o 3ήc; @sddlZddlZedZddlZddlmZmZej gdgdgdgdgdgd gd gd gd g e d Z ddZ ddZ gdZgdZgdZgdZgdZgdZddZdVddZdVddZd d!Zd"d#Zd$d%Zd&d'Zd(d)Zd*d+Zd,d-Zd.d/Zd0d1Zd2d3Z d4d5Z!d6d7Z"d8d9Z#d:d;Z$dd?Z&d@dAZ'dBdCZ(dDdEZ)dFdGZ*dHdIZ+dJdKZ,dLdMZ-dNdOZ.dPdQZ/dRdSZ0dTdUZ1dS)WNnumpy) branchings recognition) rr rrrrrr) rrrr rrr) rrrrrrr) rrrrrrr) rrrrrrrrr) rrrrrrrr) rrr rrrrr) rrrrrr rr) rrrrrrrr r)dtypecCstjttjd}|S)N create_using)nxfrom_numpy_arrayG_array MultiDiGraphGrU/tmp/pip-target-vg8gfxp4/lib/python/networkx/algorithms/tree/tests/test_branchings.pyG1"srcCs2t}|t|d8<tj|tjd}|S)N r)rcopynpnonzerorrr)GarrrrrrG2'sr )rrr"rr"r r$r rr&rr)r&r r)r r+r ))r r)rr)r" r)r+r r+r-r+r"r$r-r"r&r/r&rr-)r1)r-r& r4r&r)r+r.r2r$r r&))rr"r"r2r3r7r4r6r0r1)r r)r r)r"r r*r,r#r%r&rr r()r,r-r)r r9r#r%r'r:r(cCs,t}|D] \}}}|j|||dq|S)Nweight)rDiGraphadd_edge)edgesruvr=rrrbuild_branching}srCr=r$cs0fdd|jddD}t|ddd}|S)Ncs$g|]\}}}|||fqSr)get).0rArBdataattrdefaultrr s$z sorted_edges..TrFcSs|d|d|dfS)Nr"r$rr)xrrrszsorted_edges..)key)r@sorted)rrHrIr@rrGr sorted_edgessrPc Cst|jdd}t|jdd}t|t|ksJt|||}t|||}t||D]\}} |dd| ddks=Jtj|d| dq+dS)NTrKr")listr@lenrPziprtestingassert_almost_equal) rr rHrIedges1edges2e1e2abrrrassert_equal_branchingss  r\cC0tt}t|s Jdt|dksJdS)NT)rCoptimal_arborescence_1ris_arborescencerbranching_weightrrrrtest_optimal_branching1rbcCr]NT5)rCoptimal_branching_2arr`rrarrrrtest_optimal_branching2arcrgcCr]rd)rCoptimal_branching_2brr`rrarrrrtest_optimal_branching2brcricCr])NT3)rCoptimal_arborescence_2rr`rrarrrrtest_optimal_arborescence2rcrlcCr])NT)rCgreedy_subopt_branching_1arr`rrarrrr"test_greedy_suboptimal_branching1arcrocCr])NT)rCgreedy_subopt_branching_1brr`rrarrrr"test_greedy_suboptimal_branching1brcrrcC&t}t|}tt}t||dSN)rrgreedy_branchingrCrqr\)rBB_rrrtest_greedy_max1s rxcCsDt}|dddd=tj|dd}gd}t|}t||dS)Nr$rr=r)rI))r$rr)r'r;r#r(r,r%r9rrrurCr\rrvr@rwrrrtest_greedy_max2s  r|cCs6t}tj|dd}gd}t|}t||dddS)N)rH))r"r$r$)r&rr$)r&rr$)r r+r$)r)r"r$)r-r&r$)r-r)r$)r+r-r$r$ryrzr{rrrtest_greedy_max3s  r}cCs2t}tj|dd}gd}t|}t||dS)Nmin)kind)r$rrr!rrrr"r rrr-rr r+rr8)r-r&rrzr{rrrtest_greedy_mins  rcCrsrt)rrmaximum_branchingrCr_r\rrLx_rrrtest_edmonds1_maxbranch rcCrsrt)rrmaximum_spanning_arborescencerCr_r\rrrrtest_edmonds1_maxarborrrcCrsrt)r rrrCrfr\rrrrtest_edmonds2_maxbranchrrcCrsrt)r rrrCrkr\rrrrtest_edmonds2_maxarborrrcCs.t}t|}gd}t|}t||dS)N)r:r!rrrrr8r#)rrminimum_spanning_arborescencerCr\rrLr@rrrrtest_edmonds2_minarbor#s   rcCs*t}t|}g}t|}t||dSrt)rrminimum_branchingrCr\rrrrtest_edmonds3_minbranch16s  rcCs<t}|jddddt|}dg}t|}t||dS)Nr+r5r<)r+r5r)rr?rrrCr\rrrrtest_edmonds3_minbranch2>s  rc Cst}dddgfdddgfdddgfdddgfdd dgfdd d gfdd d gfdd dgfd d dgfd d dgfd d dgfg }|||}t|}ddhdfddhd fdd hd fdd hdfd dhd fd d hdfg}|t|ksuJ|jddD]\}}}||h|df|vsJq{dS)Nrr&r=r r$)r=r-)r=r5r")r=r+r)r=r r r=r)r))r=r/r-r5TrKr=) rGraphadd_edges_from to_directedrrnumber_of_edgesrRr@)redgelistrLr@rArBdrrrtest_mstJs6                    