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.

 

求二进制格雷码

 

两种方法:

1、递归方法:

public class Solution {
    public List<Integer> grayCode(int n) {
        List result = new ArrayList<Integer>();
        if( n == 0){
            result.add(0);
            return result;
        }else if ( n == 1){
            result.add(0);
            result.add(1);
            return result;
        }else     
            result.addAll(grayCode(n-1));
        int max = 1;
        for( int i = 1;i<n;i++){
            max*=2;
        }
        int size = result.size();
        for( int i = 1;i<=size;i++){
            result.add((int)result.get(max-i)+max);
        }        
        return result;
    }
}

2、位运算。

public List<Integer> grayCode(int n) {
        List<Integer> ret = new ArrayList<>();
        ret.add(0);
        for (int i = 1, shift = 1; i <= n; i++) {
            // mirror from previous 2 ^ (i-1) 
            for (int j = shift-1; j >= 0; j--) {
                // ret.get(j) ^ shift is more efficient here that +
                ret.add((ret.get(j) ^ shift));
            }
            shift <<= 1;
        }
        
        return ret;
    }