o o h>@s2ddlmZddlmZGdddZddZdS) combinations)GrayCodec@seZdZdZdZdZdZdZdZddZ ddZ ddZ d d Z d d Z d dZddZddZddZddZeddZeddZeddZeddZedd Zed!d"Zed#d$Zed%d&Zed'd(Zed)d*Zed+d,Zed-d.Z ed/d0Z!dS)1Subseta Represents a basic subset object. Explanation =========== We generate subsets using essentially two techniques, binary enumeration and lexicographic enumeration. The Subset class takes two arguments, the first one describes the initial subset to consider and the second describes the superset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.next_binary().subset ['b'] >>> a.prev_binary().subset ['c'] NcCsRt|t|kr td|D] }||vrtd|qt|}||_||_|S)ax Default constructor. It takes the ``subset`` and its ``superset`` as its parameters. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.subset ['c', 'd'] >>> a.superset ['a', 'b', 'c', 'd'] >>> a.size 2 zRInvalid arguments have been provided. The superset must be larger than the subset.zFThe superset provided is invalid as it does not contain the element {})len ValueErrorformatobject__new___subset _superset)clssubsetsupersetelemobjro/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/combinatorics/subsets.pyr $s zSubset.__new__cCs&t|tstS|j|jko|j|jkS)zReturn a boolean indicating whether a == b on the basis of whether both objects are of the class Subset and if the values of the subset and superset attributes are the same. ) isinstancerNotImplementedrr)selfotherrrr__eq__Bs z Subset.__eq__cCsVt|j|j}td|d|d|j}t|dd|jd}t |j|S)a This is a helper function. It iterates over the binary subsets by ``k`` steps. This variable can be both positive or negative. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.iterate_binary(-2).subset ['d'] >>> a = Subset(['a', 'b', 'c'], ['a', 'b', 'c', 'd']) >>> a.iterate_binary(2).subset [] See Also ======== next_binary, prev_binary N0) rbitlist_from_subsetrrintjoin superset_sizebinrjustsubset_from_bitlist)rkbin_listnbitsrrriterate_binaryKszSubset.iterate_binarycC |dS)a Generates the next binary ordered subset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.next_binary().subset ['b'] >>> a = Subset(['a', 'b', 'c', 'd'], ['a', 'b', 'c', 'd']) >>> a.next_binary().subset [] See Also ======== prev_binary, iterate_binary r'rrrr next_binaryf zSubset.next_binarycCr()a Generates the previous binary ordered subset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset([], ['a', 'b', 'c', 'd']) >>> a.prev_binary().subset ['a', 'b', 'c', 'd'] >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.prev_binary().subset ['c'] See Also ======== next_binary, iterate_binary r*r+rrr prev_binary|r-zSubset.prev_binarycCs|jd}t|j|j}||vrM|d|vr||dnI|||d}|dkr<||vr<|d}|dkr<||vs0|dkrL||||dn||vra|dkra|d}||vra|dksU||dg}|j}|D] }|||qot||S)a Generates the next lexicographically ordered subset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.next_lexicographic().subset ['d'] >>> a = Subset(['d'], ['a', 'b', 'c', 'd']) >>> a.next_lexicographic().subset [] See Also ======== prev_lexicographic r)rrrsubset_indicesrrremoveappendriindicesret_set super_setrrrnext_lexicographics.     zSubset.next_lexicographiccCs|jd}t|j|j}|dkr!||vr!|d}|dkr!||vs|dks+|d|vr1||n|dkrA||||d||jdg}|j}|D] }|||qPt||S)a Generates the previous lexicographically ordered subset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset([], ['a', 'b', 'c', 'd']) >>> a.prev_lexicographic().subset ['d'] >>> a = Subset(['c','d'], ['a', 'b', 'c', 'd']) >>> a.prev_lexicographic().subset ['c'] See Also ======== next_lexicographic r)rr0r4rrrprev_lexicographics    zSubset.prev_lexicographiccCs(t|j|j||j}t|j|S)a Helper function used for prev_gray and next_gray. It performs ``k`` step overs to get the respective Gray codes. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset([1, 2, 3], [1, 2, 3, 4]) >>> a.iterate_graycode(3).subset [1, 4] >>> a.iterate_graycode(-2).subset [1, 2, 4] See Also ======== next_gray, prev_gray )runrankr rank_gray cardinalityrr"r)rr# unranked_coderrriterate_graycodes zSubset.iterate_graycodecCr()a= Generates the next Gray code ordered subset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset([1, 2, 3], [1, 2, 3, 4]) >>> a.next_gray().subset [1, 3] See Also ======== iterate_graycode, prev_gray r)r?r+rrr next_gray zSubset.next_graycCr()aJ Generates the previous Gray code ordered subset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset([2, 3, 4], [1, 2, 3, 4, 5]) >>> a.prev_gray().subset [2, 3, 4, 5] See Also ======== iterate_graycode, next_gray r.r@r+rrr prev_grayrBzSubset.prev_graycCs.|jdurtdt|j|jd|_|jS)a Computes the binary ordered rank. