"""
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: 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: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n = 0 the gray code sequence is [0].
"""
from typing import List


class Solution1:
    def grayCode(self, n):
        """
        :type n: int
        :rtype: List[int]
        """
        if n < 0:
            raise ValueError
        result = [0]
        for i in range(n):
            bit = 1 << i
            for j in range(len(result) - 1, -1, -1):
                result.append(result[j] | bit)
        return result


class Solution2:
    def grayCode(self, n):
        """
        :type n: int
        :rtype: List[int]
        """
        if n < 0:
            raise ValueError
        result = []
        for i in range(1 << n):
            result.append(i ^ i >> 1)
        return result

"""
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: 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: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n = 0 the gray code sequence is [0].
"""
from typing import List


class Solution1:
    def grayCode(self, n):
        """
        :type n: int
        :rtype: List[int]
        """
        if n < 0:
            raise ValueError
        result = [0]
        for i in range(n):
            bit = 1 << i
            for j in range(len(result) - 1, -1, -1):
                result.append(result[j] | bit)
        return result


class Solution2:
    def grayCode(self, n):
        """
        :type n: int
        :rtype: List[int]
        """
        if n < 0:
            raise ValueError
        result = []
        for i in range(1 << n):
            result.append(i ^ i >> 1)
        return result

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: 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: 0 Output: [0] Explanation: We define the gray code sequence to begin with 0.              A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.              Therefore, for n = 0 the gray code sequence is [0]. :type n: int         :rtype: List[int] :type n: int         :rtype: List[int]