from __future__ import print_function, division
from sympy.core import Basic
from sympy.core.compatibility import range
import random
[docs]class GrayCode(Basic):
"""
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.
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
Examples
========
>>> from sympy.combinatorics.graycode 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']
"""
_skip = False
_current = 0
_rank = None
def __new__(cls, n, *args, **kw_args):
"""
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.graycode 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
"""
if n < 1 or int(n) != n:
raise ValueError(
'Gray code dimension must be a positive integer, not %i' % n)
n = int(n)
args = (n,) + args
obj = Basic.__new__(cls, *args)
if 'start' in kw_args:
obj._current = kw_args["start"]
if len(obj._current) > n:
raise ValueError('Gray code start has length %i but '
'should not be greater than %i' % (len(obj._current), n))
elif 'rank' in kw_args:
if int(kw_args["rank"]) != kw_args["rank"]:
raise ValueError('Gray code rank must be a positive integer, '
'not %i' % kw_args["rank"])
obj._rank = int(kw_args["rank"]) % obj.selections
obj._current = obj.unrank(n, obj._rank)
return obj
[docs] def next(self, delta=1):
"""
Returns the Gray code a distance ``delta`` (default = 1) from the
current value in canonical order.
Examples
========
>>> from sympy.combinatorics.graycode import GrayCode
>>> a = GrayCode(3, start='110')
>>> a.next().current
'111'
>>> a.next(-1).current
'010'
"""
return GrayCode(self.n, rank=(self.rank + delta) % self.selections)
@property
def selections(self):
"""
Returns the number of bit vectors in the Gray code.
Examples
========
>>> from sympy.combinatorics.graycode import GrayCode
>>> a = GrayCode(3)
>>> a.selections
8
"""
return 2**self.n
@property
def n(self):
"""
Returns the dimension of the Gray code.
Examples
========
>>> from sympy.combinatorics.graycode import GrayCode
>>> a = GrayCode(5)
>>> a.n
5
"""
return self.args[0]
[docs] def generate_gray(self, **hints):
"""
Generates the sequence of bit vectors of a Gray Code.
[1] Knuth, D. (2011). The Art of Computer Programming,
Vol 4, Addison Wesley
Examples
========
>>> from sympy.combinatorics.graycode 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
"""
bits = self.n
start = None
if "start" in hints:
start = hints["start"]
elif "rank" in hints:
start = GrayCode.unrank(self.n, hints["rank"])
if start is not None:
self._current = start
current = self.current
graycode_bin = gray_to_bin(current)
if len(graycode_bin) > self.n:
raise ValueError('Gray code start has length %i but should '
'not be greater than %i' % (len(graycode_bin), bits))
self._currents="sd"> more centred, do as follows:
>>> ="viewcode-block" id="GrayCode.generate_gray">s="n">current = gray_to_bin(s="n">current = gray_to_binf in namesn - namesn - nameswidth for for forcountclass ]19]19]19]19]19]19]19]for forcountclass ]19]19]19]19ValueErrortm(B, Ci">19Valuan s="p">]19]19]19[&qw="ne">ValueErrortm(B, Ci">19Valuan s="p">]19), graycode_bin) > **self. present, and 0 indicates that its absent.
present, and 0 indnen>5):
rv.append(face[r