Sponsored
Sponsored
This approach involves directly simulating the sequence construction up to the desired nth binary string and retrieving the k-th bit from it. Since the problem ensures n and k are constrained, this method remains efficient enough.
Time Complexity: O(2^n), as each step fully constructs the sequence of size approximately 2^n.
Space Complexity: O(2^n), owing to storing the full sequence.
1
The solution constructs each sequence iteratively using the relationship: Si = Si-1 + '1' + reverse(invert(Si-1)). We manage a buffer array S that stores each sequence step-by-step until Sn is reached, whereupon we simply return the k-th position.
This approach leverages the recursive nature and mathematical properties of the sequence to find the k-th bit without constructing the entire string. By recognizing the symmetry and structure, we use recursive calculations to directly determine the desired bit.
Time Complexity: O(n), limited by the recursion depth of n.
Space Complexity: O(n), due to recursive call stack.
1#include <stdio.h>
2
3char findKthBitRecursively(int n, int k) {
4 if (n == 1) return '0';
5 int length = (1 << n) - 1; // Length of S_n
6 int mid = (length + 1) / 2;
7 if (k == mid) return '1';
8 if (k < mid) return findKthBitRecursively(n - 1, k);
9 else {
10 char bit = findKthBitRecursively(n - 1, length - k + 1);
11 return bit == '0' ? '1' : '0';
12 }
13}
14
15int main() {
16 int n = 4, k = 11;
17 printf("Output: %c\n", findKthBitRecursively(n, k));
18 return 0;
19}The recursive approach utilizes the breakdown of the sequence into its two halves with a central break. We trace the k-th bit's location through recursion: if it's in the right half, consider the transformed position in the left. This efficient strategy provides a path to directly compute the k-th bit without constructing full strings.