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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.
1def gray_code(n):
2 size = 1 << n
3 for i in range(size):
4 gray = i ^ (i >> 1)
5 print(gray, end=' ')
6
7n = 2
8gray_code(n)This Python script computes Gray codes for the range 0 to 2n - 1 using bit manipulation: i ^ (i >> 1). Each result is printed immediately.
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
This C implementation uses recursion to build the Gray code sequence by reflecting and appending. Allocate memory for the result array and fill it with generated codes.