Gray Code

LeetCode 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.

本题以格雷码为引子，有两种解法，一种是寻找格雷码变化规律，然后模拟变化过程，得出结果；另一种是用异或。

方法一：模拟

例如当n=2时，格雷码如下：

00

01

11

10

 

当n=3时，格雷码

000

001

011

010

110

111

101

100

由以上可以看到规律：n的格雷码由n-1格雷码推导出来。在n-1格雷码左边加个0，以及在n-1的格雷码最左边加个1，然后把n-1个格雷码逆序。时间复杂度O(n^2)

根据以上规律写出代码

vector<int> grayCode(int n) 
{
	vector<int> res;

	res.push_back(0); 
	//从0--n逐个添加到res中
	for (int i = 0; i < n; i++)
	{
		//左移一位，相当于h = 2^i，也就是格雷码的	1*******，因为0******已经保存在res中了
		int h = 1 << i;
		int len = res.size();
		//逆序添加，根据以往保存在res中的数据再加上1******就是要添加的
		for (int j = len-1; j >= 0; j--)
		{
			res.push_back(h + res[j]);
		}
	}

	return res;
}

方法二、

运用格雷码和二进制的转换，参考

http://www.cnblogs.com/lihaozy/archive/2012/12/31/2840437.html

http://blog.youkuaiyun.com/tingmei/article/details/8045054

时间效率高。