*Gray Code

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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

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