【leetcode】89. Gray Code【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, 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 - 001 - 111 - 310 - 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.

在一组数的编码中，若任意两个相邻的代码只有一位二进制数不同，则称这种编码为格雷码（Gray Code），

迭代地生成该序列。例如，当n = 3，我们可以根据n = 2时得到的结果。
00,01,11,10 -> (000,001,011,010 ) (110,111,101,100)。中间的两个数字仅在其最高位不同，剩下的部分同样，对称的数字仅最高位不同。此处我们定义进位inc = 1 << i

代码如下：

public class Solution {    public List<Integer> grayCode(int n) {        List<Integer> result = new LinkedList<>();        result.add(0);        for (int i = 0; i < n; i++){            int inc = 1 << i;            for (int j = result.size() - 1; j >= 0; j--){                result.add(result.get(j) + inc);            }        }        return result;    }}