/// <summary>
/// Fix the root balance if LTDict and GTDict have good balance
/// Used to keep the depth less than 1.44 log_2 N (AVL tree)
/// </summary>
AvlNode <T> FixRootBalance()
{
int bal = Balance;
if (Math.Abs(bal) < 2)
{
return(this);
}
if (bal == 2)
{
if (_left.Balance == 1 || _left.Balance == 0)
{
//Easy case:
return(this.RotateToGT());
}
if (_left.Balance == -1)
{
//Rotate LTDict:
var newLt = _left.RotateToLT();
var newRoot = NewOrMutate(Value, newLt, _right);
return(newRoot.RotateToGT());
}
throw new Exception($"LTDict too unbalanced: {_left.Balance}");
}
if (bal == -2)
{
if (_right.Balance == -1 || _right.Balance == 0)
{
//Easy case:
return(this.RotateToLT());
}
if (_right.Balance == 1)
{
//Rotate GTDict:
var newGt = _right.RotateToGT();
var newRoot = NewOrMutate(Value, _left, newGt);
return(newRoot.RotateToLT());
}
throw new Exception($"LTDict too unbalanced: {_left.Balance}");
}
//In this case we can show: |bal| > 2
//if( Math.Abs(bal) > 2 ) {
throw new Exception($"Tree too out of balance: {Balance}");
}
