public void Sort(Action <int, int> removedEdge)
{
if (IsSorted)
{
return;
}
IsSorted = true;
ProcesseDeferredForcedDrawOrders();
int vertexCount = this.Count;
// INITIALISE
{
if (edgeBits.Length < EdgeBits.Size(vertexCount))
{
edgeBits = EdgeBits.Create(vertexCount * 2);
}
else
{
Array.Clear(edgeBits, 0, EdgeBits.Size(vertexCount));
}
}
// Step 1: Determine what items overlap and store in the edge bits:
{
// This is O(n^2) on drawn items, so we want it to be fast (later we could consider bucketing)
for (int f = 0; f < vertexCount; f++)
{
for (int t = f + 1; t < vertexCount; t++)
{
if (bounds[f].Intersects(bounds[t]))
{
edgeBits.SetEdge(vertexCount, f, t); // Abuse "edgeBits" for temporary storage
}
}
}
// Don't do ordering comparisons if we're just going to force the order:
foreach (var order in forceDrawOrder)
{
// Rather than picking the correct bit, just clear both:
edgeBits.ClearEdge(vertexCount, order.from, order.to);
edgeBits.ClearEdge(vertexCount, order.to, order.from);
}
// Don't do ordering comparisons in cases that can be handled by inheritance:
foreach (var inheritance in inheritDrawOrders)
{
for (int f = 0; f < inheritance.from; f++) // <- split loops due to ordering in edgeBits
{
if (f != inheritance.to && edgeBits.IsEdge(vertexCount, f, inheritance.from))
{
// Rather than picking the correct bit, just clear both:
edgeBits.ClearEdge(vertexCount, f, inheritance.to);
edgeBits.ClearEdge(vertexCount, inheritance.to, f);
}
}
for (int t = inheritance.from + 1; t < vertexCount; t++) // <- split loops due to ordering in edgeBits
{
if (t != inheritance.to && edgeBits.IsEdge(vertexCount, inheritance.from, t))
{
// Rather than picking the correct bit, just clear both:
edgeBits.ClearEdge(vertexCount, t, inheritance.to);
edgeBits.ClearEdge(vertexCount, inheritance.to, t);
}
}
}
}
// Step 2: Compare all overlapping items to geneate the directed graph:
{
for (int f = 0; f < vertexCount; f++)
{
for (int t = f + 1; t < vertexCount; t++)
{
if (edgeBits.IsEdge(vertexCount, f, t))
{
int compare = DrawOrdering.Compare(sortingInfo[f].animationSet, sortingInfo[t].animationSet,
sortingInfo[f].position, sortingInfo[t].position, sortingInfo[f].facingLeft, sortingInfo[t].facingLeft, null);
// If compare is negative, we basically want to leave the existing bit in place, otherwise clear it and maybe set its reverse
if (compare >= 0)
{
edgeBits.ClearEdge(vertexCount, f, t);
if (compare > 0)
{
edgeBits.SetEdge(vertexCount, t, f);
}
}
}
}
}
// Apply forced ordering:
foreach (var order in forceDrawOrder)
{
edgeBits.SetEdge(vertexCount, order.from, order.to);
}
// Apply inherited ordering:
foreach (var inheritance in inheritDrawOrders)
{
for (int i = 0; i < vertexCount; i++)
{
if (i == inheritance.from || i == inheritance.to)
{
continue;
}
uint edgeF = edgeBits.GetEdgeBit(vertexCount, inheritance.from, i);
uint edgeT = edgeBits.GetEdgeBit(vertexCount, i, inheritance.from);
if ((edgeF | edgeT) != 0) // <- if the source has an opinion, copy it
{
edgeBits.ChangeEdgeBit(vertexCount, inheritance.to, i, edgeF);
edgeBits.ChangeEdgeBit(vertexCount, i, inheritance.to, edgeT);
}
}
}
}
// Step 3: Topological Sort!
