKeys.Add(leftBits);
return;
}
var graph = new Graph(Keys.Count);
foreach (var dependency in DependencyList)
{
var str = dependency.Item1.ToBitString();
if (str.Count(c => c == '1') != 1)
{
continue;
}
var index = str.IndexOf('1');
if (!candidates.Contains(index))
{
continue;
}
for (var i = 0; i < Keys.Count; i++)
{
if (dependency.Item2[i] && candidates.Contains(i))
{
graph.AddEdge(index, i);
}
}
}
graph.GetSccs();
var sccs = new List <List <int> >();
for (var i = 0; i < candidates.Count; i++)
{
sccs.Add(new List <int>());
sccs.Last().Add(candidates[i]);
for (var j = i + 1; j < candidates.Count; j++)
{
if (graph.Scc[candidates[i]] != graph.Scc[candidates[j]])
{
continue;
}
sccs.Last().Add(candidates[j]);
candidates.RemoveAt(j);
j--;
}
}
for (var i = 0; i < candidates.Count; i++)
{
if (sccs[i].Any(candidate => DependencyList.Any(dependency => dependency.Item2[candidate] && Keys.Any(key => dependency.Item1[key] && graph.Scc[key] != graph.Scc[candidate]))))
{
continue;
}
leftBits[sccs[i][0]] = true;
foreach (var key in sccs[i])
{
_prime[key] = true;
Left.Add(key);
Middle.Remove(key);
}
sccs.RemoveAt(i);
candidates.RemoveAt(i);
i--;
}
currentCover = Reachability(leftBits);
for (var i = 0; i < candidates.Count; i++)
{
if (!currentCover[candidates[i]])
{
continue;
}
foreach (var key in sccs[i])
{
_prime[key] = false;
}
sccs.RemoveAt(i);
candidates.RemoveAt(i);
i--;
}
if (candidates.Count == 0)
{
SufficientCandidateKeys.Add(leftBits);
return;
}
// I claim by this line, the number of candidates can't be more than 16; given that the number of attributes isn't more than 4069, but who knows!
if (candidates.Count > 20)
{
throw new ConstraintException("Too many attributes!");
}
var foundSets = new List <int>();
for (var i = 1; i < (1 << candidates.Count); i++)
{
var currentSet = new BitArray(leftBits);
var newSet = false;
for (var j = 0; j < candidates.Count; j++)
{
if ((i & (1 << j)) != 0)
{
currentSet[candidates[j]] = true;
newSet |= !_prime[candidates[j]];
}
}
if (foundSets.Any(set => (i & set) == set))
{
i += i & -i;
i--;
continue;
}
if (Reachability(currentSet).ToBitString().Contains('0'))
{
continue;
}
foundSets.Add(i);
SufficientCandidateKeys.Add(currentSet);
for (var j = 0; j < candidates.Count; j++)
{
if ((i & (1 << j)) != 0 && !_prime[candidates[j]])
{
foreach (var k in sccs[j])
{
_prime[k] = true;
}
}
}
i += i & -i;
i--;
}
}