ܛ7idZddlZddlmZgdZedddZdZeddd Zd Z ed dd Z eddd Z edddZ y)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_choicecbt|Dcgc]}|j|dz c}Scc}w)zK Return sample sequence of length n from a power law distribution. )range paretovariate)nexponentseedis [/home/rose/Desktop/poly/venv/lib/python3.12/site-packages/networkx/utils/random_sequence.pyrrs/ 7z0is_valid_tree_degree_sequence..<s0CqAFCs)Fz8nontrivial tree must have strictly positive node degrees)T)listlensumany)degree_sequenceseqnumber_of_nodestwice_number_of_edgess rrr!sS*  C#hOH?22a7I 0C00P r c|dkr td|dkr td|dz }d|z} d|jz }|j}t||d|z zz}dd|z z|z}||z|dz z|dz z ||z kr |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. r zxmin < 1za <= 1.0g?r ) ValueErrorrandomint) alphaxminra1buvxts rrrAsb ax$$ z$$ B 2A  $++-  KKM qcBhK'' ( C!G_ # q5AG C (AE 1  H r$cvdg}d}|D]}||z }|j||Dcgc]}||z  c}Scc}w)zFReturns normalized cumulative distribution from discrete distribution.g)append) distributioncdf cumulativeelements rrrsO %CJg  : 14 4WGj  44 4s 6cddl}||}n#| t|}ntjdt |Dcgc]}|j }}|Dcgc]}|j ||dz } }| Scc}wcc}w)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) rr3 cdistributionrr9r4rinputseqsr!s rrrs   !%l3 F  (-Qx0x! xH04< <8a6  c1 % )8C < J 1 =s A7A<c|t|kDr tdt}t||kr*|jt ||t||kr*t |S)zReturns 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 sX  3w<899 UF f+/ ?7D12 f+/ <r$c|jt|jz}|jD]\}}||z}|dks|cSy)zuReturns a single element from a weighted sample. The input is a dictionary of items with weights as values. rN)r'rvaluesitems)rCrrndrDws rr r sI ++-#gnn./ /C 1 q 7H r$)g@N)r N)NNN)N) __doc__networkxr:networkx.utilsr__all__rrrrrr r rr$rrOs *  @@@= = @5>    r$