【LeetCode】89.Gary Code

Problem：

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

Solution:

理解格雷码和二进制的转换关系这题就很简单了。

格雷码的特点在于相邻两个数字仅有一位不同。题中给出的示例是【00,01,11,10】，原题提示中也说到格雷码的顺序可能不止一种，如【00,10,11,01】亦可，只需满足相邻两数只有一位不同这一条件。

按题示序列规则，对二进制数进行右移运算和异或运算可以得出相应格雷码，如：

// i ^(i>>1)
00(0)^00→00(0)
01(1)^00→01(1)
10(2)^01→11(3)
11(3)^01→10(2)

AC Code(C++):

 1 class Solution {
 2 public:
 3     vector<int> grayCode(int n) {
 4         vector<int> seq;
 5         for(int i=0;i<(1<<n);i++){
 6             seq.push_back(i^(i>>1));
 7         }
 8         return seq;
 9     }
10 };