public TwoThreeTree(IComparer <T> comp)
{
this._comp = comp;
this._count = 0;
this._h = 0;
this._r = null;
this._visitor = new NRVisitor <T>();//CHECK
}
//ASC ORDER
private void __NodesVals(Node <T> n, ref CSharpDataStructures.Structures.Lists.LinkedList <T> L)
{
TwoThreeNode <T> np = n as TwoThreeNode <T>;
if (np.FirstSon == null)
{
L.Add(np.Value);
}
}
//DESC ORDER.
private void __NodesVals(Node <T> n, ref CSharpDataStructures.Structures.Lists.LinkedStack <T> S)
{
TwoThreeNode <T> np = n as TwoThreeNode <T>;
if (np.FirstSon == null)
{
S.Push(np.Value);
}
}
public Node <T> Parent(Node <T> node)
{
TwoThreeNode <T> np = node as TwoThreeNode <T>;
if (np == null)//OR np.Parent
{
return(null);
}
return(np.Parent);
}
public Node <T> LeftMostChild(Node <T> node)
{
TwoThreeNode <T> np = node as TwoThreeNode <T>;
if (np == null)
{
return(null);
}
return(np.FirstSon);
}
private void __Insert2(TwoThreeNode <T> node, T item, ref TwoThreeNode <T> pnew, ref T low, ref LinkedStack <Int32> SC, ref Boolean added, ref LinkedStack <TwoThreeNode <T> > S)
{
TwoThreeNode <T> pback; //for pnew
TwoThreeNode <T> w = node; //__CreateNewNode(node,null);
Int32 child = 1;
pnew = null;
while (w.FirstSon != null)
{
if (_comp.Compare(item, w.LowOfSecond) < 0)
{
child = 1;
SC.Push(child);
S.Push(w);
w = w.FirstSon;
}
else if (w.ThirdSon == null || _comp.Compare(item, w.LowOfSecond) < 0)
{
child = 2;
SC.Push(child);
S.Push(w);
w = w.SecondSon;
}
else
{
child = 3;
SC.Push(child);
S.Push(w);
w = w.ThirdSon;
}
}
if (w.FirstSon == null) //leaf
{
if (_comp.Compare(w.Value, item) != 0) //NOT EQUALS
{
added = true;
_count += 1;
pnew = new TwoThreeNode <T>();
if (_comp.Compare(w.Value, item) < 0)
{
pnew.Value = item;
low = item;
return;
}
else
{
pnew.Value = w.Value;
w.Value = item;
low = pnew.Value;
return;
}
}
}
}
public T Max()
{
if (_count == 0)
{
return(default(T));
}
if (_count == 1)
{
return(_r.Value);
}
TwoThreeNode <T> node = _r;
while (node.FirstSon != null)
{
node = node.ThirdSon ?? node.SecondSon;
}
return(node.Value);
}
public Node <T> RightSibling(Node <T> node)
{
TwoThreeNode <T> np = node as TwoThreeNode <T>;
if (np == null || np.Parent == null)
{
return(null);
}
TwoThreeNode <T> pa = np.Parent;
if (pa.FirstSon.Equals(np))
{
return(pa.SecondSon);
}
else if (pa.SecondSon.Equals(np))
{
return(pa.ThirdSon);
}
return(null);
}
private void __Delete1(TwoThreeNode <T> node, T item, ref bool one, ref bool del, ref TwoThreeNode <T> G)
{
LinkedStack <TwoThreeNode <T> > STACK = new LinkedStack <TwoThreeNode <T> >();
LinkedStack <Int32> S2 = new LinkedStack <Int32>();
__Delete2(node, item, ref one, ref S2, ref STACK, ref del);
if (!one)//NO PROBLEM.
{
return;
}
TwoThreeNode <T> w; //Parent of the deleted leaf.
