[LeetCode] Gray Code

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.

Solution: The observation is that graycode(n) is a concatenation of the following two sequences:
1. 0 + graycode(n - 1).
2. 1 + graycode(n - 1) (reverse order).  

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

public class Solution { public List<Integer> grayCode(int n) { ArrayList<Integer> list = new ArrayList<Integer>(); if (n == 0) { list.add(0); return list; } List<Integer> li = grayCode(n - 1); list.addAll(li); int m = 1 << (n - 1); for (int i = li.size() - 1; i >= 0; i--) { list.add(m + li.get(i)); } return list; } }