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.
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
Input: 0 Output: [0] Explanation: We define the gray code sequence to begin with 0. A gray code sequence of n has size = 2^n^, which for n = 0 the size is 2^0^ = 1. Therefore, for n = 0 the gray code sequence is [0].
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设 n 阶格雷码集合为 G(n)，则 G(n+1) 阶格雷码为：
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给 G(n) 阶格雷码每个元素二进制形式前面添加 0，得到 G'(n) ；
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设 G(n) 集合倒序（镜像）为 R(n)，给 R(n) 每个元素二进制形式前面添加 1，得到 R'(n)；
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G(n+1) = G'(n) ∪ R'(n) 拼接两个集合即可得到下一阶格雷码。
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根据以上规律，可从 0 阶格雷码推导致任何阶格雷码。
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代码解析：
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由于最高位前默认为 00，因此 G'(n) = G(n)，只需在 res(即 G(n) )后添加 R'(n)即可；
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计算 R'(n)：执行
head = 1 << i计算出对应位数，以给 R(n) 前添加 1 得到对应 R'(n)； -
倒序遍历 res(即 G(n) )：依次求得 R'(n) 各元素添加至 res 尾端，遍历完成后 res(即 G(n+1))。
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这个题的解法跟 338. Counting Bits 有异曲同工之妙！
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].
link:{sourcedir}/_0089_GrayCode.java[role=include]