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.

Solution: we can solve this problem by starting from an example. Assume n=3, we have

000 - 0

001 - 1

011 - 3

010 - 2

110 - 6

111 - 7

101 - 5

100 - 4

The actual sequence of integers is,

000 - 0

001 - 1

010 - 2

011 - 3

100 - 4

101 - 5

110 - 6

111 - 7

By comparing them we find that, the highest bit does not change. Actually, there is a magic to generate the gray code.

http://en.wikipedia.org/wiki/Gray_code

Java语言: GrayCode

01 public ArrayList<Integer> grayCode(int n) {
02     ArrayList<Integer> results=new ArrayList<Integer>();
03     int totalNum=1<<n;
04     for(int i=0;i<totalNum;i++)
05     {
06         int number=i^(i>>1);
07         results.add(number);
08     }
09     return results;
10 }