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.

Example 1:

Input: 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2

For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.

00 - 0
10 - 2
11 - 3
01 - 1

Example 2:

Input: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n = 0 the gray code sequence is [0].

 

规律：

1. 如果格雷码n位数，那么返回的数组长度是2^n（即1 << n)

2. 二进制-->格雷码：如果二进制码字的第i位和i+1位相同，则对应的格雷码的第i位为0，否则为1。最高为之前可以看作还有一位0，即最高位是和0异或。

*格雷码-->二进制：最左边一位不变，从左边第二位起，将每位与左边一位解码后的值异或，作为该位解码后的值。

class Solution {
    public List<Integer> grayCode(int n) {
        int length = 1 << n; 
        List<Integer> ret = new ArrayList<Integer>();
        ret.add(0);
        int i = 1;
        int num;
        while(i < length){
            num = i^(i>>1); //异或，相同为0，不同为1
            ret.add(num);
            i++;
        }
        return ret;
    }
}