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.

Example 1:

Input: 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2

For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.

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

Example 2:

Input: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n = 0 the gray code sequence is [0].

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

每加一位都是在上一位基础上给首位补1，且呈对称状（中间两个数只差了首位0和1，然后向右）