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].
// Bit manipulation for gray code
vector<int> grayCode(int n) { // time: O(2^n); space: O(2^n)
vector<int> res(1 << n);
for (int i = 0; i < (1 << n); ++i) {
res[i] = i ^ (i >> 1);
}
return res;
}
// Iteration
// 2 numbers in the middle only differ at their most significant bit
vector<int> grayCode(int n) { // time: O(2^n); space: O(2^n)
vector<int> res;
res.reserve(1 << n);
res.push_back(0);
for (int i = 0; i < n; ++i) {
for (int j = res.size() - 1; j >= 0; --j) {
res.push_back(res[j] | (1 << i));
}
}
return res;
}