S2.Pop(); //delete one, to get position of w in GrandPa of the deleted leaf.
while (!S2.IsEmpty() && !(STACK.Count == 1)) //exlucde root.
{
Int32 child = S2.Top();
S2.Pop();
w = STACK.Top();
STACK.Pop();
if (child == 1)
{
//y has three children. y - rightsibling of w.
if (w.Parent != null && w.Parent.SecondSon != null && w.Parent.SecondSon.ThirdSon != null)
{
TwoThreeNode <T> y = w.Parent.SecondSon;
w.SecondSon = y.FirstSon;
w.SecondSon.Parent = w;
w.LowOfSecond = w.SecondSon.Value;
y.FirstSon = y.SecondSon;
y.SecondSon = y.ThirdSon;
y.LowOfSecond = y.LowOfThird;
y.LowOfThird = default(T);
y.ThirdSon = null;
one = false;
return;
}
//y has two children.
else if (w.Parent != null && w.Parent.SecondSon != null)
{
TwoThreeNode <T> y = w.Parent.SecondSon;
//Son of the w is the first son of y.
TwoThreeNode <T> temp = y.FirstSon;
y.FirstSon = w.FirstSon;
y.FirstSon.Parent = y;
y.ThirdSon = y.SecondSon;
y.SecondSon = temp;
y.LowOfSecond = temp.Value;
y.LowOfThird = y.ThirdSon.Value;
TwoThreeNode <T> grandPa = w.Parent;
//w.FirstSon = null;
grandPa.FirstSon = null;
grandPa.FirstSon = grandPa.SecondSon;
if (grandPa.ThirdSon == null)//only secondSon
{
one = true;
grandPa.LowOfSecond = default(T);
G = grandPa;
continue;
}
else
{
grandPa.SecondSon = grandPa.ThirdSon;
grandPa.LowOfSecond = grandPa.LowOfThird;
grandPa.LowOfThird = default(T);
grandPa.ThirdSon = null;
one = false;
return;
}
}
}
else if (child == 2)//now y is 1 and w is 2.
//y has three children. y - leftsibling of w.
{
if (w.Parent != null && w.Parent.FirstSon != null && w.Parent.FirstSon.ThirdSon != null)
{
TwoThreeNode <T> y = w.Parent.FirstSon;
//the third son of the y is the first son of the w.
TwoThreeNode <T> temp = w.FirstSon;
w.FirstSon = y.ThirdSon;
w.FirstSon.Parent = w;
w.SecondSon = temp;
w.LowOfSecond = temp.Value;
y.LowOfThird = default(T);
y.ThirdSon = null;
one = false;
return;
}
else if (w.Parent != null && w.Parent.FirstSon != null)//y has two children
{
TwoThreeNode <T> grandPa = w.Parent;
//z - rightsibling of w and has three children.
if (grandPa.ThirdSon != null && grandPa.ThirdSon.ThirdSon != null)
{
TwoThreeNode <T> z = grandPa.ThirdSon;
//the first son of z is the second son of the w.
w.SecondSon = z.FirstSon;
w.SecondSon.Parent = w;
w.LowOfSecond = w.SecondSon.Value;
z.FirstSon = z.SecondSon;
z.SecondSon = z.ThirdSon;
z.LowOfSecond = z.LowOfThird;
z.LowOfThird = default(T);
z.ThirdSon = null;
one = false;
return;
}
else
{
TwoThreeNode <T> y = w.Parent.FirstSon;
y.ThirdSon = w.FirstSon;
y.ThirdSon.Parent = y;
y.LowOfThird = w.FirstSon.Value;
//w.FirstSon = null;
if (grandPa.ThirdSon == null)//one son
{
one = true;
grandPa.SecondSon = null;
grandPa.LowOfSecond = default(T);
G = grandPa;
continue;
//return;//GRANDPA
}
else //two sons
{
grandPa.SecondSon = grandPa.ThirdSon;
grandPa.LowOfSecond = grandPa.ThirdSon.LowOfThird;
grandPa.ThirdSon = null;
grandPa.LowOfThird = default(T);
one = false;
return;
}
}
}
}
else if (child == 3)
{
if (w.Parent != null && w.Parent.SecondSon != null && w.Parent.SecondSon.ThirdSon != null)
{
TwoThreeNode <T> y = w.Parent.SecondSon;
//the third son of the y is the first son of the w.
