\h+PSSKJrJr SSKr"SS\5rSrSrSrSrS r g) )BasicIntegerNc\rSrSrSrSrSrSrSrSSjr \ S5r \ S 5r S r S r\ S 5r\ S 5r\S5rSrg)GrayCodea A Gray code is essentially a Hamiltonian walk on a n-dimensional cube with edge length of one. The vertices of the cube are represented by vectors whose values are binary. The Hamilton walk visits each vertex exactly once. The Gray code for a 3d cube is ['000','100','110','010','011','111','101', '001']. A Gray code solves the problem of sequentially generating all possible subsets of n objects in such a way that each subset is obtained from the previous one by either deleting or adding a single object. In the above example, 1 indicates that the object is present, and 0 indicates that its absent. Gray codes have applications in statistics as well when we want to compute various statistics related to subsets in an efficient manner. Examples ======== >>> from sympy.combinatorics import GrayCode >>> a = GrayCode(3) >>> list(a.generate_gray()) ['000', '001', '011', '010', '110', '111', '101', '100'] >>> a = GrayCode(4) >>> list(a.generate_gray()) ['0000', '0001', '0011', '0010', '0110', '0111', '0101', '0100', '1100', '1101', '1111', '1110', '1010', '1011', '1001', '1000'] References ========== .. [1] Nijenhuis,A. and Wilf,H.S.(1978). Combinatorial Algorithms. Academic Press. .. [2] Knuth, D. (2011). The Art of Computer Programming, Vol 4 Addison Wesley FrNcUS:d[U5U:wa[SU-5e[U5nU4U-n[R"U/UQ76nSU;aIUSUl[ UR 5U:a#[S[ UR 5U4-5eU$SU;af[US5US:wa[SUS-5e[US5UR-UlURXR5UlU$)a Default constructor. It takes a single argument ``n`` which gives the dimension of the Gray code. The starting Gray code string (``start``) or the starting ``rank`` may also be given; the default is to start at rank = 0 ('0...0'). Examples ======== >>> from sympy.combinatorics import GrayCode >>> a = GrayCode(3) >>> a GrayCode(3) >>> a.n 3 >>> a = GrayCode(3, start='100') >>> a.current '100' >>> a = GrayCode(4, rank=4) >>> a.current '0110' >>> a.rank 4 z6Gray code dimension must be a positive integer, not %istart?Gray code start has length %i but should not be greater than %irankz1Gray code rank must be a positive integer, not %i) int ValueErrorrr__new___currentlen selections_rankunrank)clsnargskw_argsobjs T/var/www/auris/envauris/lib/python3.13/site-packages/sympy/combinatorics/graycode.pyrGrayCode.__new__6s: q5CFaKH1LN N AJtd{mmC'$' g "7+CL3<< 1$ "036s||3Da2H"IJJ% w 76?#wv6 ""6?"+,,GFO,s~~=CI::a3CL c^[URURU-UR-S9$)a Returns the Gray code a distance ``delta`` (default = 1) from the current value in canonical order. Examples ======== >>> from sympy.combinatorics import GrayCode >>> a = GrayCode(3, start='110') >>> a.next().current '111' >>> a.next(-1).current '010' )r )rrr r)selfdeltas rnext GrayCode.nextfs' dii%&74??%JKKrc SUR-$)z Returns the number of bit vectors in the Gray code. Examples ======== >>> from sympy.combinatorics import GrayCode >>> a = GrayCode(3) >>> a.selections 8 )rrs rrGrayCode.selectionsxs$&&yrc URS$)z Returns the dimension of the Gray code. Examples ======== >>> from sympy.combinatorics import GrayCode >>> a = GrayCode(5) >>> a.n 5 r)rr$s rr GrayCode.nsyy|rc+Z# URnSnSU;aUSnO)SU;a#[RURUS5nUbX0lURn[ U5n[ U5UR:a[S[ U5U4-5e[US5Ul[SRU5S5n[USU-5HLnUR(aSUl OURv XwS-- nXS- - n URU - UlMN S Ulg7f) a Generates the sequence of bit vectors of a Gray Code. Examples ======== >>> from sympy.combinatorics import GrayCode >>> a = GrayCode(3) >>> list(a.generate_gray()) ['000', '001', '011', '010', '110', '111', '101', '100'] >>> list(a.generate_gray(start='011')) ['011', '010', '110', '111', '101', '100'] >>> list(a.generate_gray(rank=4)) ['110', '111', '101', '100'] See Also ======== skip References ========== .. [1] Knuth, D. (2011). The Art of Computer Programming, Vol 4, Addison Wesley Nr r r r#r Fr) rrrrcurrent gray_to_binrrr joinrange_skip) rhintsbitsr r* graycode_bin graycode_intibbtcgbtcs r generate_grayGrayCode.generate_grays8vv e 'NE u_OODFFE&M:E  !M,,"7+ | tvv %%(+L(94'@AB BGQ 277<0!4 |Q$Y/Azz" ll"QKDAI&D!]]T1DM0 sD)D+cSUlg)a Skips the bit generation. Examples ======== >>> from sympy.combinatorics import GrayCode >>> a = GrayCode(3) >>> for i in a.generate_gray(): ... if i == '010': ... a.skip() ... print(i) ... 