【Leetcode】Gray Code

题目链接：https://leetcode.com/problems/gray-code/

题目：

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.

思路：

1. 1位格雷码有两个码字
2. (n+1)位格雷码中的前2 n个码字等于n位格雷码的码字，按顺序书写，加前缀0
3. (n+1)位格雷码中的后2 n个码字等于n位格雷码的码字，按逆序书写，加前缀1

算法：

public List<Integer> grayCode(int n) {
		if (n == 0) {
			List<Integer> tmp = new ArrayList<Integer>();
			tmp.add(0);
			return tmp;
		}
		List<Integer> l1 = grayCode(n - 1);
		int addNum = 1 << (n - 1);// 将1左移n-1位
		List<Integer> l2 = new ArrayList<Integer>(l1);
		for (int i = l1.size() - 1; i >= 0; i--) {
			l2.add(addNum + l1.get(i));
		}
		return l2;
	}