/// 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;
}
