89. Gray Code

Problem:

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.

For now, the judge is able to judge based on one instance of gray code sequence. Sorry about that.

Analysis:

We can conclude from the above image that, n can get from  n - 1. n == 1, code is 0, 1. Add 0 to front we have 00, 01. Then add 1 to front and reverse the code, we get 11, 10. Thus we have n == 2's code: 00, 01, 11, 10.

Solution:

class Solution {
    public List<Integer> grayCode(int n) {
        List<Integer> res = new ArrayList<>();
        res.add(0);
        for (int i = 0; i < n; i++) {
            int size = res.size();
            for (int j = size - 1; j >= 0; j--)
                res.add(res.get(j) | 1 << i);
        }
        return res;
    }
}