9iSrSSKrSSKJr /SQr\"S5SSj5rSr\"S5SS j5rS r \"S 5SS j5r \"S5SS j5r \"S5SSj5r g)zS Utilities for generating random numbers, random sequences, and random selections. N)py_random_state)powerlaw_sequenceis_valid_tree_degree_sequencezipf_rvcumulative_distributiondiscrete_sequencerandom_weighted_sampleweighted_choicecf[U5Vs/sHo2RUS- 5PM sn$s snf)zC Return sample sequence of length n from a power law distribution. )range paretovariate)nexponentseedis ^/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/networkx/utils/random_sequence.pyrrs- 70is_valid_tree_degree_sequence..<s0CqFCs)Fz8nontrivial tree must have strictly positive node degrees)T)listlensumany)degree_sequenceseqnumber_of_nodestwice_number_of_edgess rrr!sV*  C#hOH?22a7I 0C000P r cUS:a [S5eUS::a [S5eUS- nSU-nSUR5- nUR5n[XSU- *--5nSSU- -U-nXg-US- -US- - X- ::aU$M])aReturns a random value chosen from the Zipf distribution. The return value is an integer drawn from the probability distribution .. math:: p(x)=\frac{x^{-\alpha}}{\zeta(\alpha, x_{\min})}, where $\zeta(\alpha, x_{\min})$ is the Hurwitz zeta function. Parameters ---------- alpha : float Exponent value of the distribution xmin : int Minimum value seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- x : int Random value from Zipf distribution Raises ------ ValueError: If xmin < 1 or If alpha <= 1 Notes ----- The rejection algorithm generates random values for a the power-law distribution in uniformly bounded expected time dependent on parameters. See [1]_ for details on its operation. Examples -------- >>> nx.utils.zipf_rv(alpha=2, xmin=3, seed=42) 8 References ---------- .. [1] Luc Devroye, Non-Uniform Random Variate Generation, Springer-Verlag, New York, 1986. r zxmin < 1za <= 1.0g?r ) ValueErrorrandomint) alphaxminra1buvxts rrrAsb ax$$ z$$ B 2A  $++-  KKM cBhK'' ( C!G_ # 5AG C (AE 1  H r%c|S/nSnUHnX#- nURU5 M UVs/sHo3U- PM sn$s snf)zFReturns normalized cumulative distribution from discrete distribution.g)append) distributioncdf cumulativeelements rrrsK %CJ  : 14 4Wj  44 4s9cSSKnUbUnO%Ub [U5nO[R"S5e[ U5Vs/sHocR 5PM nnUVs/sHoR XX5S- PM n nU $s snfs snf)a  Return sample sequence of length n from a given discrete distribution or discrete cumulative distribution. One of the following must be specified. distribution = histogram of values, will be normalized cdistribution = normalized discrete cumulative distribution rNz8discrete_sequence: distribution or cdistribution missingr )bisectrnx NetworkXErrorrr( bisect_left) rr4 cdistributionrr:r5rinputseqsr"s rrrs   !%l3 F  (-Qx0x! xH04< <8a  c % )8C < J 1 =s A=BcU[U5:a [S5e[5n[U5U:a+UR[ X55 [U5U:aM+[ U5$)zxReturns k items without replacement from a weighted sample. The input is a dictionary of items with weights as values. zsample larger than population)rr'setaddr r)mappingkrsamples rr r sV  3w<899 UF f+/ ?712 f+/ <r%cUR5[UR55-nUR5Hup4X$-nUS:dMUs $ g)zmReturns a single element from a weighted sample. The input is a dictionary of items with weights as values. rN)r(rvaluesitems)rDrrndrEws rr r sE ++-#gnn./ /C   7H r%)g@N)r N)NNN)N) __doc__networkxr;networkx.utilsr__all__rrrrrr r rr%rrPs *  @@@= = @5>    r%