o o hU@shdZddlZddlmZddlmZddlmZddlm Z GdddeZ d d Z d d Z d dZ dS)z The Schur number S(k) is the largest integer n for which the interval [1,n] can be partitioned into k sum-free sets.(https://mathworld.wolfram.com/SchurNumber.html) N)S)Basic)Function)Integerc@s$eZdZdZeddZddZdS) SchurNumbera\ This function creates a SchurNumber object which is evaluated for `k \le 5` otherwise only the lower bound information can be retrieved. Examples ======== >>> from sympy.combinatorics.schur_number import SchurNumber Since S(3) = 13, hence the output is a number >>> SchurNumber(3) 13 We do not know the Schur number for values greater than 5, hence only the object is returned >>> SchurNumber(6) SchurNumber(6) Now, the lower bound information can be retrieved using lower_bound() method >>> SchurNumber(6).lower_bound() 536 cCsb|jr-|tjur tjS|jrtjS|jr|jrtddddddd}|dkr/t||SdSdS) Nzk should be a positive integer ,)rrr) is_NumberrInfinityis_zeroZero is_integer is_negative ValueErrorr)clskfirst_known_schur_numbersrt/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/combinatorics/schur_number.pyeval's   zSchurNumber.evalcCsZ|jd}|dkr tdS|dkrtdS|jr%d||ddSd|ddS) Nriir rr )argsr is_Integerfunc lower_bound)selff_rrrr!4s zSchurNumber.lower_boundN)__name__ __module__ __qualname____doc__ classmethodrr!rrrrr s   rcCsX|tjur td|dkrtd|dkrd}t|Sttd|dd}t|S)NzInput must be finiterz&n must be a non-zero positive integer.r rr )rrrmathceillogr)nmin_krrr_schur_subsets_numberAs r.cCst|tr |js tdt|}|dkrdgg}n|dkr#ddgg}n|dkr-gdg}nddgddgg}t||kr`t||}ddtt||dddD}|d |7<t||ks;|S) a This function returns the partition in the minimum number of sum-free subsets according to the lower bound given by the Schur Number. Parameters ========== n: a number n is the upper limit of the range [1, n] for which we need to find and return the minimum number of free subsets according to the lower bound of schur number Returns ======= List of lists List of the minimum number of sum-free subsets Notes ===== It is possible for some n to make the partition into less subsets since the only known Schur numbers are: S(1) = 1, S(2) = 4, S(3) = 13, S(4) = 44. e.g for n = 44 the lower bound from the function above is 5 subsets but it has been proven that can be done with 4 subsets. Examples ======== For n = 1, 2, 3 the answer is the set itself >>> from sympy.combinatorics.schur_number import schur_partition >>> schur_partition(2) [[1, 2]] For n > 3, the answer is the minimum number of sum-free subsets: >>> schur_partition(5) [[3, 2], [5], [1, 4]] >>> schur_partition(8) [[3, 2], [6, 5, 8], [1, 4, 7]] zInput value must be a numberrr r )rr r rcSsg|]}d|dqSr rr.0rrrr sz#schur_partition..) isinstancerrrr.len_generate_next_listrange)r,number_of_subsetssum_free_subsetsmissed_elementsrrrschur_partitionOs /     $ r;cstg}|D]}fdd|D}fdd|D}||}||qfddtt|dD}|||}|S)Ncs g|] }|dkr|dqS)r rr1numberr,rrr2s z'_generate_next_list..cs(g|]}|ddkr|ddqSr/rr<r>rrr2(cs(g|]}d|dkrd|dqSr/rr0r>rrr2r?r)appendr7r5) current_listr,new_listitemtemp_1temp_2new_item last_listrr>rr6s  r6)r'r) sympy.corersympy.core.basicrsympy.core.functionrsympy.core.numbersrrr.r;r6rrrrs    5 D