private void DeleteImpl(VEBTree tree, int x)
{
if (tree.min == tree.max)
{
min = max = null;
}
else if (tree.universeSize == 2)
{
if (x == 0)
{
tree.min = 1;
}
else
{
tree.min = 0;
}
tree.max = tree.min;
}
else
{
if (x == tree.min)
{
int firstCluster = MinimumImpl(tree.summary).Value;
x = Index(firstCluster, MinimumImpl(tree.cluster[firstCluster]).Value);
tree.min = x;
}
DeleteImpl(tree.cluster[HighBits(x)], LowBits(x));
if (MinimumImpl(tree.cluster[HighBits(x)]) == null)
{
DeleteImpl(tree.summary, HighBits(x));
if (x == tree.max)
{
var summaryMax = MaximumImpl(tree.summary);
if (summaryMax == null)
{
tree.max = tree.min;
}
else
{
tree.max = Index(summaryMax.Value, MaximumImpl(tree.cluster[summaryMax.Value]).Value);
}
}
}
else if (x == tree.max)
{
tree.max = Index(HighBits(x), MaximumImpl(tree.cluster[HighBits(x)]).Value);
}
}
}
public VEBTree(int size)
{
if (size < 0 || (size & (size - 1)) != 0)
{
throw new Exception("The size has to be a power of 2 and positive");
}
universeSize = size;
if (universeSize > 1)
{
int upperSqrt = UpperSqrt(universeSize);
summary = new VEBTree(upperSqrt);
cluster = new VEBTree[upperSqrt];
for (int i = 0; i < upperSqrt; i++)
{
cluster[i] = new VEBTree(LowerSqrt(universeSize));
}
}
}
private int? SuccessorImpl(VEBTree tree, int x)
{
if (tree.universeSize == 2)
{
if (x == 0 && tree.max == 1)
{
return 1;
}
else
{
return null;
}
}
else if (tree.min != null && x < tree.min)
{
return tree.min;
}
else
{
var maxLow = MaximumImpl(tree.cluster[HighBits(x)]);
if (maxLow != null && LowBits(x) < maxLow.Value)
{
var offset = SuccessorImpl(tree.cluster[HighBits(x)], LowBits(x));
return Index(HighBits(x), offset.Value);
}
else
{
var succCluster = SuccessorImpl(tree.summary, HighBits(x));
if (succCluster == null)
{
return null;
}
else
{
var offset = MinimumImpl(tree.cluster[succCluster.Value]);
return Index(succCluster.Value, offset.Value);
}
}
}
}
private int? PredecessorImpl(VEBTree tree, int x)
{
if (tree.universeSize == 2)
{
if (x == 1 && tree.min == 0)
{
return 0;
}
else
{
return null;
}
}
else if (tree.max != null && x > tree.max)
{
return tree.max;
}
else
{
var minLow = MinimumImpl(tree.cluster[HighBits(x)]);
if (minLow != null && LowBits(x) > minLow)
{
var offset = PredecessorImpl(tree.cluster[HighBits(x)], LowBits(x));
return Index(HighBits(x), offset.Value);
}
else
{
var predCluster = PredecessorImpl(tree.summary, HighBits(x));
if (predCluster == null)
{
if (tree.min != null && x > tree.min)
{
return tree.min;
}
else
{
return null;
}
}
else
{
var offset = MaximumImpl(tree.cluster[predCluster.Value]);
return Index(predCluster.Value, offset.Value);
}
}
}
}
private int? MinimumImpl(VEBTree tree)
{
return tree.min;
}
private bool MemberImpl(VEBTree tree, int x)
{
if (x == tree.min || x == tree.max)
{
return true;
}
else if (tree.universeSize == 2)
{
return false;
}
return MemberImpl(tree.cluster[HighBits(x)], LowBits(x));
}
private int? MaximumImpl(VEBTree tree)
{
return tree.max;
}
private void InsertImpl(VEBTree tree, int x)
{
if (tree.min == null)
{
EmptyTreeInsertImpl(tree, x);
}
else if (x < tree.min.Value)
{
var tmp = x;
x = tree.min.Value;
tree.min = tmp;
if (tree.universeSize == 2)
{
if (MinimumImpl(tree.cluster[HighBits(x)]) == null)
{
InsertImpl(tree.summary, HighBits(x));
EmptyTreeInsertImpl(tree.cluster[HighBits(x)], LowBits(x));
}
else
{
InsertImpl(tree.cluster[HighBits(x)], LowBits(x));
}
}
if (x > tree.max.Value)
{
tree.max = x;
}
}
}
private void EmptyTreeInsertImpl(VEBTree tree, int x)
{
tree.min = x;
tree.max = x;
}
