/// Returns the amount the flow can be augmented over the paths, 0 if no path can be found. ##TSnap::FindAugV
int FindAugV (const PNEANet &Net, const int& CapIndex, TIntV &Flow, TIntQ &FwdNodeQ, TIntH &PredEdgeH, TIntQ &BwdNodeQ, TIntH &SuccEdgeH, TIntV &MidToSrcAugV, TIntV &MidToSnkAugV, const int& SrcNId, const int& SnkNId) {
int MidPtNId = IntFlowBiDBFS(Net, CapIndex, Flow, FwdNodeQ, PredEdgeH, BwdNodeQ, SuccEdgeH, SrcNId, SnkNId);
if (MidPtNId == -1) { return 0; }
int MinAug = TInt::Mx, NId = MidPtNId, AugFlow = 0;
// Build the path from the midpoint back to the source by tracing through the PredEdgeH
for (int EId = PredEdgeH.GetDat(NId); NId != SrcNId; EId = PredEdgeH.GetDat(NId)) {
MidToSrcAugV.Add(EId);
const TNEANet::TEdgeI &EI = Net->GetEI(EId);
if (EI.GetSrcNId() == NId) {
NId = EI.GetDstNId();
AugFlow = Flow[EId];
} else {
NId = EI.GetSrcNId();
AugFlow = Net->GetIntAttrIndDatE(EId, CapIndex) - Flow[EId];
}
if (AugFlow < MinAug) { MinAug = AugFlow; }
}
NId = MidPtNId;
// Build the path from the midpoint back to the sink by tracing through the SuccEdgeH
for (int EId = SuccEdgeH.GetDat(NId); NId != SnkNId; EId = SuccEdgeH.GetDat(NId)) {
MidToSnkAugV.Add(EId);
const TNEANet::TEdgeI &EI = Net->GetEI(EId);
if (EI.GetDstNId() == NId) {
NId = EI.GetSrcNId();
AugFlow = Flow[EId];
} else {
NId = EI.GetDstNId();
AugFlow = Net->GetIntAttrIndDatE(EId, CapIndex) - Flow[EId];
}
if (AugFlow < MinAug) { MinAug = AugFlow; }
}
return MinAug;
}
int GetMaxFlowIntEK (PNEANet &Net, const int &SrcNId, const int &SnkNId) {
IAssert(Net->IsNode(SrcNId));
IAssert(Net->IsNode(SnkNId));
if (SrcNId == SnkNId) { return 0; }
int CapIndex = Net->GetIntAttrIndE(CapAttrName);
TIntV Flow(Net->GetMxEId());
// Initialize flow values to 0, and make sure capacities are nonnegative
for (TNEANet::TEdgeI EI = Net->BegEI(); EI != Net->EndEI(); EI++) {
IAssert(Net->GetIntAttrIndDatE(EI, CapIndex) >= 0);
Flow[EI.GetId()] = 0;
}
// Return 0 if user attempts to flow from a node to itself.
