*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 - 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.

思路：
例举grey code序列，并找规律 :

n = 0: 0
n = 1: 0, 1

n = 2: 00, 01, 11, 10  (0, 1, 3, 2)

n = 3: 000, 001, 011, 010, 110, 111, 101, 100 (0, 1, 3, 2, 6, 7, 5, 4)

以n = 3为例，grey code中前4个包括了n = 2的所有gray code。后4个则是前4个逆序后加上2^2。

推广：n = i的grey code的前一半包括了n = i-1的所有grey code，而后一半则为前一半逆序后家上2^(i-1)。

 

public class Solution {
public List<Integer> grayCode(int n) {
    List<Integer> result = new LinkedList<>();
    if(n<0) return result;
    result.add(0);
    int inc = 1;
    for (int i = 0; i < n; i++) 
    {
        int size = result.size(); 
        for(int j=size-1;j>=0;j--)
        {
            result.add(result.get(j)+inc);
        }
        inc = inc<<1;

    }
    return result;
}
}

解法二：O(n)

public class Solution {
public List<Integer> grayCode(int n) {
    List<Integer> result = new LinkedList<>();
    for (int i = 0; i < 1<<n; i++) result.add(i ^ i>>1);  //1<<n = 2^n
    return result;
}
}

reference：

http://bangbingsyb.blogspot.com/2014/11/leetcode-gray-code.html