【leetcode】Gray Code

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题目：

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.

这是一道非常有意思的题。初看无下手之处，不过列举出前几项就很容易看出规律啦：

n = 1时：

0 （0）

1 （1）

n = 2时：

00 (0)

01 (1)

11 (3)

10 (2)

n = 3时：

000 (0)

001 (1)

011 (3)

010 (2)

110 (6)

111 (7)

101 (5)

100 (4)

可看出n每增加一位，结果数量翻倍，且前一半和n-1的结果是一样的，而后一半其实就是前半部分的镜像对称，再在最高位加上1.

所以完全可以用递归，通过n-1得到n的结果。代码如下：

public List<Integer> grayCode(int n) {
		 List<Integer> result = new ArrayList<Integer>();
		 if(n<=1) {
			 for(int i =0; i<=n; i++) {
				 result.add(i);
			 }
			 return result;
		 }
		 result = grayCode(n-1);
		 List<Integer> r1 = reverse(result);
		 int x = 1<<(n-1);
		 for(int i = 0; i< r1.size(); i++) {
			 r1.set(i, r1.get(i)+x);
		 }
		 result.addAll(r1);
		 return result;
	 }
	 
	 public List<Integer> reverse(ArrayList<Integer> r) {
		List<Integer> result = new ArrayList<Integer>();
		for(int i = r.size()-1; i>=0; i--) {
			result.add(r.get(i));
		}
		return result;
	 }

【leetcode】Gray Code

标签：style   blog   color   io   os   java   ar   for   2014   

原文地址：http://blog.csdn.net/he_wolf/article/details/39268455