1545. Find Kth Bit in Nth Binary String

Description

Given two positive integers n and k, the binary string Sn is formed as follows:

• S1 = "0"
• Si = Si - 1 + "1" + reverse(invert(Si - 1)) for i > 1

Where + denotes the concatenation operation, reverse(x) returns the reversed string x, and invert(x) inverts all the bits in x (0 changes to 1 and 1 changes to 0).

For example, the first four strings in the above sequence are:

• S1 = "0"
• S2 = "011"
• S3 = "0111001"
• S4 = "011100110110001"

Return the kth bit in Sn. It is guaranteed that k is valid for the given n.

 

Example 1:

Input: n = 3, k = 1
Output: "0"
Explanation: S3 is "0111001".
The 1st bit is "0".

Example 2:

Input: n = 4, k = 11
Output: "1"
Explanation: S4 is "011100110110001".
The 11th bit is "1".

 

Constraints:

• 1 <= n <= 20
• 1 <= k <= 2n - 1

 

Solutions

Solution: Recursion

• Time complexity: O(n)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number} n
 * @param {number} k
 * @return {character}
 */
const findKthBit = function (n, k) {
  if (n === 1) return '0';
  const size = 2 ** n - 1;
  const mid = (size + 1) / 2;

  if (mid === k) return '1';
  if (mid < k) {
    return findKthBit(n - 1, size - k + 1) === '0' ? '1' : '0';
  }
  return findKthBit(n - 1, k);
};