<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:

    int count(int x)
    {
        int ans = 0;
        while(x) {
         if(x&1)ans++;
         x >>= 1;   
        }

        return ans;
    }

    bool solve(vector<int>& visit, vector<int>& ans, int l, int n, int ind)
    {
       // cout << l << endl;
        int p = pow(2, n);
        if(ind == p){
            if(count((l^0)) == 1) {
                return true;
            }
            return false;
        }

        for(int i = 0; i < p; i++) {
            int b = l&(1<<i);
            int new_num;
            if(b == 0) new_num = l | (1<<i);
            else if(b != 0) new_num = l ^ (1<<i);

            if(visit[new_num] == -1) {
                visit[new_num] = 1;
                ans[ind] = new_num;
                if(solve(visit, ans, new_num, n, ind + 1)) return true;
                visit[new_num] = -1;

            }
        }

        return false;
    }
    vector<int> grayCode(int n) {

        int tot = pow(2, n);

        vector<int> dp(tot, -1);
        vector<int> ans(tot, 0);
        ans[0] = 0;

        dp[0] = 0;
        solve(dp, ans, 0, n, 1);

        return ans;
        
    }
};
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