格雷码生成【grey 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.

解题思路

　　递归生成码表
　　这种方法基于格雷码是反射码的事实，利用递归的如下规则来构造：
　　1位格雷码有两个码字
　　(n+1)位格雷码中的前2n个码字等于n位格雷码的码字，按顺序书写，加前缀0
　　(n+1)位格雷码中的后2n个码字等于n位格雷码的码字，按逆序书写，加前缀1

代码实现

package algorithms;

import java.util.LinkedList;
import java.util.List;

public class Solution {
    public static List<Integer> grayCode(int n) {
    	List<Integer> result = new LinkedList<Integer>();
    	result.add(0);
    	int t = 1;
    	for(int i = 0; i < n; i++) {
    		for(int j = result.size() - 1; j >= 0; j--) {
    			result.add(result.get(j) ^ t);
    		}
    		t <<= 1;
    	}
    	return result;
    }
    public static void main(String[] args) {
		System.out.println((grayCode(3).toString()));
	}
}

要点

利用位异或操作；

从低位到高位递归进行；