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 - 001 - 111 - 310 - 2Note: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 numbers in case n = 4. besides, [6, 7, 5, 4] = [2 +, 4, 3 +, 4, 1 +, 4 + 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 }

 

Leetcode: Gray Code