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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.
1#include <stdio.h>
2#include <math.h>
3
4void grayCode(int n) {
5 int size = pow(2, n);
6 for (int i = 0; i < size; i++) {
7 int gray = i ^ (i >> 1);
8 printf("%d ", gray);
9 }
10}
11
12int main() {
13 int n = 2;
14 grayCode(n);
15 return 0;
16}This C program calculates Gray codes by iterating from 0 to 2n - 1, computing each Gray code number using i ^ (i >> 1) for each integer i.
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.