<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>

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> ans;
        vector<string> b_ver_ans;
        int size = 2;
        string str(n, '0');
        int decimal = stoi(str, nullptr, 2);
        ans.push_back(decimal);
        b_ver_ans.push_back(str);
        str[n-1] = '1';
        decimal = stoi(str, nullptr, 2);
        ans.push_back(decimal);
        b_ver_ans.push_back(str);
        
        mirror(ans, size, b_ver_ans, n-2);
        return ans;
    }
    void mirror(vector<int>& ans, int size, vector<string>& bans, int digit) {
        if (digit == -1) return;
        for (int i = size-1; i >= 0; i--) {
            string str = bans[i];
            str[digit] = '1';
            bans.push_back(str);
            int decimal = stoi(str, nullptr, 2);
            ans.push_back(decimal);
            size++;
        }
        mirror(ans, size, bans, digit-1);
    }

};
/*
inni
0000000
0000001
mirror
0000011
0000010
mirror
0000110
0000111
0000101
0000100
mirror
0001100
0001101

int decimal = std::stoi(binaryString, nullptr, 2); // 第三個參數指定基數為2
*/
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