Concept: Adding Two Polynomials Using Linked List

Introduction: Adding two polynomials using a linked list involves representing each polynomial as a linked list where each node contains the coefficient and exponent of a term. This approach allows efficient manipulation and addition of polynomials.

Steps to Add Two Polynomials:

• Represent each polynomial as a linked list where each node contains two fields: coefficient and exponent.
• Traverse both linked lists simultaneously, comparing the exponents of the current nodes.
• If the exponents are equal, add the coefficients and create a new node with the sum and the common exponent.
• If one exponent is greater, copy the term with the larger exponent to the result and move to the next node in that list.
• Continue until all terms from both polynomials are processed.
• Attach any remaining terms from either polynomial to the result.

Key Observations:

• Efficiently handles sparse polynomials by skipping zero coefficients.
• Maintains the order of terms based on descending exponents.
• Uses dynamic memory allocation, making it flexible for polynomials of varying sizes.

Advantages:

• Dynamic memory usage ensures efficient handling of large polynomials.
• Easy to implement and extend for other polynomial operations like subtraction or multiplication.

Disadvantages:

• Overhead of dynamic memory allocation and pointer management.
• Requires careful handling to avoid memory leaks.

Time Complexity:

• O(max(m, n)), where m and n are the number of terms in the two polynomials.