Spreadsheet applications like Microsoft Excel have become an integral part of modern computing. Interestingly, the way Excel names its columns can be modeled as an algorithm problem. In this comprehensive article, we will delve into the Excel Sheet Column Title problem listed on LeetCode, unpack different methods for solving it, and write the solutions in Python.

## Problem Statement

The Excel Sheet Column Title problem is listed as problem number 168 on LeetCode. Here’s the problem statement:

Given an integer columnNumber, return its corresponding column title as it appears in an Excel sheet.

For example:

```
1 -> A
2 -> B
3 -> C
...
26 -> Z
27 -> AA
28 -> AB
...
```

Example 1:

Input: columnNumber = 1

Output: “A”

Example 2:

Input: columnNumber = 28

Output: “AB”

Example 3:

Input: columnNumber = 701

Output: “ZY”

## Understanding the Problem

Excel sheet columns are named with letters. The first 26 columns are labeled A to Z, and after that, AA to AZ, followed by BA to BZ, and so on. Essentially, this is a base-26 numbering system, where A is 1, B is 2, …, Z is 26, AA is 27, AB is 28, and so on.

Our task is to convert a given integer into this base-26 letter notation.

## Approach 1: Iterative Conversion

Let’s start by converting the given number into a base-26 representation, where A corresponds to 0, B corresponds to 1, …, Z corresponds to 25.

For instance, if we have the number 28, we can represent it as 1 * 26^0 + 1 * 26^1, which corresponds to AB.

We will repeatedly divide the number by 26 and find the remainder. The remainder will tell us what letter to append to the left of our answer string.

```
def convertToTitle(columnNumber):
result = ""
while columnNumber:
# decrement the columnNumber by 1, because 1 -> A
columnNumber -= 1
remainder = columnNumber % 26
# convert remainder to character
result = chr(65 + remainder) + result
# divide by 26
columnNumber //= 26
return result
```

This approach has a time complexity of O(log n), where n is the column number, and a space complexity of O(1).

## Approach 2: Recursive Conversion

We can solve this problem recursively as well. Instead of using a while loop, we can write a recursive function to compute the title.

```
def convertToTitle(columnNumber):
# Base case
if columnNumber == 0:
return ""
# Convert the number to base 26 and call recursively
columnNumber -= 1
return convertToTitle(columnNumber // 26) + chr(65 + columnNumber % 26)
```

The time and space complexity of this recursive approach is the same as the iterative one. However, recursion uses an internal call stack which might cause a stack overflow for very large inputs.

## Conclusion

We’ve explored two different approaches to solve the Excel Sheet Column Title problem on LeetCode using Python – iterative and recursive. These approaches demonstrate the application of modular arithmetic and conversion between different numbering systems.

Being able to manipulate numbers and convert them into different representations is an essential skill in algorithm design and problem-solving. The Excel Sheet Column Title problem serves as a great example of how abstract concepts can be applied to real-world applications. It also shows how seemingly simple operations in everyday software have underlying algorithms that developers need to think through and implement efficiently.