Add Two Numbers

Algorithms
Medium
Cisco
134.3K views

You are given two non-empty linked lists representing two non-negative integers. The digits are stored in reverse order, and each of their nodes contains a single digit. Add the two numbers and return the sum as a linked list.

Why Interviewers Ask This

Cisco evaluates candidates on their ability to manipulate low-level data structures efficiently. This question tests logical precision in handling edge cases like carry propagation and unequal list lengths. It specifically assesses whether you can implement a linear time solution while maintaining code clarity, a critical skill for network infrastructure development where performance is paramount.

How to Answer This Question

1. Clarify the input format immediately, confirming that digits are stored in reverse order and lists may vary in length. 2. Propose a dummy head node strategy to simplify pointer management and avoid null checks during iteration. 3. Outline a single-pass loop logic that processes nodes from both lists simultaneously, calculating the sum and carry at each step. 4. Explicitly mention how you will handle remaining nodes if one list is longer than the other after the main loop. 5. Conclude by analyzing time complexity as O(max(m,n)) and space complexity as O(max(m,n)), demonstrating your understanding of algorithmic efficiency required by Cisco engineers.

Key Points to Cover

  • Explicitly mentioning the use of a dummy head node to streamline pointer logic
  • Correctly handling the carry propagation when the sum exceeds nine
  • Accounting for lists of unequal lengths by treating missing nodes as zero
  • Ensuring the loop continues until all nodes are processed AND no carry remains
  • Stating the time complexity is linear relative to the longer input list

Sample Answer

To solve this problem, I first visualize the linked lists as stacks of digits in reverse order, similar to how we add numbers manually. I would start by initializing a dummy head node to act as a placeholder for the result list, which keeps my current pointer clean. I also initialize a variable called 'carry' to zero. Next, I iterate through both lists using a while loop that continues as long as either list has nodes or there is a non-zero carry value. Inside the loop, I extract the values from the current nodes of both lists, defaulting to zero if a list is exhausted. I then calculate the total sum by adding these two values along with the current carry. The digit to store in the new node is the sum modulo ten, and the new carry becomes the integer division of the sum by ten. After creating the new node and linking it to my result list, I advance the pointers for both input lists. Once the loop finishes, I return the next node of my dummy head, effectively skipping the placeholder. For example, adding 342 and 465 represented as [2,4,3] and [5,6,4] results in [7,0,8]. This approach ensures we handle different list lengths and final carries correctly in a single pass.

Common Mistakes to Avoid

  • Forgetting to check for a remaining carry after the main loop finishes, leading to missing the final digit
  • Using complex conditional logic inside the loop instead of treating missing nodes as zero values
  • Attempting to reverse the input lists before processing, which adds unnecessary O(N) overhead
  • Failing to initialize the carry variable to zero, causing incorrect calculations from the start

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