000 001 011 010 111 101 100 See Also ======== generate_gray TN)r.r$s rskip GrayCode.skips 6 rc|URc$[[UR5S5UlUR$)a Ranks the Gray code. A ranking algorithm determines the position (or rank) of a combinatorial object among all the objects w.r.t. a given order. For example, the 4 bit binary reflected Gray code (BRGC) '0101' has a rank of 6 as it appears in the 6th position in the canonical ordering of the family of 4 bit Gray codes. Examples ======== >>> from sympy.combinatorics import GrayCode >>> a = GrayCode(3) >>> list(a.generate_gray()) ['000', '001', '011', '010', '110', '111', '101', '100'] >>> GrayCode(3, start='100').rank 7 >>> GrayCode(3, rank=7).current '100' See Also ======== unrank References ========== .. [1] https://web.archive.org/web/20200224064753/http://statweb.stanford.edu/~susan/courses/s208/node12.html r#)rr r+r*r$s rr GrayCode.ranks0F :: [6:DJzzrcUR=(d Sn[U[5(d[U5SSnUR UR S5$)z Returns the currently referenced Gray code as a bit string. Examples ======== >>> from sympy.combinatorics import GrayCode >>> GrayCode(3, start='100').current '100' 0r#N)r isinstancestrbinrjustr)rrvs rr*GrayCode.currentsC]] !c"c""RBxx$$rc ^U4SjmT"X!5$)a Unranks an n-bit sized Gray code of rank k. This method exists so that a derivative GrayCode class can define its own code of a given rank. The string here is generated in reverse order to allow for tail-call optimization. Examples ======== >>> from sympy.combinatorics import GrayCode >>> GrayCode(5, rank=3).current '00010' >>> GrayCode.unrank(5, 3) '00010' See Also ======== rank c>US:Xa[US-5$SUS- -nX:aST"XS- 5-$ST"X U-- S- US- 5-$)Nr r#r>1)r@)krm_unranks rrJ GrayCode.unrank.._unrank8s^Av1q5z!AE AuWQA...!eq!a%88 8r)rrr rJs @rrGrayCode.unrank s0 9tr)rrr.)r )__name__ __module__ __qualname____firstlineno____doc__r.rrrr propertyrrr6r9r r* classmethodr__static_attributes__rLrrrrs)V EH E.`L$    3j:$$L%%   rrcSR[U5Vs/sHn[R"S5PM sn5$s snf)z Generates a random bitlist of length n. Examples ======== >>> from sympy.combinatorics.graycode import random_bitstring >>> random_bitstring(3) # doctest: +SKIP 100 r)01)r,r-randomchoice)rr3s rrandom_bitstringrZBs2 77q:AFMM$': ;;:s Ac US/n[S[U55H$nU[[XS- X:g55- nM& SR U5$)z Convert from Gray coding to binary coding. We assume big endian encoding. Examples ======== >>> from sympy.combinatorics.graycode import gray_to_bin >>> gray_to_bin('100') '111' See Also ======== bin_to_gray rr r)r-rr@r r,bin_listbr3s rr+r+PsS$ ! A 1c(m $ SQ1uX,- ..% 771:rc US/n[S[U55H-nU[[X5[XS- 5- 5- nM/ SR U5$)z Convert from binary coding to gray coding. We assume big endian encoding. Examples ======== >>> from sympy.combinatorics.graycode import bin_to_gray >>> bin_to_gray('111') '100' See Also ======== gray_to_bin rr r)r\r]s r bin_to_grayrahsX$ ! A 1c(m $ SX[!CQ$88 99% 771:rc[U5[U5:wa [S5e[U5VVs/sHup#XS:XdMXPM snn$s snnf)a9 Gets the subset defined by the bitstring. Examples ======== >>> from sympy.combinatorics.graycode import get_subset_from_bitstring >>> get_subset_from_bitstring(['a', 'b', 'c', 'd'], '0011') ['c', 'd'] >>> get_subset_from_bitstring(['c', 'a', 'c', 'c'], '1100') ['c', 'a'] See Also ======== graycode_subsets z$The sizes of the lists are not equalrG)rr enumerate) super_set bitstringr3js rget_subset_from_bitstringrgsZ$ 9~Y'?@@%.y%9 $%9TQ|s" IL%9 $$ $s AAc## [[[U55R55Hn[ X5v M g7f)a0 Generates the subsets as enumerated by a Gray code. Examples ======== >>> from sympy.combinatorics.graycode import graycode_subsets >>> list(graycode_subsets(['a', 'b', 'c'])) [[], ['c'], ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'], ['a', 'c'], ['a']] >>> list(graycode_subsets(['a', 'b', 'c', 'c'])) [[], ['c'], ['c', 'c'], ['c'], ['b', 'c'], ['b', 'c', 'c'], ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'], ['a', 'b', 'c', 'c'], ['a', 'b', 'c'], ['a', 'c'], ['a', 'c', 'c'], ['a', 'c'], ['a']] See Also ======== get_subset_from_bitstring N)listrrr6rg) gray_code_setres rgraycode_subsetsrks5*(3}#56DDFG ' AAHsAA) sympy.corerrrXrrZr+rargrkrLrrrms4% y uy x <00$0Br