# 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;
}
};