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Gray code can be generated using a simple bit manipulation technique. For a given integer k, the corresponding Gray code is obtained by XORing k with (k >> 1). This technique ensures that each step in changing numbers results in transitioning only one bit.
Time complexity: O(2n), traversing all numbers.
Space complexity: O(1), using constant extra space.
1function grayCode(n) {
2 const size = 1 << n;
3 const result = [];
4 for (let i = 0; i < size; i++) {
5 result.push(i ^ (i >> 1));
6 }
7 console.log(result.join(' '));
8}
9
10grayCode(2);This JavaScript function calculates Gray codes for a sequence from 0 to 2n - 1 using i ^ (i >> 1) and stores results in an array, which is logged.
The Gray code can be recursively generated by reflecting the existing sequence. Start with a base case of n=1: [0,1]. For each subsequent n, reflect the current list, prepend a bit to the reflected part, and concatenate the results: if Gn-1 = [0, 1], then Gn = [0Gn-1, 1Gn-1].
Time complexity: O(2n), where recursions reflect and build upon previous results.
Space complexity: O(2n), allocating for the result array.
1#include <vector>
std::vector<int> grayCode(int n) {
if (n == 0) return {0};
std::vector<int> lower = grayCode(n - 1);
std::vector<int> result = lower;
int size = lower.size();
for (int i = size - 1; i >= 0; i--) {
result.push_back(lower[i] | (1 << (n - 1)));
}
return result;
}
int main() {
int n = 2;
std::vector<int> gray = grayCode(n);
for (int code : gray) {
std::cout << code << " ";
}
return 0;
}C++ recursive implementation that builds Gray code by reflecting lower and appending prefixed values. The base case starts with least significant bit.