<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:
#define rep(n) FOR(i, 0, n)
#define pb push_back
// Function to convert binary string to decimal
    int bd(string& binaryStr) {
        int decimalValue = 0;
        int length = binaryStr.length();

        for (int i = 0; i < length; ++i) {
            if (binaryStr[length - i - 1] == '1') {
                decimalValue += pow(2, i);
            }
        }

        return decimalValue;
    }

    int c;
    vector<string> ans;
    void rec(int level,vector<string>& s) {
        // base case
        if (level == c - 2) {
            for (int i = 0; i < s.size(); ++i) {
                ans.push_back("0" + s[i]);
            }
            for (int i = s.size() - 1; i >= 0; --i) {
                ans.push_back("1" + s[i]);
            }
            return;
        }

        // Compute and transition
        vector<string> temp = s;
        for (int i = 0; i < s.size(); ++i) {
            s[i] = "0" + s[i];
        }
        for (int i = temp.size() - 1; i >= 0; --i) {
            s.push_back("1" + temp[i]);
        }

        rec(level + 1, s);
    }

    vector<int> grayCode(int n) {
        vector<string> s = {"0", "1"};

        if (n == 1) {
            return {0, 1};
        }

        c = n;
        rec(0, s);
        vector<int> v;
        for (int i = 0; i < ans.size(); ++i) {
            v.push_back(bd(ans[i]));
        }
        return v;
    }
};
35666