Gray code¶
Time: O(2^N); Space: O(1); medium
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.
Example 1:
Input: n = 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2
For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.
00 - 0
10 - 2
11 - 3
01 - 1
Example 2:
Input: n = 0
Output: [0]
Explanation:
We define the gray code sequence to begin with 0.
A gray code sequence of n has size = 2^n, which for n = 0 the size is 2^0 = 1.
Therefore, for n = 0 the gray code sequence is [0].
Notes:
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.
[1]:
class Solution1(object):
def grayCode(self, n):
"""
:type n: int
:rtype: List[int]
"""
result = [0]
for i in range(n):
for n in reversed(result):
result.append(1 << i | n)
return result
[2]:
s = Solution1()
n = 0
assert s.grayCode(n) == [0]
n = 2
assert s.grayCode(n) == [0, 1, 3, 2]
Proof of closed form formula could be found here
[5]:
class Solution2(object):
def grayCode(self, n):
"""
:type n: int
:rtype: List[int]
"""
return [i >> 1 ^ i for i in range(1 << n)]
[6]:
s = Solution2()
n = 0
assert s.grayCode(n) == [0]
n = 2
assert s.grayCode(n) == [0, 1, 3, 2]