TwoThreeNode <T> temp = w.FirstSon;
w.FirstSon = y.ThirdSon;
w.FirstSon.Parent = w;
w.SecondSon = temp;
w.LowOfSecond = temp.Value;
y.LowOfThird = default(T);
y.ThirdSon = null;
one = false;
return;
}
else if (w.Parent != null && w.Parent.SecondSon != null)
{
TwoThreeNode <T> y = w.Parent.SecondSon;
TwoThreeNode <T> grandPa = w.Parent;
y.ThirdSon = w.FirstSon;
y.ThirdSon.Parent = y;
y.LowOfThird = w.FirstSon.Value;
grandPa.LowOfSecond = grandPa.ThirdSon.LowOfThird;//remove the third son. (w)
grandPa.ThirdSon = null;
grandPa.LowOfThird = default(T);
one = false;
return;//GRANDPA
}
}
}
}
//DESCENT TO THE LEAVES.
private void __Delete2(TwoThreeNode <T> node, T item, ref bool onlyOne, ref LinkedStack <Int32> SC, ref LinkedStack <TwoThreeNode <T> > S, ref bool deleted)
{
TwoThreeNode <T> w = node;
onlyOne = false;
deleted = false;
Int32 child = 1;
while (w.FirstSon != null)
{
if (_comp.Compare(item, w.LowOfSecond) < 0)
{
child = 1;
SC.Push(child);
S.Push(w);
w = w.FirstSon;
//S.Push(w);
}
else if (w.ThirdSon == null || _comp.Compare(item, w.LowOfSecond) < 0)
{
child = 2;
SC.Push(child);
S.Push(w);
w = w.SecondSon;
//S.Push(w);
}
else
{
child = 3;
SC.Push(child);
S.Push(w);
w = w.ThirdSon;
//S.Push(w);
}
}//leaf.
//wp ->> node.
if (w.FirstSon == null)
{
TwoThreeNode <T> wp = w.Parent;
if (wp.ThirdSon != null)
{
if (_comp.Compare(item, wp.ThirdSon.Value) == 0)//EQUALS third node.
{
wp.ThirdSon = null;
wp.LowOfThird = default(T);
deleted = true;
}
else if (_comp.Compare(item, wp.SecondSon.Value) == 0) //EQAULS second node
{
wp.SecondSon = wp.ThirdSon; //3 moves to the second
wp.LowOfSecond = wp.LowOfThird; //update lowOfSecond
wp.ThirdSon = null;
wp.LowOfThird = default(T); //delete lowOfThird.
deleted = true;
}
else if (_comp.Compare(item, wp.FirstSon.Value) == 0)//EQUALS first node.
{
wp.FirstSon = wp.SecondSon;
wp.SecondSon = wp.ThirdSon;
wp.LowOfSecond = wp.LowOfThird;
wp.ThirdSon = null;
wp.LowOfThird = default(T);
deleted = true;
}
}
else //2 nodes -> onlyOne
{
if (_comp.Compare(item, wp.SecondSon.Value) == 0)//EQAULS second node
{
wp.SecondSon = null;
wp.LowOfSecond = default(T);
onlyOne = true;
deleted = true;
}
else if (_comp.Compare(item, wp.FirstSon.Value) == 0)//EQUALS first node
{
wp.FirstSon = wp.SecondSon;
wp.LowOfSecond = default(T);
onlyOne = true;
deleted = true;
}
}
}
}
private bool __Insert0(TwoThreeNode <T> r, T item)
{
if (item == null)
{
return(false);
}
if (_count == 0)
{
_r = new TwoThreeNode <T>();//leaf
_r.Value = item;
_count += 1;
return(true);
}
else if (_count == 1)
{
if (_comp.Compare(_r.Value, item) == 0)//IF EQUALS
{
return(false);
}
TwoThreeNode <T> f1 = _r;
T v1 = _r.Value;
_r = new TwoThreeNode <T>();
if (_comp.Compare(v1, item) > 0)//item -> FirstSon.
