<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> v;
        int cnt = 1 << n;
        v.reserve(cnt);
        set.clear();
        set.insert(0);
        v.push_back(0);
        find_next(0, n, cnt, v);
        return v;
    }

private:
    unordered_set<int> set;
    bool is_last(int num, int digits) {
        int ones = 0;
        for (int i = 0; i < digits; ++i) {
            if ((num & 0x01) != 0x00) ++ones;
            if (ones > 1) break;
            num = num >> 1;
        }
        return ones == 1;
    }

    //to find the next possible number
    bool find_next(int num, int digits, int cnt, vector<int>&v) {
        if (set.size() == cnt) {
            if (is_last(num, digits)) return true;
            return false;
        }
        int mask = 0x01;
        for (int i = 0; i < digits; ++i) {
            int num1 = num ^ mask;
            if (set.find(num1) == set.end()) {
                set.insert(num1);
                v.push_back(num1);
                if (find_next(num1, digits, cnt, v)) return true;
                set.erase(num1);
                v.pop_back();
            }
            mask = mask << 1;
        }
        return false;
    }
};

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