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].

Solution

Approach 1: Iteration.

Code (Python)

Approach 1:

Code (C++)

Approach 1:

// n=0: {0}
// n=1:   0+{0}           +   1+{0}           = {0,1}
// n=2:  00+{0,1}         +  10+{1,0}         = {00,01,11,10}
// n=3: 000+{00,01,11,10} + 100+{10,11,01,00} = {000,001,011,010,110,111,101,100}
class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> codes;
        codes.push_back(0);
        for (int i = 1; i <= n; ++i)
        {
            int codesSize = codes.size();
            for (int j = codesSize - 1; j >= 0; --j)
            {
                codes.push_back(codes[j] + (1 << (i - 1)));
            }
        }
        return codes;
    }
};