{
_r.FirstSon = new TwoThreeNode <T>();
_r.FirstSon.Value = item;
_r.FirstSon.Parent = _r;//PARENT
_r.SecondSon = f1;
_r.SecondSon.Value = v1;
_r.SecondSon.Parent = _r;//PARENT
_r.LowOfSecond = v1;
_count += 1;
_h = 1;
return(true);
}
_r.FirstSon = f1;
_r.SecondSon = new TwoThreeNode <T>();
_r.FirstSon.Value = v1;
_r.SecondSon.Value = item;
_r.FirstSon.Parent = _r; //PARENT
_r.SecondSon.Parent = _r; //PARENT
_r.LowOfSecond = item;
_count += 1;
_h = 1;
return(true);
}
else if (_count == 2)//JUST INSERT item as the third child of the ROOT.
{
if (_comp.Compare(_r.FirstSon.Value, item) == 0)
{
return(false);
}
else if (_comp.Compare(_r.SecondSon.Value, item) == 0)
{
return(false);
}
else if (_comp.Compare(item, _r.FirstSon.Value) < 0)//x < y < z
{
TwoThreeNode <T> leaf = _r.FirstSon;
TwoThreeNode <T> temp = _r.SecondSon;
T oldmin = _r.LowOfSecond;
_r.FirstSon = new TwoThreeNode <T>();
_r.FirstSon.Value = item;
_r.FirstSon.Parent = _r;//PARENT
_r.SecondSon = leaf;
_r.ThirdSon = temp;
_r.LowOfSecond = _r.SecondSon.Value;
_r.LowOfThird = oldmin;
_count += 1;
return(true);
}
else if (_comp.Compare(item, _r.SecondSon.Value) < 0)//y < x < z.
{
TwoThreeNode <T> leaf = _r.SecondSon;
T oldmin = _r.LowOfSecond;
_r.SecondSon = new TwoThreeNode <T>();
_r.SecondSon.Value = item;
_r.SecondSon.Parent = _r;//PARENT
_r.ThirdSon = leaf;
_r.LowOfSecond = _r.SecondSon.Value;
_r.LowOfThird = oldmin;
_count += 1;
return(true);
}
else //y < z < x
{
_r.ThirdSon = new TwoThreeNode <T>();
_r.ThirdSon.Value = item;
_r.ThirdSon.Parent = _r;//PARENT
_r.LowOfThird = item;
_count += 1;
return(true);
}
}
Boolean added = false;
TwoThreeNode <T> pback = null; //pback is returned by Insert1 procedure
T lowback = default(T); //lowvalue in pback.
TwoThreeNode <T> saveS;
__Insert1(r, item, ref pback, ref lowback, ref added);
if (pback != null)
{
//Console.WriteLine("new node");
saveS = r; //__CreateNewNode(r,null);
r = new TwoThreeNode <T>(); //new(Root)
r.FirstSon = saveS;
r.SecondSon = pback;
r.FirstSon.Parent = r; //PARENT
r.SecondSon.Parent = r; //PARENT
r.LowOfSecond = lowback;
r.ThirdSon = null;
this._r = r;//IMPORTANT
this._h += 1;
//__ComputeH();
return(true);
}
//__ComputeH();
return(added);
}
private bool __Member(TwoThreeNode <T> node, T item)
{
if (item == null)
{
return(false);
}
while (node != null)
{
if (node.ThirdSon != null)//iterior with 3 sons.
