79 /// where m is the number of edges, n is the number of vertices, and v(f) is the
83 /// The input is a set of edges with specified costs and capacities, and a pair
96     Edges = std::vector<std::vector<Edge>>(NodeCount, std::vector<Edge>());  in initialize()
107     // flow along its edges  in run()
114       for (auto &Edge : Edges[Src]) {  in run()
131   /// Multiple edges between a pair of nodes are allowed but self-edges
142     SrcEdge.RevEdgeIndex = Edges[Dst].size();  in addEdge()
149     DstEdge.RevEdgeIndex = Edges[Src].size();  in addEdge()
151     Edges[Src].push_back(SrcEdge);  in addEdge()
152     Edges[Dst].push_back(DstEdge);  in addEdge()
164     for (const auto &Edge : Edges[Src]) {  in getFlow()
174     for (const auto &Edge : Edges[Src]) {  in getFlow()
184   /// flow along its edges. The method returns the number of applied iterations.
221       auto &Edge = Edges[Pred][Nodes[Now].ParentEdgeIndex];  in computeAugmentingPathCapacity()
250       // Although the residual network contains edges with negative costs  in findAugmentingPath()
251       // (in particular, backward edges), it can be shown that there are no  in findAugmentingPath()
269       // Process adjacent edges  in findAugmentingPath()
270       for (uint64_t EdgeIdx = 0; EdgeIdx < Edges[Src].size(); EdgeIdx++) {  in findAugmentingPath()
271         auto &Edge = Edges[Src][EdgeIdx];  in findAugmentingPath()
299       auto &Edge = Edges[Pred][Nodes[Now].ParentEdgeIndex];  in augmentFlowAlongPath()
300       auto &RevEdge = Edges[Now][Edge.RevEdgeIndex];  in augmentFlowAlongPath()
313   /// runs in O(MaxDfsCalls * |Edges| + |Nodes|) time.
321     //  - the next edge to scan is Edges[NodeIdx][EdgeIdx]  in findAugmentingDAG()
345       // If we haven't scanned all edges out of NodeIdx, continue scanning  in findAugmentingDAG()
346       if (EdgeIdx < Edges[NodeIdx].size()) {  in findAugmentingDAG()
347         auto &Edge = Edges[NodeIdx][EdgeIdx];  in findAugmentingDAG()
384     // Phase 2: Extract all forward (DAG) edges and fill in AugmentingEdges  in findAugmentingDAG()
387       for (auto &Edge : Edges[Src]) {  in findAugmentingDAG()
395              "incorrectly constructed augmenting edges");  in findAugmentingDAG()
459     // Because of rounding, not all flow can be sent along the edges of Src.  in augmentFlowAlongDAG()
476     // Phase 4: Update flow values along all edges  in augmentFlowAlongDAG()
484         auto &RevEdge = Edges[Edge->Dst][Edge->RevEdgeIndex];  in augmentFlowAlongDAG()
496   /// Identify candidate (shortest) edges for augmentation.
499     // To make sure the augmentation DAG contains only edges with large residual  in identifyShortestEdges()
500     // capacity, we prune all edges whose capacity is below a fraction of  in identifyShortestEdges()
502     // (All edges of the path itself are always in the DAG)  in identifyShortestEdges()
505     // Decide which edges are on a shortest path from Source to Target  in identifyShortestEdges()
511       for (auto &Edge : Edges[Src]) {  in identifyShortestEdges()
572   /// The set of network edges.
573   std::vector<std::vector<Edge>> Edges;  member in __anon5aecd1f00111::MinCostMaxFlow
578   /// Augmenting edges.
746   /// and avoid changing branch probability of outgoing edges drastically,
750   ///   - minimizes total multiplicative Flow increase for the remaining edges.
1083     // Edges from S and to T  in initializeNetwork()
1093     // Add the corresponding edges to the network  in initializeNetwork()
1102   // Initialize edges of the flow network  in initializeNetwork()
1113     // Add the corresponding edges to the network  in initializeNetwork()
1232   // Verify that there are no parallel edges  in verifyInput()
1237       assert(It.second && "input CFG contains parallel edges");  in verifyInput()
1285   // One could modify FlowFunction to hold edges indexed by the sources, which  in verifyOutput()
1294   // Run BFS from the source along edges with positive flow  in verifyOutput()
1311   // along edges with a positive flow  in verifyOutput()