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset([], ['a','b','c','d']) >>> a.rank_binary 0 >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.rank_binary 3 See Also ======== iterate_binary, unrank_binary Nrr) _rank_binaryrrrrrrr+rrr rank_binary&s zSubset.rank_binarycs>|jdurfddt|j|j}||d|j|_|jS)aa Computes the lexicographic ranking of the subset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.rank_lexicographic 14 >>> a = Subset([2, 4, 5], [1, 2, 3, 4, 5, 6]) >>> a.rank_lexicographic 43 Ncs^|gks||kr dS||vr||d|||d|Sd||d|||d|S)Nrr)r)r2)r subset_indexr5r%_ranklexrrrHRs  "z+Subset.rank_lexicographic.._ranklexr) _rank_lexrr1rrr)rr6rrGrrank_lexicographicAs  zSubset.rank_lexicographiccCs4|jdurt|j|j}tt||dj|_|jS)a Computes the Gray code ranking of the subset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c','d'], ['a','b','c','d']) >>> a.rank_gray 2 >>> a = Subset([2, 4, 5], [1, 2, 3, 4, 5, 6]) >>> a.rank_gray 27 See Also ======== iterate_graycode, unrank_gray N)start)_rank_graycoderrrrrrrank)rr&rrrr<]s zSubset.rank_graycC|jS)aU Gets the subset represented by the current instance. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.subset ['c', 'd'] See Also ======== superset, size, superset_size, cardinality )r r+rrrrwz Subset.subsetcC t|jS)a4 Gets the size of the subset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.size 2 See Also ======== subset, superset, superset_size, cardinality )rrr+rrrsize z Subset.sizecCrN)aK Gets the superset of the subset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.superset ['a', 'b', 'c', 'd'] See Also ======== subset, size, superset_size, cardinality )r r+rrrrrOzSubset.supersetcCrP)a9 Returns the size of the superset. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.superset_size 4 See Also ======== subset, superset, size, cardinality )rrr+rrrrrRzSubset.superset_sizecCs d|jS)aD Returns the number of all possible subsets. Examples ======== >>> from sympy.combinatorics import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.cardinality 16 See Also ======== subset, superset, size, superset_size r)rr+rrrr=rRzSubset.cardinalitycCsRt|t|kr tdg}tt|D]}||dkr#|||qt||S)a/ Gets the subset defined by the bitlist. Examples ======== >>> from sympy.combinatorics import Subset >>> Subset.subset_from_bitlist(['a', 'b', 'c', 'd'], '0011').subset ['c', 'd'] See Also ======== bitlist_from_subset z$The sizes of the lists are not equal1)rrranger3r)rr8bitlistr7r5rrrr"s  zSubset.subset_from_bitlistcCsBdgt|}t|tr|j}t||D]}d||<qd|S)a, Gets the bitlist corresponding to a subset. Examples ======== >>> from sympy.combinatorics import Subset >>> Subset.bitlist_from_subset(['c', 'd'], ['a', 'b', 'c', 'd']) '0011' See Also ======== subset_from_bitlist rrSr)rrrrr1r)rrrrUr5rrrrs    zSubset.bitlist_from_subsetcCs(t|ddt|d}t||S)a5 Gets the binary ordered subset of the specified rank. Examples ======== >>> from sympy.combinatorics import Subset >>> Subset.unrank_binary(4, ['a', 'b', 'c', 'd']).subset ['b'] See Also ======== iterate_binary, rank_binary rNr)r r!rrr")rrMrr&rrr unrank_binary s zSubset.unrank_binarycCstt||}t||S)a{ Gets the Gray code ordered subset of the specified rank. Examples ======== >>> from sympy.combinatorics import Subset >>> Subset.unrank_gray(4, ['a', 'b', 'c']).subset ['a', 'b'] >>> Subset.unrank_gray(0, ['a', 'b', 'c']).subset [] See Also ======== iterate_graycode, rank_gray )rr;rrr")rrMrgraycode_bitlistrrr unrank_gray s zSubset.unrank_graycs`||}}t|}it|D]\}}||vr$||<|||s$nqgSfdd|DS)aReturn indices of subset in superset in a list; the list is empty if all elements of ``subset`` are not in ``superset``. Examples ======== >>> from sympy.combinatorics import Subset >>> superset = [1, 3, 2, 5, 4] >>> Subset.subset_indices([3, 2, 1], superset) [1, 2, 0] >>> Subset.subset_indices([1, 6], superset) [] >>> Subset.subset_indices([], superset) [] csg|]}|qSrr).0bidrr Ssz)Subset.subset_indices..)set enumerater2)rrrabsbr5airr[rr16s  zSubset.subset_indices)"__name__ __module__ __qualname____doc__rDrIrLr r r rr'r,r/r9r:r?rArCpropertyrErJr<rrQrrr= classmethodr"rrVrXr1rrrrrsV -(            rcCs t||S)a Finds the subsets of size ``k`` in lexicographic order. This uses the itertools generator. Examples ======== >>> from sympy.combinatorics.subsets import ksubsets >>> list(ksubsets([1, 2, 3], 2)) [(1, 2), (1, 3), (2, 3)] >>> list(ksubsets([1, 2, 3, 4, 5], 2)) [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] See Also ======== Subset r)rr#rrrksubsetsVs rjN) itertoolsrsympy.combinatorics.graycoderrrjrrrrs  T