89. Gray Code Leetcode Java

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.

Solution:

It is not hard to find the pattern of the gray code, gray[0]={0}, gray[1]=[0,1],gray[2]=[0"+"gray[1],1"+"gray[1].reverse()]=[00,01,11,10], gray[3]=[000,001,011,010; 110,111,101,100]. Here "+" kinda means concatenate eg. 1"+" 111= 1111. 0 "+" x= x, while 1 "+" x = 1*2^n +x, here n is the number of bits of the number. So the idea to get gray[n] is to reverse all gray[n-1] and add each number with 2^n, which is also the length of gray[n-1] and add the summation to the list of gray[n-1] one by one and the resulted list will be gray[n].
Time complexity: O(2^n) because the size of the result list will be expanded at exponential level. 

 public List<Integer> grayCode(int n) {  
    List<Integer> res=new ArrayList<Integer>();  
    if(n<0) return res;  
    res.add(0);    
    for(int i=1;i<=n;i++){  
      int l=res.size();  
      for(int j=l-1;j>=0;j--){  
        res.add(res.get(j)+l);  
      }   
    }  
    return res;  
   }