<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<string> fun(int n)
    {
        if(n == 1)
        {
            return {"00","01"};
        }
        if(n == 2)
        {
            return {"00","01","11","10"};
        }
       // cout<<"fun"<<n<<" "<<endl;
        vector<string> arr = fun(n-1);
        vector<string> newArr;
        int sz = 1;
        for(int i=0;i<arr.size();i++)
        {
            newArr.push_back(arr[i]);
        }
        sz = arr[arr.size()-1].length()+1;
        for(int i=arr.size()-1;i>=0;i--)
        {
            string s = arr[i];
            if(s.length()+1 != sz)
            {
                while(s.length()+1 != sz)
                {
                    s.insert(s.begin(),'0');
                }
            }
            s.insert(s.begin(),'1');
            newArr.push_back(s);
        }
        return newArr;
    }
    vector<int> grayCode(int n) {
        vector<string> res = fun(n);
        vector<int> ans;
        for(int i=0;i<res.size();i++)
        {
            string s = res[i];
          //  cout<<s<<" ";
            int index = 0;
            int num = 0;
            for(int j=s.length()-1;j>=0;j--)
            {
                num+=(pow(2,index))*(s[j]-'0');
                index++;
            }
            ans.push_back(num);
        }
      //  cout<<endl;
        return ans;
    }
};
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