Lecture 224:-  Student Challenge Polynomial Representation Using Linked List

 

Representing polynomials using a linked list is a common way to efficiently store and manipulate polynomials, especially when dealing with sparse polynomials (polynomials with many zero coefficients). In this representation, each term of the polynomial is stored as a node in the linked list. Each node contains the coefficient and the exponent of the term. Here's a basic implementation of polynomial representation using a linked list in Python:

Let's start by defining the data structures for the polynomial:

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class Node:    def __init__(self, coefficient, exponent):        self.coefficient = coefficient        self.exponent = exponent        self.next = None class Polynomial:    def __init__(self):        self.head = None

Next, we can add methods to insert terms into the polynomial:

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class Polynomial:    # ... (previous code)    def insert_term(self, coefficient, exponent):        new_node = Node(coefficient, exponent)        if not self.head:            self.head = new_node        else:            current_node = self.head            prev_node = None            while current_node:                if current_node.exponent == exponent:                    # Merge terms with the same exponent                    current_node.coefficient += coefficient                    return                elif current_node.exponent < exponent:                    # Insert new term in descending order of exponents                    if prev_node:                        prev_node.next = new_node                    new_node.next = current_node                    return                prev_node = current_node                current_node = current_node.next            # Insert at the end if the exponent is largest            prev_node.next = new_node    def display(self):        current_node = self.head        while current_node:            coefficient = current_node.coefficient            exponent = current_node.exponent            if coefficient != 0:                print(f"{coefficient}x^{exponent}", end=" ")                        current_node = current_node.next        print()

With these methods, you can create and manipulate polynomials using the linked list representation. Here's an example of how you can use it:

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# Create a polynomial 3x^4 + 5x^3 - 2x^2 + 7x - 9 poly = Polynomial() poly.insert_term(3, 4) poly.insert_term(5, 3) poly.insert_term(-2, 2) poly.insert_term(7, 1) poly.insert_term(-9, 0) # Display the polynomial poly.display()  # Output: 3x^4 + 5x^3 - 2x^2 + 7x - 9 # Insert another term: 4x^3 poly.insert_term(4, 3) # Display the updated polynomial poly.display()  # Output: 3x^4 + 9x^3 - 2x^2 + 7x - 9

Remember that this is a basic implementation for demonstration purposes. Depending on your requirements, you can add more functionality, such as addition, subtraction, and multiplication of polynomials.