grid47 Exploring patterns and algorithms
Sep 23, 2024
7 min read
Solution to LeetCode 445: Add Two Numbers II Problem
You are given two non-empty linked lists where each node contains a single digit representing a non-negative integer. Add the two numbers and return the sum as a linked list, ensuring the most significant digit is at the head of the list.
Problem
Approach
Steps
Complexity
Input: Each linked list represents a number where each node contains a single digit. The lists do not have leading zeros, except for the number 0 itself.
Example: [3,4,2], [6,5,7]
Constraints:
• 1 <= Number of nodes in each linked list <= 100
• Node.val >= 0 and Node.val <= 9
• No leading zeros in the numbers except for 0 itself
Output: The output should be a linked list representing the sum of the two numbers with the most significant digit at the head.
Example: [9,0,0,9]
Constraints:
• The result linked list must be formatted in the same way as the input.
Goal: Add two numbers represented by two linked lists and return the sum as a linked list.
Steps:
• 1. Use two stacks to store the digits of the linked lists as we traverse them.
• 2. Pop the digits from the stacks, add them with the carry, and create new nodes to store the result.
• 3. If a carry exists after processing both lists, create a new node for the carry.
• 4. Ensure that the final linked list is built without reversing the input lists.
Goal: The linked lists represent valid numbers without leading zeros except 0 itself.
Steps:
• 1 <= Number of nodes in each linked list <= 100
• 0 <= Node.val <= 9
• Do not reverse the input linked lists.
Assumptions:
• The linked lists are not empty and contain valid digits.
• Input: [3,4,2], [6,5,7]
• Explanation: The two numbers are 342 and 657. Their sum is 999, which is represented as [9, 0, 0, 9].
• Input: [1,2], [3,4,5]
• Explanation: The two numbers are 12 and 345. Their sum is 357, represented as [3, 5, 7].
Approach: This problem can be solved by simulating the addition process using stacks to reverse the linked lists and adding corresponding digits along with a carry.
Observations:
• The problem asks to avoid reversing the linked lists, which suggests using a stack to reverse the order temporarily.
• We can use two stacks to simulate the addition process from the most significant digit to the least significant digit.
Steps:
• 1. Create two stacks to store the digits of both linked lists.
• 2. Traverse both lists, pushing each digit onto its respective stack.
• 3. Pop digits from both stacks, add them with the carry, and store the result in a new linked list.
• 4. If there's any carry left after processing both lists, create a new node for the carry.
• 5. Return the result as the new linked list.
Empty Inputs:
• If any linked list is empty, it should be treated as 0.
Large Inputs:
• For larger inputs (up to 100 nodes), ensure that the solution handles the carry correctly and efficiently.
Special Values:
• Consider cases where the numbers involve carry overs, such as adding [9,9] and [1].
Constraints:
• Ensure that the algorithm runs in O(n) time and uses O(n) space for stack operations.
