98. 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.

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分析：在纸上多写几个找到规律之后再下手写代码就容易。

 给定位数，求其对应的格雷码。
* 如n=3
* 00 - 0
* 01 - 1
* 11 - 3
* 10 - 2
* 110 - 6
* 111 - 7
* 101 - 5
* 100 - 4
* 相比较于n=2时，n=3时相等于在n=2时的四个数字前分别加上0和对称地四个数字前分别加上1得到了其对应的八个数字。
* 所以，对应于已知i-1位的格雷码，就可以推出i位的格雷码。

/**
	 * 给定位数，求其对应的格雷码。
	 * 如n=3
	 * 00 - 0
	 * 01 - 1
	 * 11 - 3
	 * 10 - 2
	 * 110 - 6
	 * 111 - 7
	 * 101 - 5
	 * 100 - 4
	 * 相比较于n=2时，n=3时相等于在n=2时的四个数字前分别加上0和对称地四个数字前分别加上1得到了其对应的八个数字。
	 * 所以，对应于已知i-1位的格雷码，就可以推出i位的格雷码。
	 *  
	 */
	public List<Integer> grayCode(int n) {
		ArrayList<Integer> list = new ArrayList<Integer>();
		if(n<0){
			return list;
		}
		list.add(0);//n=0时默认为一个格雷码
		/*已知i-1位的格雷码，就可以推出i位的格雷码。*/
		for(int i =1;i<=n;i++){
			int size = list.size();//先得到i-1位时的格雷码种类数
			int num = (int) Math.pow(2, i-1);
			for(int j=size-1;j>=0;j--){
				list.add(list.get(j)+num);
			}
		}
		
        return list;
    }