{
Int32 i = _comp.Compare(item, node.LowOfSecond);
if (i == 0)//x == y.
{
return(true);
}
else if (i < 0)//x < y
{
node = node.FirstSon;
}
else
{
i = _comp.Compare(item, node.LowOfThird);
}
if (i == 0)//x == z
{
return(true);
}
else if (i < 0)//x < z
{
node = node.SecondSon;
}
else//x > z
{
node = node.ThirdSon;
}
//Console.WriteLine("down");
}
else if (node.SecondSon != null)//iterior with 2 sons.
{
Int32 i = _comp.Compare(item, node.LowOfSecond);
if (i == 0)//x == y.
{
return(true);
}
else if (i < 0)//x < y
{
node = node.FirstSon;
}
else
{
node = node.SecondSon;
}
//Console.WriteLine("down");
}
else //leaf
{
if (_comp.Compare(item, node.Value) == 0)
{
return(true);
}
return(false);
}
}
return(false);
}
private void __PrintVal(Node <T> n, ref StringBuilder sb)
{
TwoThreeNode <T> np = n as TwoThreeNode <T>;
sb.Append(np.FirstSon == null ? n.Value.ToString() + " " : "");//Print values of the leaves of the TREE.
}
//MAKENULL
public void Clear()
{
this._count = 0;
this._h = 0;
this._r = null;
}
private bool __Delete0(TwoThreeNode <T> r, T item)
{
if (item == null)
{
return(false);
}
if (_count == 0)
{
return(false);
}
else if (_count == 1)//only root.
{
if (_comp.Compare(_r.Value, item) == 0)
{
_r = null;
_count -= 1;
return(true);
}
return(false);
}
else if (_count == 2)//one level tree. (root with two children)
{
if (_comp.Compare(_r.FirstSon.Value, item) == 0)
{
this._r = _r.SecondSon;
this._r.Parent = null;
this._count -= 1;
this._h = 0;
return(true);
}
else if (_comp.Compare(_r.SecondSon.Value, item) == 0)
{
this._r = _r.FirstSon;
this._r.Parent = null;
this._count -= 1;
this._h = 0;
return(true);
}
else
{
return(false);
}
}
else if (_count == 3)//root with three children.
{
if (_comp.Compare(_r.ThirdSon.Value, item) == 0)
{
this._r.LowOfThird = default(T);
this._r.ThirdSon = null;
this._count -= 1;
return(true);
}
else if (_comp.Compare(_r.SecondSon.Value, item) == 0)
{
_r.LowOfSecond = _r.LowOfThird;
_r.LowOfThird = default(T);
_r.SecondSon = _r.ThirdSon;
_r.ThirdSon = null;
_count -= 1;
return(true);
}
else if (_comp.Compare(_r.FirstSon.Value, item) == 0)
{
_r.LowOfSecond = _r.LowOfThird;
_r.LowOfThird = default(T);
_r.FirstSon = _r.SecondSon;
_r.SecondSon = _r.ThirdSon;
_r.ThirdSon = null;
_count -= 1;
return(true);
}
else
{
return(false);
}
}
bool del = false;
bool one = false;
TwoThreeNode <T> G = null;
__Delete1(r, item, ref one, ref del, ref G);
if (one)
{
_count -= 1;
this._r = G.FirstSon;
this._r.Parent = null;
this._h -= 1;
//__ComputeH();
return(true);
}
//__ComputeH();
return(del);
}
//NON-RECURSIVE.
private void __Insert1(TwoThreeNode <T> node, T item, ref TwoThreeNode <T> pnew, ref T low, ref Boolean added)
{
TwoThreeNode <T> pback = null;
T lowback = default(T);
LinkedStack <TwoThreeNode <T> > STACK = new LinkedStack <TwoThreeNode <T> >();
LinkedStack <Insert1StackEntry <T> > S2 = new LinkedStack <Insert1StackEntry <T> >();
LinkedStack <Int32> S3 = new LinkedStack <Int32>();
//move down to the leaf. return leaf as pback and its minValue as lowback.
