Gray_Code.cpp

// 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:
// For a given n, a gray code sequence is not uniquely defined.
// For example, [0,2,3,1] is also a valid gray code sequence according to the above definition.

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> result;
        result.push_back(0);
        if (n == 0)
            return result;
        if (n == 1) {
            result.push_back(1);    
            return result;
        }
        result = grayCode(n-1);
        int high = 1 << (n-1);  // add up the first bit
        for (int i = result.size()-1; i >= 0; i--) {
            result.push_back(high | result[i]);
        }
        return result;
    }
};