/// <summary>
/// Partions the vertices based on the pivot value.
/// </summary>
/// <typeparam name="TEdgeData"></typeparam>
/// <param name="graph">The graph to sort.</param>
/// <param name="n">The hilbert accuracy.</param>
/// <param name="left">The first vertex to consider.</param>
/// <param name="right">The last vertex to consider.</param>
/// <return>The new left.</return>
private static uint SortHilbertPartition <TEdgeData>(GraphBase <TEdgeData> graph, int n, uint left, uint right)
where TEdgeData : struct, IGraphEdgeData
{ // get the pivot value.
uint start = left;
ulong pivotValue = graph.HilbertDistance(n, left);
left++;
while (true)
{
ulong leftValue = graph.HilbertDistance(n, left);
while (left <= right && leftValue <= pivotValue)
{ // move the left to the first value bigger than pivot.
left++;
leftValue = graph.HilbertDistance(n, left);
}
ulong rightValue = graph.HilbertDistance(n, right);
while (left <= right && rightValue > pivotValue)
{ // move the right to the first value smaller than pivot.
right--;
rightValue = graph.HilbertDistance(n, right);
}
if (left > right)
{ // we are done searching, left is to the right of right.
// make sure the pivot value is where it is supposed to be.
graph.Switch(start, left - 1);
return(left);
}
// swith left<->right.
graph.Switch(left, right);
}
}
/// <summary>
/// Sorts the vertices in the given graph based on a hilbert curve.
/// </summary>
/// <typeparam name="TEdgeData"></typeparam>
public static void BuildHilbertRank <TEdgeData>(this GraphBase <TEdgeData> graph, int n,
HugeArrayBase <uint> ranks)
where TEdgeData : struct, IGraphEdgeData
{
if (graph == null)
{
throw new ArgumentNullException("graph");
}
if (graph.VertexCount != ranks.Length - 1)
{
throw new ArgumentException("Graph and ranks array must have equal sizes.");
}
for (uint i = 0; i <= graph.VertexCount; i++)
{ // fill with default data.
ranks[i] = i;
}
if (graph.VertexCount == 1)
{ // just return the rank for the one vertex.
ranks[0] = 0;
ranks[1] = 1;
}
// sort the complete graph and keep the transformations.
QuickSort.Sort((i) => graph.HilbertDistance(n, ranks[i]), (i, j) =>
{
var temp = ranks[i];
ranks[i] = ranks[j];
ranks[j] = temp;
}, 1, graph.VertexCount);
}