89. 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 - 001 - 111 - 310 - 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.

思路:

0000 0

0001 1

0011 3

0010 2

0110 6

0111 7

0101 5

0100 4

可以看出，第i个值等于第2i-pow(2,count2bit(i))的值加上pow(2,count2bit(i))

代码如下(已通过leetcode)

   public List<Integer> grayCode(int n) {
    List<Integer> list=new ArrayList<Integer>();
    if(n==0) {
    list.add(0);
    return list;
    }
    list.add(0);
    list.add(1);
    int i=2;
    while(i<=n) {
    int length=list.size();
    for(int j=length-1;j>=0;j--) {
    list.add(list.get(j)+(int)Math.pow(2, i-1));
    }
    i++;
    }
    return list;
   }
}