leetCode 89.Gray Code （格雷码） 解题思路和方法

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.

此题不算难，主要是要掌握什么是格雷码。然后才干做这道题，详细格雷码概念參考百度就可以，详细解法是遍历，逐一试探就可以。

代码例如以下：

public class Solution {
    public List<Integer> grayCode(int n) {
        
        List<Integer> list = new ArrayList<Integer>();
        //去除反复
        Set<String> set = new HashSet<String>();

        //表示二进制数的数组
        char[] c = new char[n];
        Arrays.fill(c, '0');//所有为0
        set.add(new String(c));
        list.add(0);
        int i = 1;//从1開始
        //格雷码长度
        int len = (int) Math.pow(2, n);
        while(i++ < len){
        	//逐个尝试
        	for(int j = c.length - 1; j >= 0; j--){
        		c[j] = c[j] == '1' ? '0':'1';//每一位均异或
        		String b = new String(c);
        		//成功则加入结果集。并结束循环
        		if(set.add(b)){
        			//二进制转换为十进制
        			list.add(Integer.valueOf(b, 2));
        			break;
        		}else{
        			//假设不是则数值变换回来
        			c[j] = c[j] == '1' ? '0':'1';
        		}
        	}
        }
        return list;
    }
}