Leetcode: 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.

Analysis:

Try one more example, n = 3:

000 - 0

001 - 1

011 - 3

010 - 2

110 - 6

111 - 7

101 - 5

100 - 4 

Comparing n = 2: [0,1,3,2] and n=3: [0,1,3,2,6,7,5,4], we found that the first four numbers in case n=3 are the same as the the numbers in case n=4.  Besides, [6,7,5,4] = [2+4,3+4,1+4,0+4].  Which means remaining numbers in case n=3 can also be calculated from the numbers in case n=4 in reversing order.  Therefore, we decided to use recursive approach to form the resulting ArrayList.

 1 public class Solution {

 2     public ArrayList<Integer> grayCode(int n) {

 3         ArrayList<Integer> res = new ArrayList<Integer>();

 4         if(n == 0) {

 5             res.add(0);

 6         }

 7         else {

 8             ArrayList<Integer> pre = grayCode(n-1);

 9             res.addAll(pre);

10             for (int i=pre.size()-1; i>=0; i--) {

11                 res.add(pre.get(i) + (int)Math.pow(2, n-1));

12             }

13         }

14         return res;

15     }

16 }

 另一种不同的书写风格：

 1 public class Solution {

 2     public List<Integer> grayCode(int n) {

 3         ArrayList<Integer> res = new ArrayList<Integer>();

 4         if (n < 0) return res;

 5         helper(res, n);

 6         return res;

 7     }

 8     

 9     public void helper(ArrayList<Integer> res, int n) {

10         if (n == 0) {

11             res.add(0);

12             return;

13         }

14         helper(res, n-1);

15         for (int i=res.size()-1; i>=0; i--) {

16             res.add(res.get(i)+(int)Math.pow(2, n-1));

17         }

18     }

19 }

 这些代码都要注意一个细节，即input为0时，output为[0]，并不是[]