private List <Tangle> getTanglesWithNCrossings(int n)
{
if (n <= 0)
{
throw new ArgumentException("The number must be between 1 and the number of crossings.");
}
List <Tangle> tangles = new List <Tangle>();
List <int> crossings = Enumerable.Range(1, NumberOfCrossings).ToList();
//generate all n choose k combinations of crosses (avoid negative)
IEnumerable <List <int> > combinations = Extensions.Tools.Choose <int>(crossings, n);
foreach (List <int> list in combinations)
{
Tangle t = new Tangle(list.ToArray());
if (IsValidTangle(t))
{
tangles.Add(t);
}
}
//return all valid combinations
return(tangles);
}
private int[] GetTangleEnds(Tangle t)
{
List <int> indexes = new List <int>();
foreach (int c in t.Crosses)
{
indexes.Add(this.GaussCode.IndexOf(c));
indexes.Add(this.GaussCode.IndexOf(-c));
}
indexes.Sort();
int a = Tools.Mod(indexes.First() - 1, this.GaussCode.Count);
int b = Tools.Mod(indexes.Last() + 1, this.GaussCode.Count);
if (this.IsContiguousTangle(t))
{
return(new int[] { a, b });
}
else
{
int m = 0, n = 0;
for (int i = 0; i < indexes.Count - 1; i++)
{
m = Tools.Mod(indexes[i] + 1, this.GaussCode.Count);
n = indexes[i + 1];
if (m != n)
{
n--;
break;
}
}
return(new int[] { a, m, n, b });
}
}
public override bool Equals(object obj)
{
if (obj is Tangle)
{
Tangle other = (Tangle)obj;
if (this.nCrosses == other.nCrosses)
{
bool equals = true;
for (int i = 0; i < this.nCrosses; i++)
{
equals &= this.Crosses[i] == other.Crosses[i];
}
return(equals);
}
}
return(false);
}
private bool IsContiguousTangle(Tangle t)
{
List <int> fullTangle = new List <int>();
fullTangle.Add(t.Crosses[0]);
int indexFirst = this.GaussCode.IndexOf(t.Crosses[0]);
bool expandSx = true;
bool expandDx = true;
int expand = 1;
int index = 0;
while (expandSx || expandDx)
{
if (expandSx)
{
index = Tools.Mod((indexFirst - expand), this.GaussCode.Count);
if (t.Crosses.Contains(Math.Abs(this.GaussCode[index])) && !fullTangle.Contains(this.GaussCode[index]))
{
fullTangle.Insert(0, this.GaussCode[index]);
}
else
{
expandSx = false;
}
}
if (expandDx)
{
index = Tools.Mod((indexFirst + expand), this.GaussCode.Count);
if (t.Crosses.Contains(Math.Abs(this.GaussCode[index])) && !fullTangle.Contains(this.GaussCode[index]))
{
fullTangle.Add(this.GaussCode[index]);
}
else
{
expandDx = false;
}
}
expand++;
}
return(fullTangle.Count == (t.nCrosses * 2));
}
private bool IsValidTangle(Tangle t)
{
MovableCircularList <int> crosses = new MovableCircularList <int>();
foreach (int c in t.Crosses)
{
crosses.Add(this.GaussCode.IndexOf(c));
crosses.Add(this.GaussCode.IndexOf(-c));
}
crosses.Sort();
int leaps = 0;
for (int i = 0; i < crosses.Count - 1; i++)
{
if (Tools.Mod(crosses[i] + 1, this.GaussCode.Count) != crosses[i + 1])
{
leaps++;
}
}
return(leaps < 2);
}
private bool IsValidTangleOld(Tangle t)
{
int t_hash = t.Hash();
List <int> firstSet = new List <int>();
int indexFirst = this.GaussCode.IndexOf(t.Crosses[0]);
firstSet.Add(this.GaussCode[indexFirst]);
bool expandSx = true;
bool expandDx = true;
int expand = 1;
int index = 0;
while (expandSx || expandDx)
{
if (expandSx)
{
index = Tools.Mod((indexFirst - expand), this.GaussCode.Count);
if (t.Crosses.Contains(Math.Abs(this.GaussCode[index])) && !firstSet.Contains(Math.Abs(this.GaussCode[index])))
{
firstSet.Add(this.GaussCode[index]);
}
else
{
expandSx = false;
}
}
if (expandDx)
{
index = Tools.Mod((indexFirst + expand), this.GaussCode.Count);
if (t.Crosses.Contains(Math.Abs(this.GaussCode[index])) && !firstSet.Contains(Math.Abs(this.GaussCode[index])))
{
firstSet.Add(this.GaussCode[index]);
}
else
{
expandDx = false;
}
}
expand++;
}
Tangle firstT = new Tangle(firstSet.ToArray());
int firstT_hash = firstT.Hash();
int sizeSecondSet = t.nCrosses * 2 - firstSet.Count;
int[] secondSet = new int[sizeSecondSet];
for (int i = 0; i < this.GaussCode.Count; i++)
{
for (int j = 0; j < sizeSecondSet; j++)
{
secondSet[j] = this.GaussCode[Tools.Mod(i + j, this.GaussCode.Count)];
}
Tangle secondT = new Tangle(secondSet);
int secondT_hash = secondT.Hash();
if (firstT != secondT && firstT_hash == secondT_hash)
{
bool contain = true;
foreach (int n in secondSet)
{
contain &= t.Crosses.Contains(Math.Abs(n));
}
if (contain)
{
return(true);
}
}
}
return(false);
}
private void PerformTranslationMove1(int cross, int insertIndex1, int insertIndex2, Tangle t)
{
for (int i = 0; i < this.GaussCode.Count; i++)
{
if (t.Crosses.Contains(Math.Abs(this.GaussCode[i])))
{
this.GaussCode[i] = -this.GaussCode[i];
}
}
int posIndex = this.GaussCode.IndexOf(cross);
int negIndex = this.GaussCode.IndexOf(-cross);
this.GaussCode.Move(posIndex, insertIndex1);
this.GaussCode.Move(negIndex, insertIndex2);
}
private int[] getPositionsForReductionMove2()
{
int sign(int a)
{
if (a >= 0)
{
return(1);
}
return(-1);
}
List <int[]> adj = new List <int[]>();
List <int> temp = new List <int>();
for (int i = 0; i < this.GaussCode.Count; i++)
{
temp = new List <int>();
for (int j = i; j < this.GaussCode.Count; j++)
{
if (sign(this.GaussCode[j]) == sign(this.GaussCode[j + 1]))
{
temp.Add(this.GaussCode[j]);
temp.Add(this.GaussCode[j + 1]);
int[] add = temp.Distinct().ToArray();
adj.Add(add);
}
else
{
break;
}
}
}
adj = adj.OrderByDescending(a => a.Length).ToList();
foreach (int[] t in adj)
{
Tangle test = new Tangle(t);
int firstIndex = this.GaussCode.IndexOf(-t[0]);
int tempFirst = firstIndex;
int[] found = new int[t.Length];
bool dx = true;
for (int i = 0; i < t.Length; i++)
{
if (dx)
{
if (t.Contains(-this.GaussCode[firstIndex]))
{
found[i] = -this.GaussCode[firstIndex];
firstIndex++;
}
else
{
dx = false;
i--;
}
}
else
{
firstIndex = tempFirst - 1;
if (t.Contains(-this.GaussCode[firstIndex]))
{
found[i] = -this.GaussCode[firstIndex];
firstIndex--;
}
}
}
Tangle TFound = new Tangle(found);
if (test.Hash() == TFound.Hash())
{
return(t);
}
}
return(null);
}