{
sortedOrder = forgivingTopologicalSort.Sort(vertexCount, edgeBits, removedEdge);
}
}
SCC[] bestSCCs; // count is a local
/// <summary>NOTE: Returns a reference to an internal array which is cleared on subsequent sorts. May be longer than the passed in vertexCount - excess data is garbage.</summary>
public int[] Sort(int vertexCount, uint[] edgeBits, Action <int, int> removedEdge)
{
//
// INITIALIZE:
//
{
if (primaryVertices == null || primaryVertices.Length < vertexCount)
{
// NOTE: Lazy over-allocate here, to avoid reallocation
primaryVertices = new int[vertexCount * 2];
primarySCCStack = new SCC[(vertexCount * 2) / 3]; // worst-case capacity required is that every vertex triplet is an SCC
// Secondary stage (NOTE: worst-case is that the whole of primary is a SCC, so this must be the same size)
secondaryEdgeBits = EdgeBits.Create(vertexCount * 2); // NOTE: This allocates 4x as much memory as was passed in for edges
secondaryVertices = new int[vertexCount * 2];
secondarySCCs = new SCC[(vertexCount * 2) / 3];
bestVertices = new int[vertexCount * 2];
bestSCCs = new SCC[(vertexCount * 2) / 3];
tempOutput = new int[vertexCount * 2];
}
else
{
// NOTE: Nothing to clear (all items have counts and get re-initialized up to their count upon usage)
}
}
//
// RUN:
//
{
// Primary:
// --------
TarjanOutput primaryOutput = new TarjanOutput();
primaryOutput.sccList = primarySCCStack;
primaryOutput.vertexList = primaryVertices;
ta.FindStronglyConnectedComponents(vertexCount, edgeBits, ref primaryOutput);
// Secondary: (this is a greedy search)
// ----------
// Try to resolve any SCCs remaining in the output
// Note that changes to a SCC do not affect the ordering of the surrounding DAG
while (primaryOutput.sccCount > 0)
{
SCC workingSCC = primaryOutput.sccList[--primaryOutput.sccCount]; // Pop
// The secondary stage uses indirect indices (ie: vertex number in primary = scc[vertex number in secondary])
// This allows the secondary stage to use implicit vertex numbers (0 to N-1, rather than having to access workingSCC)
// This requires rebuilding edges to match this indexing scheme (secondaryEdge[v, w] = primaryEdge[scc[v], scc[w]])
// But this is desireable, because the access pattern into the primary edges would be cache-unfriendly
// Also secondary is generally much smaller than primary (because it works on individual SCCs, which are usually relatively small)
// Rebuild edge bits:
int v, w; // v is "from", w is "to"
for (v = 0; v < workingSCC.count; v++)
{
for (w = 0; w < workingSCC.count; w++)
{
secondaryEdgeBits.ChangeEdgeBit(workingSCC.count, v, w,
edgeBits.GetEdgeBit(vertexCount, primaryVertices[workingSCC.index + v], primaryVertices[workingSCC.index + w]));
}
}
int bestSCCCount = 0;
int bestSCCMaximumSize = workingSCC.count; // The size of the largest SCCs <- used to select "best" (reduces size of O(N^2) problem -- unverified -AR)
int bestSCCCumulativeSize = workingSCC.count; // Number of vertices in all SCCs <- used as a tie-break (reduces size of O(N) problem -- unverified -AR)
// These are for logging
int bestRemovedV = 0;
int bestRemovedW = 0;
// Try to find the best constraint (ie: edge) to remove:
for (v = 0; v < workingSCC.count; v++)
{
for (w = 0; w < workingSCC.count; w++)
{
if (secondaryEdgeBits.IsEdge(workingSCC.count, v, w)) // PERF: Consider only looking at "backwards" edges (requires primary input is spatially sorted, then compare primary indices)
{
TarjanOutput secondaryOutput = new TarjanOutput();
secondaryOutput.sccList = secondarySCCs;
secondaryOutput.vertexList = secondaryVertices;
secondaryEdgeBits.ClearEdge(workingSCC.count, v, w); // Temporarly remove an edge (see if it improves the result)
ta.FindStronglyConnectedComponents(workingSCC.count, secondaryEdgeBits, ref secondaryOutput);
int secondarySCCMaximumSize = 0;
int secondarySCCCumulativeSize = 0;
for (int i = 0; i < secondaryOutput.sccCount; i++)
{
int count = secondaryOutput.sccList[i].count;
if (count > secondarySCCMaximumSize)
{
secondarySCCMaximumSize = count;
}
secondarySCCCumulativeSize += count;
}
// NOTE: If we change to only looking at "backwards" edges, should probably add tie-break to select rearmost edge to remove
// (May require pre-sorting the SCC, to handle the early-out case properly)
if (secondaryOutput.sccCount == 0 ||
secondarySCCMaximumSize < bestSCCMaximumSize ||
(secondarySCCMaximumSize == bestSCCMaximumSize && secondarySCCCumulativeSize < bestSCCCumulativeSize))
{
bestRemovedV = v;
bestRemovedW = w;
bestSCCCount = secondaryOutput.sccCount;
bestSCCMaximumSize = secondarySCCMaximumSize;
bestSCCCumulativeSize = secondarySCCCumulativeSize;
Swap(ref bestSCCs, ref secondarySCCs);
Swap(ref bestVertices, ref secondaryVertices);
}
if (secondaryOutput.sccCount == 0)
{
goto earlyOut; // Found optimal solution
}
secondaryEdgeBits.SetEdge(workingSCC.count, v, w); // Restore Edge
}
}
}
if (bestSCCMaximumSize == workingSCC.count) // Failed to find any improvement for this SCC - give up!
{
// Just leave the primary output in its original order
// NOTE: If we change to sorted input (for "backwards" edges), consider re-sorting this SCC in output
continue;
}
earlyOut: // skips the above
// Notify any debug output that an edge was removed. NOTE: Before the SCC in primary gets re-ordered!
if (removedEdge != null)
{
removedEdge(primaryVertices[workingSCC.index + bestRemovedV], primaryVertices[workingSCC.index + bestRemovedW]);
}
// Apply the new ordering
for (int i = 0; i < workingSCC.count; i++)
{
tempOutput[i] = primaryVertices[workingSCC.index + bestVertices[i]];
}
Array.Copy(tempOutput, 0, primaryVertices, workingSCC.index, workingSCC.count);
// Transfer new SCCs to primary:
for (int i = 0; i < bestSCCCount; i++)
{
primaryOutput.sccList[primaryOutput.sccCount++] = new SCC(workingSCC.index + bestSCCs[i].index, bestSCCs[i].count);
}
}
// At this point, primarySCC stack is empty -- we're done
return(primaryVertices);
}
}
