grayCode

/*

The gray code is a binary numeral system where two successive values differ in only one bit.

Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code. 
A gray code sequence must begin with 0.

For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:

00 - 0
01 - 1
11 - 3
10 - 2

Note: 
Given n=3, the gray code sequence is:
000
001
011
010
110
111
101
100
Thus, the sequence of n=k, say S(k) is S(k-1)+ reverse of S(k-1) with 1 on highest bit

*/

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> out;
        out.push_back(0);
        for (int i=0; i<n; i++) {
            int x = 1 << i;
            for (int j=out.size()-1; j>=0; j--) {
                out.push_back(out[j] + x);
            }
        }
        return out;
    }
};