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089 Gray Code.py
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089 Gray Code.py
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"""
The gray code is a binary numeral system where two successive values differ in only one bit.
Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code. A
gray code sequence must begin with 0.
For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:
00 - 0
01 - 1
11 - 3
10 - 2
Note:
For a given n, a gray code sequence is not uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence according to the above definition.
For now, the judge is able to judge based on one instance of gray code sequence. Sorry about that.
"""
__author__ = 'Danyang'
class Solution:
def grayCode(self, n):
"""
Graycode: The reflected binary code solves this problem by changing only one switch at a time, so there is never
any ambiguity of position,
Dec Gray Binary
0 000 000
1 001 001
2 011 010
3 010 011
4 110 100
5 111 101
6 101 110
7 100 111
Algorithm:
Dec Gray Binary
0 0 000
1 1 001
2 11 010
3 10 011
4 110 100
5 111 101
6 101 110
7 100 111
k-bit graycodes is the reversed sequence of (k-1)-bit graycodes appending 1 at the most significant bit
:param n:
:return: list of integers (dec_repr)
"""
if n==0:
return [0]
result = [0, 1]
for num_of_bit in range(2, n+1):
msb = 1<<num_of_bit-1
for element in reversed(result):
result.append(msb+element)
return result
def grayCode_math(self, n):
"""
a-th gray code is a>>1 XOR a
:param n:
:return: list of integers (dec_repr)
"""
return [(x>>1)^x for x in xrange(1<<n)]