LeetCode-Gray Code

Description：
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].

题意：给定一个非负整数代表二进制的位数，求所有满足其位数长度的​​格雷码​​，如图所示，为0-15（二进制长度为4）的格雷码，每相邻的两个格雷码仅有一个位置不相同；

解法：参照wikipadia里面的描述，我们定义如下

• $b_i$为非负整数的二进制表示（i=0,1,…）
• $g_i$为$b_i$所对应的格雷码表示(i=0,1,…)
• $b_0=g_0, b_i=g_i \bigoplus b_{i-1}$

因此，我们可以得到格雷码（根据二进制编码）：
$g_0=b_0 \\ g_i=g_i \bigoplus b_{i-1} \bigoplus b_{i-1}=b_i \bigoplus b_{i-1}$

Java

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