btjdZddlZddlmZgdZedddZdZeddd Zd Z ed dd Z edddZ ed ddZ dS)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_choice@c>fdt|DS)zK Return sample sequence of length n from a power law distribution. c@g|]}dz S) paretovariate).0iexponentseeds \/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/networkx/utils/random_sequence.py z%powerlaw_sequence..s+ ? ? ?D  x!| , , ? ? ?)range)nrrs ``rrrs* @ ? ? ? ?eAhh ? ? ??rct|}t|}t|}d|z|z dkrdS|dgkrtd|DrdSdS)a$Check if a degree sequence is valid for a tree. Two conditions must be met for a degree sequence to be valid for a tree: 1. The number of nodes must be one more than the number of edges. 2. The degree sequence must be trivial or have only strictly positive node degrees. Parameters ---------- degree_sequence : iterable Iterable of node degrees. Returns ------- bool Whether the degree sequence is valid for a tree. str Reason for invalidity, or dummy string if valid. r )Fz1tree must have one more node than number of edgesrc3"K|] }|dkV dS)rN)rds r z0is_valid_tree_degree_sequence..<s&00qAF000000r)Fz8nontrivial tree must have strictly positive node degrees)T)listlensumany)degree_sequenceseqnumber_of_nodestwice_number_of_edgess rrr!su*   C#hhOHH?22a77II 00C00000PP 8rrcB|dkrtd|dkrtd|dz }d|z} d|z }|}t||d|z zz}dd|z z|z}||z|dz z|dz z ||z krni|S)awReturns 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. rzxmin < 1za <= 1.0g?r ) ValueErrorrandomint) alphaxminra1buvxts rrrAsb axx$$$ zz$$$ B 2A $++--  KKMM qcBhK'' ( ( C!G_ # q5AG C (AE 1 1   Hrchdg}d|D]}|z |fd|DS)zFReturns normalized cumulative distribution from discrete distribution.gcg|]}|z Srr)relement cumulatives rrz+cumulative_distribution..s 4 4 4WGj 4 4 4r)append) distributioncdfr7r8s @rrrsY %CJg  : 4 4 4 4 4 4 44rcddl||n&|t|ntjdfdt |D}fd|D}|S)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 missingc8g|]}Sr)r+)rrrs rrz%discrete_sequence..s!000! 000rcBg|]}|dz Sr) bisect_left)rsbisectr;s rrz%discrete_sequence..s. < < rVsE ******    @@@@@= = = = @555>          r