格雷码

题目描述

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

题目解答

gray code中文名叫格雷码，写几个例子出来找规律。
以3位格雷码为例。
0 0 0
0 0 1
0 1 1
0 1 0
1 1 0
1 1 1
1 0 1
1 0 0
可以看到第n位的格雷码由两部分构成，一部分是n-1位格雷码，再加上 1<<(n-1)和n-1位格雷码的逆序的和。

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