89. Gray Code

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.

Solution:

We can find the pattern of Gray code:

n = 0
0

n = 1
0 1

n = 2
00 01 11 10

n = 3
000 001 011 010 110 111 101 100

We can find the first half of Gray code with n, are the Gray code with n - 1.

The second half of Gray code with n, are the reverse order of the Gray code with n - 1, plus 2^{^}(n - 1).



Code:

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