Excel spreadsheets are ubiquitous in today’s world, and interestingly, the naming convention of columns in Excel lends itself to an intriguing algorithmic problem. In this comprehensive article, we will unpack the Excel Sheet Column Number problem listed on LeetCode, explore various methods to tackle it, and write Python code for the solutions.

## Problem Statement

The Excel Sheet Column Number problem is listed as problem number 171 on LeetCode. Here’s the problem statement:

Given a column title as appears in an Excel sheet, return its corresponding column number.

For example:

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

Example 1:

Input: columnTitle = “A”

Output: 1

Example 2:

Input: columnTitle = “AB”

Output: 28

Example 3:

Input: columnTitle = “ZY”

Output: 701

## Understanding the Problem

This problem is essentially the inverse of the Excel Sheet Column Title problem. Instead of converting numbers to a base-26 representation using letters, we need to convert a string of letters into a base-10 number. The letters A-Z are analogous to the numbers 1-26 in base-10, and the string “AA” would represent 27 (1 * 26^1 + 1 * 26^0), “AB” would represent 28, and so on.

## Approach 1: Iterative Calculation

One of the most straightforward approaches to this problem is to iterate through each character in the string and calculate its contribution based on its position.

Imagine the string as a number in base-26, where ‘A’ is 1, ‘B’ is 2, …, ‘Z’ is 26. For a string “AB”, this can be calculated as 1 * 26^1 + 2 * 26^0, which equals 28.

Let’s see how this can be done in Python:

```
def titleToNumber(columnTitle):
result = 0
for i, char in enumerate(reversed(columnTitle)):
# Convert character to number ('A' -> 1, 'B' -> 2, ..., 'Z' -> 26)
num = ord(char) - ord('A') + 1
result += num * (26 ** i)
return result
```

This approach has a time complexity of O(n), where n is the length of the column title. The space complexity is O(1).

## Approach 2: Accumulative Multiplication

A more concise way to calculate the column number is to use accumulative multiplication. For each character in the string, we can multiply the result so far by 26 and add the value of the current character.

This is similar to how we convert a binary number to decimal. For example, the binary number 1101 is equivalent to 1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0.

Let’s see how this can be implemented in Python:

```
def titleToNumber(columnTitle):
result = 0
for char in columnTitle:
num = ord(char) - ord('A') + 1
result = result * 26 + num
return result
```

This approach also has a time complexity of O(n) and space complexity of O(1), but it’s more concise and arguably clearer.

## Practical Applications

While this problem is relatively simple, it reflects real-world applications, particularly in converting between different numeral systems. This knowledge is not only applicable to spreadsheet software but also useful in various fields such as computer science, cryptography, and mathematics.

## Conclusion

The Excel Sheet Column Number problem provides an excellent example to familiarize oneself with the conversion between numeral systems and to understand the role of positional notation in number representation. We have explored two slightly different iterative methods for solving this problem. Such exercises are essential in building algorithmic thinking and problem-solving skills, which are crucial for computer science and programming.