<p>An <strong>n-bit gray code sequence</strong> is a sequence of <code>2<sup>n</sup></code> integers where:</p>

<ul>
	<li>Every integer is in the <strong>inclusive</strong> range <code>[0, 2<sup>n</sup> - 1]</code>,</li>
	<li>The first integer is <code>0</code>,</li>
	<li>An integer appears <strong>no more than once</strong> in the sequence,</li>
	<li>The binary representation of every pair of <strong>adjacent</strong> integers differs by <strong>exactly one bit</strong>, and</li>
	<li>The binary representation of the <strong>first</strong> and <strong>last</strong> integers differs by <strong>exactly one bit</strong>.</li>
</ul>

<p>Given an integer <code>n</code>, return <em>any valid <strong>n-bit gray code sequence</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> [0,1,3,2]
<strong>Explanation:</strong>
The binary representation of [0,1,3,2] is [00,01,11,10].
- 0<u>0</u> and 0<u>1</u> differ by one bit
- <u>0</u>1 and <u>1</u>1 differ by one bit
- 1<u>1</u> and 1<u>0</u> differ by one bit
- <u>1</u>0 and <u>0</u>0 differ by one bit
[0,2,3,1] is also a valid gray code sequence, whose binary representation is [00,10,11,01].
- <u>0</u>0 and <u>1</u>0 differ by one bit
- 1<u>0</u> and 1<u>1</u> differ by one bit
- <u>1</u>1 and <u>0</u>1 differ by one bit
- 0<u>1</u> and 0<u>0</u> differ by one bit
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [0,1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 16</code></li>
</ul>

import math

log = math.log


class Solution(object):
    def grayCode(self, n):
        """
        :type n: int
        :rtype: List[int]
        """

        # [[0]]
        # [[1]]
        #

        bnums = [[0], [1]]

        if n != 1:
            for i in range(n - 1):
                for j in range(len(bnums) - 1, -1, -1):
                    bnums.append(bnums[j].copy())
                for j in range(int(len(bnums) / 2)):
                    bnums[j].insert(0, 0)
                for j in range(int(len(bnums) / 2), len(bnums)):
                    bnums[j].insert(0, 1)

        for i in range(len(bnums)):
            dnum = 0
            for b in range(n):
                if bnums[i][b]:
                    dnum += pow(2, b)
            bnums[i] = dnum

        # print(bnums)
        return bnums


# 0,0
#   ^
# 0,1
# ^
# 1,1
#   ^
# 1,0
# ^
#

32600