if (SrcNId == SnkNId) { return 0; }
int MaxFlow = 0, MinAug, CurNId;
while (true) {
TIntV MidToSrcAugV; TIntV MidToSnkAugV;
TIntQ FwdNodeQ; TIntQ BwdNodeQ;
TIntH PredEdgeH; TIntH SuccEdgeH;
MinAug = FindAugV(Net, CapIndex, Flow, FwdNodeQ, PredEdgeH, BwdNodeQ, SuccEdgeH, MidToSrcAugV, MidToSnkAugV, SrcNId, SnkNId);
if (MinAug == 0) { break; }
MaxFlow += MinAug;
CurNId = SrcNId;
for (int i = MidToSrcAugV.Len() - 1; i >= 0; i--) {
int NextEId = MidToSrcAugV[i];
const TNEANet::TEdgeI &EI = Net->GetEI(NextEId);
if (EI.GetSrcNId() == CurNId) {
Flow[NextEId] += MinAug;
CurNId = EI.GetDstNId();
} else {
Flow[NextEId] -= MinAug;
CurNId = EI.GetSrcNId();
}
}
for (int i = 0; i < MidToSnkAugV.Len(); i++) {
int NextEId = MidToSnkAugV[i];
const TNEANet::TEdgeI &EI = Net->GetEI(NextEId);
if (EI.GetSrcNId() == CurNId) {
Flow[NextEId] += MinAug;
CurNId = EI.GetDstNId();
} else {
Flow[NextEId] -= MinAug;
CurNId = EI.GetSrcNId();
}
}
}
return MaxFlow;
}
// Returns the NId where the two directions of search meet up, or -1 if no augmenting path exists. ##TSnap::IntFlowBiDBFS
int IntFlowBiDBFS (const PNEANet &Net, const int& CapIndex, TIntV &Flow, TIntQ &FwdNodeQ, TIntH &PredEdgeH, TIntQ &BwdNodeQ, TIntH &SuccEdgeH, const int& SrcNId, const int& SnkNId) {
FwdNodeQ.Push(SrcNId);
PredEdgeH.AddDat(SrcNId, -1);
BwdNodeQ.Push(SnkNId);
SuccEdgeH.AddDat(SnkNId, -1);
while (!FwdNodeQ.Empty() && !BwdNodeQ.Empty()) {
// Forward search
const TNEANet::TNodeI &FwdNI = Net->GetNI(FwdNodeQ.Top()); FwdNodeQ.Pop();
// Check all edges that point into the current node for those over which flow can be returned.
for (int EdgeN = 0; EdgeN < FwdNI.GetInDeg(); EdgeN++) {
int NextNId = FwdNI.GetInNId(EdgeN);
int NextEId = FwdNI.GetInEId(EdgeN);
if (!PredEdgeH.IsKey(NextNId) && Flow[NextEId] > 0) {
PredEdgeH.AddDat(NextNId, NextEId);
if (SuccEdgeH.IsKey(NextNId)) {
return NextNId;
}
FwdNodeQ.Push(NextNId);
}
}
// Check all edges that point out of the current node for those over which flow can be added.
for (int EdgeN = 0; EdgeN < FwdNI.GetOutDeg(); EdgeN++) {
int NextNId = FwdNI.GetOutNId(EdgeN);
int NextEId = FwdNI.GetOutEId(EdgeN);
if (!PredEdgeH.IsKey(NextNId) && Net->GetIntAttrIndDatE(NextEId, CapIndex) > Flow[NextEId]) {
PredEdgeH.AddDat(NextNId, NextEId);
if (SuccEdgeH.IsKey(NextNId)) {
return NextNId;
}
FwdNodeQ.Push(NextNId);
}
}
// Backward search
const TNEANet::TNodeI &BwdNI = Net->GetNI(BwdNodeQ.Top()); BwdNodeQ.Pop();
// Check all edges that point out of the current node for those over which flow can be returned.
for (int EdgeN = 0; EdgeN < BwdNI.GetOutDeg(); EdgeN++) {
int PrevNId = BwdNI.GetOutNId(EdgeN);
int PrevEId = BwdNI.GetOutEId(EdgeN);
if (!SuccEdgeH.IsKey(PrevNId) && Flow[PrevEId] > 0) {
SuccEdgeH.AddDat(PrevNId, PrevEId);
if (PredEdgeH.IsKey(PrevNId)) {
return PrevNId;
}
BwdNodeQ.Push(PrevNId);
}
}
// Check all edges that point into the current node for those over which flow can be added.
for (int EdgeN = 0; EdgeN < BwdNI.GetInDeg(); EdgeN++) {
int PrevNId = BwdNI.GetInNId(EdgeN);
int PrevEId = BwdNI.GetInEId(EdgeN);
if (!SuccEdgeH.IsKey(PrevNId) && Net->GetIntAttrIndDatE(PrevEId, CapIndex) > Flow[PrevEId]) {
SuccEdgeH.AddDat(PrevNId, PrevEId);
if (PredEdgeH.IsKey(PrevNId)) {
return PrevNId;
}
BwdNodeQ.Push(PrevNId);
}
}
}
return -1;
}