GrayCode.java

/*
 * 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, find the sequence of gray code.
A gray code sequence must begin with 0 and with cover all 
2n integers.

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.

[0,2,3,1] is also a valid gray code sequence according to 
the above definition.

Challenge
O(2n) time.
 */
public class GrayCode {

    /**
     * @param n a number
     * @return Gray code
     */
    public ArrayList<Integer> grayCode(int n) {
        ArrayList<Integer> result = new ArrayList<Integer>();
        for (int i = 0; i < (1 << n); ++i) {
            result.add(i ^ (i >> 1));
        }
        return result;
    }

}