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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.
1using System.Collections.Generic;
class Program {
static List<int> GrayCode(int n) {
if (n == 0) return new List<int> { 0 };
List<int> lower = GrayCode(n - 1);
List<int> result = new List<int>(lower);
int addOn = 1 << (n - 1);
for (int i = lower.Count - 1; i >= 0; i--) {
result.Add(lower[i] | addOn);
}
return result;
}
static void Main() {
int n = 2;
List<int> gray = GrayCode(n);
Console.WriteLine(string.Join(" ", gray));
}
}This C# program recursively generates Gray code by first getting a baseline sequence, reflecting it and adjusting with bitwise operations, storing each new sequence state.