89. 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.

Example 1:

Input: 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2

For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.

00 - 0
10 - 2
11 - 3
01 - 1

Example 2:

Input: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n = 0 the gray code sequence is [0].

 

AC code:

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> res;
        
        for (int i = 0; i < 1 << n; ++i) {
            res.push_back(i ^ i >> 1);
        }
        
        return res;
    }
};

Runtime: 4 ms, faster than 71.82% of C++ online submissions for Gray Code.

 

there are some regular patterns:

i = 0

i^i>>1　　00

i = 1

i^i>>1　　01

i = 2

i^i>>1　　11

i = 3

i^i>>1　　10