Solution Explanation:

This problem involves adding two polynomials represented as linked lists. Each node in the linked list represents a term in the polynomial, with coefficient and power attributes. The goal is to efficiently add these polynomials and return the resulting polynomial as a linked list.

The optimal approach is to use a two-pointer technique to iterate through both linked lists simultaneously. We compare the powers of the terms in poly1 and poly2.

Algorithm:

1. Initialization: Create a dummy node to simplify the handling of the head of the resulting list. A curr pointer will track the current node during the construction of the sum.

2. Iteration: While both poly1 and poly2 have nodes:

   • If poly1.power > poly2.power, append the poly1 node to the result and move poly1 to the next node.
   • If poly1.power < poly2.power, append the poly2 node to the result and move poly2 to the next node.
   • If poly1.power == poly2.power, add the coefficients. If the sum is non-zero, create a new node with the sum and the power, and append it to the result. Then move both poly1 and poly2 to their next nodes.

3. Remaining Nodes: After one of the lists is exhausted, append the remaining nodes from the other list to the result.

4. Return: Return the next of the dummy node (the actual head of the sum).

Time Complexity: O(m + n), where 'm' and 'n' are the lengths of poly1 and poly2 respectively. We traverse each list at most once.

Space Complexity: O(m + n) in the worst case, where the resulting polynomial has a length equal to the sum of the lengths of the input polynomials. This occurs when no powers are the same. In the best case (all powers match and cancel out) or if there's significant overlap resulting in fewer terms, the space complexity can be O(min(m,n))

Code Examples (Python, Java, C++, JavaScript, C#):

The code examples in various languages provided in the original response efficiently implement this algorithm. They all follow the same fundamental approach of comparing powers, adding coefficients, and handling remaining nodes. The only differences are in syntax and how linked list nodes are defined and manipulated in each language. Each code snippet includes comments to explain the logic in detail.