LeetCode 63 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 -> 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.

分析：

一开始没有思路，就从最简单的情况考虑：

1位：0,1

2位：00,01,11,10

3位：000,001,011,010,110,111,101,100

规律就是：每多1位，就是在原来基础上加上高位是0，高位是1的两种情况就可以。

这本身跟顺序没有关系，但由于leetcode序列化的限制，所以加高位的时候要在原来结果中从后往前遍历。

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

这道题教会我的是，没有思路的就从最简单的情况入手。