[leetcode]Gray Code

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.

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.

这道题木有思路主要是因为不了解什么叫格雷码。

算法思路：

思路1：

格雷码公式法：gray = (binary) xor (binary >> 1)

代码

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

思路2：

不知道公式也没关系，只要弄明白格雷码的定义就好了，递归实现法也不难

代码如下：

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