Solution Explanation

This problem involves converting a positive integer representing a column number in an Excel sheet to its corresponding column title (e.g., 1 -> "A", 27 -> "AA"). The solution leverages the base-26 number system (where digits are A-Z instead of 0-9).

Algorithm:

1. Iterative Conversion: The core idea is to repeatedly divide the input columnNumber by 26. The remainder of each division represents a digit in the base-26 system (0 maps to 'A', 1 to 'B', ..., 25 to 'Z').

2. Remainder Handling: Before converting the remainder to a character, we decrement columnNumber by 1. This is because the remainders are 0-indexed, but Excel columns are 1-indexed.

3. Character Conversion: The remainder is converted to its corresponding character using ASCII values ('A' has ASCII value 65).

4. String Building: The resulting characters are appended to a string or array. Since we process the digits from least to most significant, the string is reversed before returning.

Time and Space Complexity:

• Time Complexity: O(log₂₆(columnNumber)). The number of iterations is proportional to the number of digits in the base-26 representation of the input number. This is logarithmic because the number of digits increases slowly with the input size.

• Space Complexity: O(log₂₆(columnNumber)). The space used to store the result string (or array) is proportional to the number of digits in the base-26 representation, making it logarithmic.

Code Explanation (Python):

class Solution:
    def convertToTitle(self, columnNumber: int) -> str:
        res = []
        while columnNumber:
            columnNumber -= 1  # Adjust for 1-based indexing
            res.append(chr(ord('A') + columnNumber % 26)) #Append character to the list
            columnNumber //= 26  # Integer division
        return ''.join(res[::-1]) # Reverse the list and join it to create a string.
 

The Python code directly implements the algorithm. It iteratively calculates the remainders, converts them to characters, and builds the result string. The [::-1] slicing efficiently reverses the list.

Code Explanation (Java):

class Solution {
    public String convertToTitle(int columnNumber) {
        StringBuilder res = new StringBuilder();
        while (columnNumber != 0) {
            columnNumber--; // Adjust for 1-based indexing
            res.append((char) ('A' + columnNumber % 26)); //Append character to the StringBuilder
            columnNumber /= 26; //Integer division
        }
        return res.reverse().toString(); //Reverse the StringBuilder and convert it to a String.
    }
}

The Java code uses a StringBuilder for efficient string manipulation. It's functionally equivalent to the Python code.

The other languages (Go, TypeScript, Rust, C#) follow similar logic, adapting the syntax and data structures accordingly. The core algorithm remains consistent across all implementations.