/// <summary>
/// Tests if two implicants have the same set of items
/// and difference is only in one item sign.
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="commonImplicant">Common intersection of implicants only if returns true.</param>
/// <param name="signDifferenceIndex">Single item index difference only if returns true.</param>
/// <returns></returns>
public static bool TestDifferenceInOneSign(
Implicant a,
Implicant b,
out Implicant commonImplicant,
out int signDifferenceIndex)
{
commonImplicant = null;
signDifferenceIndex = -1;
if (a.Count != b.Count)
{
return(false);
}
var common = new List <InputSign>();
List <int> signDifferenceIndexes = new List <int>();
for (int i = 0; i < a.Count; i++)
{
InputSign aItem = a.Items[i];
InputSign bItem = b.Items[i];
if (aItem.Index != bItem.Index)
{
return(false);
}
if (aItem.IsInversed == bItem.IsInversed)
{
common.Add(aItem);
}
else
{
signDifferenceIndexes.Add(aItem.Index);
}
}
if (signDifferenceIndexes.Count == 0)
{
return(false);
}
else if (signDifferenceIndexes.Count == 1)
{
commonImplicant = new Implicant(common);
signDifferenceIndex = signDifferenceIndexes[0];
return(true);
}
else
{
return(false);
}
}
/// <summary>
/// Petrick's method (https://en.wikipedia.org/wiki/Petrick%27s_method) is too complicated for lab work programming.
/// Thats why lets implement primitive method based on teacher's explanation.
/// </summary>
private static List <Implicant> GetMinimalDisjunctionNormalForm(List <Implicant> constituents, List <Implicant> implicants)
{
var coreImplicants = new HashSet <Implicant>();
foreach (Implicant implicant in implicants)
{
foreach (Implicant constituent in constituents)
{
List <Implicant> implicantsInConstituent = implicants.Where(i => i.IsSubsetOf(constituent)).ToList();
if (implicantsInConstituent.Count == 1 && implicantsInConstituent.Contains(implicant))
{
coreImplicants.Add(implicant);
continue;
}
}
}
List <Implicant> noncoreImplicants = implicants.Except(coreImplicants).ToList();
List <Implicant> notCoveredConstituents = constituents
.Where(c => !coreImplicants.Any(coreImplicant => coreImplicant.IsSubsetOf(c))).ToList();
List <Implicant> resultImplicants = coreImplicants.ToList();
while (notCoveredConstituents.Count > 0)
{
noncoreImplicants = noncoreImplicants
.OrderBy(i => notCoveredConstituents.Where(c => i.IsSubsetOf(c)).Count()).ToList();
Implicant noncoreTopRatedImplicant = noncoreImplicants[noncoreImplicants.Count - 1];
noncoreImplicants.RemoveAt(noncoreImplicants.Count - 1);
bool covers = false;
for (int i = notCoveredConstituents.Count - 1; i >= 0; i--)
{
if (noncoreTopRatedImplicant.IsSubsetOf(notCoveredConstituents[i]))
{
notCoveredConstituents.RemoveAt(i);
covers = true;
}
}
if (covers)
{
resultImplicants.Add(noncoreTopRatedImplicant);
}
}
return(resultImplicants);
}
private static bool EvaluateImplicant(uint input, Implicant implicant)
{
foreach (InputSign inputSign in implicant)
{
bool bit = BitTools.GetBit(input, bitIndex: inputSign.Index);
if (inputSign.IsInversed)
{
bit = !bit;
}
if (!bit)
{
return(false);
}
}
return(true);
}
/// <param name="implicants">Implicants ordered from short to long.</param>
private static List <Implicant> AbsorpImplicantsToShortDisjunctionNormalForm(List <Implicant> implicants)
{
List <Implicant> resultList = implicants.ToList();
for (int absorperIndex = 0; absorperIndex < resultList.Count - 1; absorperIndex++)
{
Implicant absorper = resultList[absorperIndex];
for (int absorpedIndex = resultList.Count - 1; absorpedIndex > absorperIndex; absorpedIndex--)
{
Implicant absorped = resultList[absorpedIndex];
if (absorper.IsSubsetOf(absorped))
{
resultList.RemoveAt(absorpedIndex);
}
}
}
return(resultList);
}
private static IReadOnlyList <IReadOnlyList <Implicant> > GetImplicantsGroupedByDifferencePosition(
IEnumerable <Tuple <Implicant, Implicant> > constituentPairs)
{
var implicantsGroupped = new SortedDictionary <int, List <Implicant> >();
foreach (Tuple <Implicant, Implicant> item in constituentPairs)
{
Implicant commonImplicant;
int signDifferenceIndex;
if (Implicant.TestDifferenceInOneSign(item.Item1, item.Item2, out commonImplicant, out signDifferenceIndex))
{
List <Implicant> group;
if (!implicantsGroupped.TryGetValue(signDifferenceIndex, out group))
{
group = new List <Implicant>();
implicantsGroupped[signDifferenceIndex] = group;
}
group.Add(commonImplicant);
}
}
return(implicantsGroupped.Values.ToList());
}
internal bool IsSubsetOf(Implicant other)
{
return(this.indexSet.IsSubsetOf(other.indexSet));
}
public bool Equals(Implicant other) => this.indexSet.SetEquals(other.indexSet);