Solution Explanation

This problem involves converting a string of lowercase English letters into an integer, then repeatedly summing its digits until a single-digit integer is obtained. Let's break down the steps and the code:

1. Conversion:

• Each character in the input string s is replaced by its position in the alphabet (a=1, b=2, ..., z=26).
• This creates a new string representing the integer.

2. Transformation:

• The integer (represented as a string) is repeatedly transformed by summing its digits. This step is repeated k times.
• Each transformation reduces the number of digits until we're left with a single digit.

3. Algorithm:

The algorithm efficiently handles these steps:

1. Convert String to Integer String: The first step iterates through the input string s. Each character is converted to its numerical equivalent (1-26), and it's appended to a new string.

2. Repeated Digit Summation: The next step uses a loop that continues until k transformations are done. Inside the loop:

   • The digits are summed to a new total.
   • The total becomes the new string for the next iteration.

4. Time and Space Complexity Analysis:

• Time Complexity: The conversion step takes O(n) time, where n is the length of the input string. The digit summation step, in the worst case, takes O(nk) time because in each iteration the time to sum the digits can be proportional to the number of digits (which could be as large as n initially). Therefore, the overall time complexity is O(n + nk), which simplifies to O(n*k) if k is not a constant, or just O(n) if k is a constant.

• Space Complexity: The space complexity is dominated by the space needed to store the intermediate strings and the sum variables. In the worst case, the space required could be proportional to the initial string length n. Therefore the space complexity is O(n).

5. Code Explanation (Python Example):

class Solution:
    def getLucky(self, s: str, k: int) -> int:
        s = ''.join(str(ord(c) - ord('a') + 1) for c in s) # convert to integer string
        for _ in range(k): # repeat k times
            t = sum(int(c) for c in s) # sum the digits
            s = str(t) # update string for next iteration
        return int(s) # return the final single-digit integer
 

The other language examples follow the same algorithmic approach, adapting the syntax and data structures accordingly. They all achieve the same time and space complexity.