U mdo@sndZddlmZddlZdddddd gZGd ddZGd ddZGd ddZd dZ ddZ dd Z dS)z< Utility classes and functions for network flow algorithms. )dequeN CurrentEdgeLevelGlobalRelabelThresholdbuild_residual_networkdetect_unboundednessbuild_flow_dictc@s4eZdZdZdZddZddZddZd d Zd S) rzMechanism for iterating over out-edges incident to a node in a circular manner. StopIteration exception is raised when wraparound occurs. )_edges_it_currcCs||_|jr|dSN)r _rewind)selfedgesrW/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/networkx/algorithms/flow/utils.py__init__szCurrentEdge.__init__cCs|jSr )r rrrrgetszCurrentEdge.getcCs4zt|j|_Wntk r.|YnXdSr )nextr r StopIterationr rrrr move_to_next"s zCurrentEdge.move_to_nextcCs t|j|_t|j|_dSr )iterr itemsr rr rrrrr )szCurrentEdge._rewindN) __name__ __module__ __qualname____doc__ __slots__rrrr rrrrrs c@seZdZdZdZddZdS)rz%Active and inactive nodes in a level.)activeinactivecCst|_t|_dSr )setrr rrrrr3szLevel.__init__N)rrrrrrrrrrr.sc@s0eZdZdZddZddZddZdd Zd S) rzVMeasurement of work before the global relabeling heuristic should be applied. cCs$|r|||ntd|_d|_dS)Ninfr)float _threshold_work)rnmfreqrrrr=szGlobalRelabelThreshold.__init__cCs|j|7_dSr r%)rZworkrrradd_workAszGlobalRelabelThreshold.add_workcCs |j|jkSr )r%r$rrrr is_reachedDsz!GlobalRelabelThreshold.is_reachedcCs d|_dS)Nrr)rrrr clear_workGsz!GlobalRelabelThreshold.clear_workN)rrrrrr*r+r,rrrrr8s cs"|rtdt}||tdfdd|jddD}dtfdd |Dpfd |r|D]Z\}}}t | }| ||s|j |||d |j ||d d qt||||d <qtnB|D]<\}}}t | }|j |||d |j |||d qֈ|j d<|S)aBuild a residual network and initialize a zero flow. The residual network :samp:`R` from an input graph :samp:`G` has the same nodes as :samp:`G`. :samp:`R` is a DiGraph that contains a pair of edges :samp:`(u, v)` and :samp:`(v, u)` iff :samp:`(u, v)` is not a self-loop, and at least one of :samp:`(u, v)` and :samp:`(v, u)` exists in :samp:`G`. For each edge :samp:`(u, v)` in :samp:`R`, :samp:`R[u][v]['capacity']` is equal to the capacity of :samp:`(u, v)` in :samp:`G` if it exists in :samp:`G` or zero otherwise. If the capacity is infinite, :samp:`R[u][v]['capacity']` will have a high arbitrary finite value that does not affect the solution of the problem. This value is stored in :samp:`R.graph['inf']`. For each edge :samp:`(u, v)` in :samp:`R`, :samp:`R[u][v]['flow']` represents the flow function of :samp:`(u, v)` and satisfies :samp:`R[u][v]['flow'] == -R[v][u]['flow']`. The flow value, defined as the total flow into :samp:`t`, the sink, is stored in :samp:`R.graph['flow_value']`. If :samp:`cutoff` is not specified, reachability to :samp:`t` using only edges :samp:`(u, v)` such that :samp:`R[u][v]['flow'] < R[u][v]['capacity']` induces a minimum :samp:`s`-:samp:`t` cut. z0MultiGraph and MultiDiGraph not supported (yet).r"cs4g|],\}}}||kr|dkr|||fqSr)r.0uvattrcapacityr"rr lsz*build_residual_network..T)datac3s0|](\}}}|kr|kr|VqdSr rr.r3rr }s z)build_residual_network..)r4rr4)Z is_multigraphnxZ NetworkXErrorZDiGraphZadd_nodes_fromr#rsumZ is_directedminrZhas_edgeZadd_edgegraph)Gr4RZ edge_listr0r1r2rrr3rrKs8       c Cs|t|g}|h}|jd}|rx|}||D]B\}}|d|kr2||kr2||kr`td||||q2qdS)z*Detect an infinite-capacity s-t path in R.r"r4z-Infinite capacity path, flow unbounded above.N)rr=popleftrr:ZNetworkXUnboundedaddappend) r?stqseenr"r0r1r2rrrrs   cCsHi}|D]:}dd||D||<||dd||Dq|S)z0Build a flow dictionary from a residual network.cSsi|] }|dqSr-r)r/r1rrr sz#build_flow_dict..css*|]"\}}|ddkr||dfVqdS)ZflowrNr)r/r1r2rrrr8s z"build_flow_dict..)updater)r>r?Z flow_dictr0rrrrs ) r collectionsrZnetworkxr:__all__rrrrrrrrrrs   Q