89. Gray Code

• Difficulty: Medium

• Topics: Backtracking

• Similar Questions:

  • 1-bit and 2-bit Characters

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.

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].

Solutions:

class Solution {
public:
    vector<int> grayCode(int n) {
        if (n < 0)  return {};
        vector<int> ret = {0};
        for (int i = 0; i < n; ++i) {
            int size = ret.size();
            for (int j = size - 1; j >= 0; --j) {
                ret.push_back(ret[j] + (1 << i));
            }
        }

        return ret;
    }
};