rcCs@t}dddgfdddgfg}|||}t|}dS)Nrr&r1)rrrrrr)rrrLrrrtest_mixed_nodetypesms  rcCs\ddtD}tjt tjd}t|}tg}t||t |}t|}t||dS)NcSsg|] \}}}||| fqSrr)rErArBwrrrrJysz+test_edmonds1_minbranch..r) r_rrrr>rrrCr\r)r@rrLrrrrtest_edmonds1_minbranchvs   rcCst}ddgdfddgdfddgdfg}||t|}|jdddd }|ddd dks6J|ddd d ksBJdS) Nrr$r) otherattrr$) otherattr2r&r"r)rr")rr"r)rr&)rr$r=T)preserve_attrsseedrrr&)rrrrEdmonds find_optimumrredrvrrr-test_edge_attribute_preservation_normal_graphs     rcCst}ddgdfddgdfddgdfg}||dt|}|jddd }|dddd dks9J|dddd d ksGJdS) Nrr$rr"rrr=Trrrr&)r MultiGraphrrrrrrrr+test_edge_attribute_preservation_multigraphs     rcCst}ddgdfddgdfddgdfg}||t|}|jddd }|dd}tt |d }WddS1sDwYdS) Nrr$rr"rrr=Frr) rrrrrrpytestraisesKeyError)rrrrv edge_dict_rrrtest_edge_attribute_discards        "rcCstjttjd}tjj|ddd<tjj|ddd<tjj|ddd<tjj|ddd<tjj|ddd<gd}tj|dd }t t ||d S) zi Test that we can generate minimum spanning arborescences which respect the given partition. rr&r partitionr"r-r))rrr'r%rr8rr9)rN) rrrr> EdgePartitionEXCLUDEDINCLUDEDrrr\rC)r actual_edgesrvrrr$test_partition_spanning_arborescences rcCs`tjttjd}d}tj }t|D]}|d7}|jdd}||ks%J|}q|dks.JdS)a Tests the arborescence iterator. A brute force method found 680 arboresecences in this graph. This test will not verify all of them individually, but will check two things * The iterator returns 680 arboresecences * The weight of the arborescences is non-strictly increasing for more information please visit https://mjschwenne.github.io/2021/06/10/implementing-the-iterators.html rrr$r=r<N rrrr>mathinfrArborescenceIteratorsizerarborescence_countarborescence_weightrvnew_arborescence_weightrrrtest_arborescence_iterator_mins  rcCsbtjttjd}d}tj}tj|ddD]}|d7}|jdd}||ks&J|}q|dks/Jd S) a Tests the arborescence iterator. A brute force method found 680 arboresecences in this graph. This test will not verify all of them individually, but will check two things * The iterator returns 680 arboresecences * The weight of the arborescences is non-strictly decreasing for more information please visit https://mjschwenne.github.io/2021/06/10/implementing-the-iterators.html rrF)minimumr$r=r<rNrrrrrtest_arborescence_iterator_maxs  rcCstjttjd}gd}gd}d}tj }tj|||fdD],}|d7}|jdd}||ks1J|}|D] }||j vs>Jq5|D] }||j vsJJqAq|d ksRJd S) a$ Tests the arborescence iterator with three included edges and three excluded in the initial partition. A brute force method similar to the one used in the above tests found that there are 16 arborescences which contain the included edges and not the excluded edges. r))r$r)r r))r+r-))rr")r&r))r$r r)init_partitionr$r=r<N) rrrr>rrrrrr@)rincluded_edgesexcluded_edgesrrrvrerrr,test_arborescence_iterator_initial_partitions$    r)r=r$)2rr importorskiprnetworkxrnetworkx.algorithms.treerrarrayintrrr r_rfrhrkrnrqrCrPr\rbrgrirlrorrrxr|r}rrrrrrrrrrrrrrrrrrrrrrsp            #