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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.
1function invertChar(c) {
2 return c === '0' ? '1' : '0';
3}
4
5function invertAndReverse(s) {
6 return s.split('').map(invertChar).reverse().join('');
7}
8
9function findKthBit(n, k) {
10 let S = "0";
11 for (let i = 2; i <= n; i++) {
12 S = S + '1' + invertAndReverse(S);
13 }
14 return S[k - 1];
15}
16
17const n = 4;
18const k = 11;
19console.log(`Output: ${findKthBit(n, k)}`);Using iteratively constructed strings, the JavaScript approach forms each sequence by appending inverted and reversed prior sequences. It efficiently constructs the required binary string pattern before accessing the desired bit.
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
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.