//also return path from the root to the parent of the leaf. (PARENT(pback))
//path includes parameter child which is contained in the S3.
//parent is the Top of the STACK.
//child option is the Top of the S3.
__Insert2(node, item, ref pback, ref lowback, ref S3, ref added, ref STACK);
S2.Push(new Insert1StackEntry <T>(pback, lowback));//pback lowback - first.
//AFTER DESCENT.
while (!STACK.IsEmpty() && !S3.IsEmpty() && !S2.IsEmpty())
{
Int32 child = S3.Top();
node = STACK.Top();//w2,w3 => w2,w1 ::S, nleaf as pback
pback = S2.Top().LowBack;
lowback = S2.Top().Low;
S2.Pop();
STACK.Pop();
S3.Pop();
if (pback != null) //ADD NEW SON TO THE NODE
{
if (node.ThirdSon == null) //Two children.
{
if (child == 2)
{
node.ThirdSon = pback;//__CreateNewNode(pback,parent: node);//pback;
node.ThirdSon.Parent = node;
node.LowOfThird = lowback;
pnew = null;
return;//INSERTED
}
else //child == 1.
{
node.ThirdSon = node.SecondSon; //__CreateNewNode(node.SecondSon,node);
node.LowOfThird = node.LowOfSecond;
node.SecondSon = pback; //__CreateNewNode(pback,node);
node.SecondSon.Parent = node;
node.LowOfSecond = lowback;
pnew = null;
return;//INSERTED.
}
}//INSERTED:: pnew and low are still null.
else //node has three children. UPDATE pback and lowback!
{
TwoThreeNode <T> _pnew = new TwoThreeNode <T>();//ITERIOR NODE
if (child == 3) //pback and thirdchild are sons of new node.
{
_pnew.FirstSon = node.ThirdSon; //__CreateNewNode(node.ThirdSon,_pnew);
_pnew.SecondSon = pback; //__CreateNewNode(pback,_pnew);
_pnew.ThirdSon = null;
_pnew.LowOfSecond = lowback;
_pnew.FirstSon.Parent = _pnew;
_pnew.SecondSon.Parent = _pnew;
low = node.LowOfThird;
pnew = _pnew;
node.ThirdSon = null;
}
else //child <= 2 the third child of node moving to -> pnew
{
_pnew.SecondSon = node.ThirdSon;//__CreateNewNode(node.ThirdSon,_pnew);
_pnew.LowOfSecond = node.LowOfThird;
//if(_pnew.SecondSon != null)
_pnew.SecondSon.Parent = _pnew;
_pnew.ThirdSon = null;
node.ThirdSon = null;
}
if (child == 2) //pback is firstSon of pnew
{
_pnew.FirstSon = pback; //__CreateNewNode(pback,_pnew);
_pnew.FirstSon.Parent = _pnew;
low = lowback;
pnew = _pnew;
}
if (child == 1) //the second child of node move to -> pnew, pback is 2 son of node
{
_pnew.FirstSon = node.SecondSon; //__CreateNewNode(node.SecondSon,_pnew);
//if(_pnew.FirstSon != null)
_pnew.FirstSon.Parent = _pnew;
low = node.LowOfSecond;
node.SecondSon = pback;//__CreateNewNode(pback,node);
node.SecondSon.Parent = node;
node.LowOfSecond = lowback;
pnew = _pnew;
}
S2.Push(new Insert1StackEntry <T>(_pnew, low));
} //endElse
} //endIf
} //endWhile
}
public Insert1StackEntry(TwoThreeNode <T> lowback, T low)
{
this._lb = lowback;
this._l = low;
}