Add Two Numbers Leetcode Problem 2 [Python Solution]

Problem Overview

The LeetCode problem Add Two Numbers is a medium difficulty problem in the category of Linked Lists.

It's a common problem that tests your understanding of linked lists and basic arithmetic operations.

The task is to add two non-empty linked lists, representing two non-negative integers.

The digits are stored in reverse order, and each node of the linked list contains a single digit.

The goal is to add the two numbers and return the sum as a linked list.

Here's the problem statement:

Given two non-empty linked lists representing two non-negative integers, add them and return the sum as a linked list.

You can assume that the two numbers do not contain any leading zeros, except for the number 0 itself.

Example 1:

Let's take an example to understand the problem:

Input:

l1 = [2, 4, 3]
l2 = [5, 6, 4]


Output:

[7, 0, 8]


Explanation:

342 + 465 = 807


This problem is a great exercise in working with linked lists and handling edge cases.

It's a fundamental concept that forms the basis of many more complex problems in computer science and programming.

Understanding Constraints

Before we dive into solving this problem, let's take a closer look at the constraints:

• The number of nodes in each linked list is in the range [1, 100].
• The values of the nodes (digits) are in the range of 0 to 9.
• It is guaranteed that the linked list represents a number without leading zeros.

These constraints are essential to understanding the problem's scope and will help guide our solution.

Add Two Numbers LeetCode Problem Solution

Bruteforce Approach

To solve this problem, we can follow a straightforward approach:

1. Initialize a dummy node to simplify the code for handling the edge cases.
2. Create a pointer, cur, that will move through the result linked list.
3. Initialize a carry variable to 0, which will store the carry during addition.
4. Iterate through both linked lists while at least one of them has nodes.
5. For each iteration, get the values from the two linked lists, or assume them as 0 if the linked list is shorter.
6. Add the values of the two nodes and the carry.
7. Update the carry for the next iteration (carry = val // 10).
8. Create a new node with the calculated value and add it to the result linked list.
9. Update the pointers and move to the next nodes in the input lists.

Here's the Python code for the bruteforce approach:

def addTwoNumbers(self, l1: ListNode, l2: ListNode) -> ListNode:
    dummy = ListNode()
    cur = dummy

    carry = 0
    while l1 or l2 or carry:
        v1 = l1.val if l1 else 0
        v2 = l2.val if l2 else 0

        # Calculate the new digit
        val = v1 + v2 + carry
        carry = val // 10
        val = val % 10

        # Create a new node and add it to the result list
        cur.next = ListNode(val)

        # Update pointers
        cur = cur.next
        l1 = l1.next if l1 else None
        l2 = l2.next if l2 else None

    return dummy.next

This code takes care of the primary logic of adding two numbers, considering the edge cases, and returning the result as a linked list.

Time and Space Complexity

Time Complexity: The time complexity of this solution is O(max(N, M)), where N and M are the lengths of the two input linked lists.

We iterate through both lists once, and the length of the resulting list will be max(N, M) + 1 in the worst case.

Space Complexity: The space complexity is O(max(N, M)) because we need to create a new linked list of this size to store the result.

Reasoning Behind Our Approach

The approach described above is efficient and works well for this problem.

We start with a dummy node to simplify handling edge cases and carry values.

By iterating through the input linked lists while considering the carry, we can add the numbers digit by digit and create the resulting linked list.

The use of a dummy node avoids dealing with the head of the resulting linked list separately and simplifies the code.

Additionally, by checking if both input lists are empty, we handle cases where one list is longer than the other.

The algorithm is efficient, and its time complexity is linear, making it a practical solution for this problem.

It is a good example of how to work with linked lists and efficiently perform basic arithmetic operations in a real-world coding scenario.

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Conclusion

The Add Two Numbers problem on LeetCode is a valuable exercise in working with linked lists and basic arithmetic operations.

By following the bruteforce approach we've discussed, you can efficiently add two numbers represented by linked lists and return the result as a new linked list.

If you're a beginner, this problem is an excellent way to practice your coding skills and gain a deeper understanding of linked lists.

To further enhance your learning, don't forget to explore more problems on LeetCode and other coding platforms.

Remember, understanding the problem's constraints and reasoning behind your approach are essential steps in problem-solving.

As you continue your coding journey, you'll encounter more complex problems that build on these fundamental concepts.

So, keep practicing, stay curious, and happy coding!

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