## Introduction

In this comprehensive article, we will discuss and solve the ‘Add Strings’ problem on Leetcode. We will analyze different approaches, including simulating the manual addition process and using built-in functions, and consider their time complexities.

## Problem Statement

The ‘Add Strings’ problem is listed as problem number 415 on Leetcode. The problem statement is as follows:

Given two non-negative integers, `num1`

and `num2`

represented as string, return the sum of `num1`

and `num2`

as a string.

You must solve the problem without using any built-in library for handling large integers (such as BigInteger). You must also not convert the strings to integers directly.

### Example:

```
Input: num1 = "11", num2 = "123"
Output: "134"
Input: num1 = "456", num2 = "77"
Output: "533"
```

## Approach 1: Simulating the Manual Addition Process

- Start by initializing an empty string
`result`

that will store the final sum, and a variable`carry`

to keep track of the carry value. - Use two pointers, initially positioned at the end of both strings.
- Iterate through the strings from right to left, simulating the process of manual addition: a. Convert each character to its integer value. b. Add the two integers along with the carry from the previous step. c. Update the carry for the next iteration. d. Append the units place of the sum to the result string.
- After the loop, if there is any carry left, append it to the result.
- Reverse the result string as we have built it in reverse order.
- Return the result string.

```
def addStrings(num1, num2):
result = []
carry = 0
p1, p2 = len(num1) - 1, len(num2) - 1
while p1 >= 0 or p2 >= 0:
n1 = int(num1[p1]) if p1 >= 0 else 0
n2 = int(num2[p2]) if p2 >= 0 else 0
temp_sum = n1 + n2 + carry
carry = temp_sum // 10
result.append(str(temp_sum % 10))
p1 -= 1
p2 -= 1
if carry:
result.append(str(carry))
return ''.join(reversed(result))
```

### Time Complexity

The time complexity of this approach is O(max(N, M)), where N and M are the lengths of the input strings.

## Approach 2: Using Python Built-in Functions (For Educational Purposes)

It is important to note that this approach does not follow the constraints of not using direct conversions or built-in libraries for handling large integers. This is only for educational purposes to demonstrate Python’s flexibility.

- Use the built-in
`int`

function to convert both strings to integers. - Add the two integers.
- Convert the sum back into a string and return it.

```
def addStrings(num1, num2):
return str(int(num1) + int(num2))
```

### Time Complexity

The time complexity of this approach is dependent on the implementation of Python’s built-in functions. Theoretically, it is O(N + M), but it may vary based on optimizations within Python’s libraries.

## Conclusion

The ‘Add Strings’ problem on Leetcode is an interesting challenge that tests one’s understanding of string manipulation and simulating a real-world process programmatically. While Python offers built-in functions that can simplify this task, the problem’s constraints require us to simulate the manual addition process. Understanding how to operate with strings representing numerical data without converting them directly into numerical types is an essential skill, especially for problems involving very large numbers that may exceed the standard numerical data types.