leetcode 89 Gray Code ----- 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.

 

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;
    }