Question

In this assignment, you will implement a Polynomial linked list, the coefficients and exponents of the polynomial are defined as a node. The following 2 classes should be defined.

Answer 1

Solution: 
Input:
     1st number = 5x^2 + 4x^1 + 2x^0
     2nd number = 5x^1 + 5x^0
Output:
        5x^2 + 9x^1 + 7x^0
Input:
     1st number = 5x^3 + 4x^2 + 2x^0
     2nd number = 5x^1 + 5x^0
Output:
        5x^3 + 4x^2 + 5x^1 + 7x^0

// C++ program for addition of two polynomials

// using Linked Lists

#include<bits/stdc++.h>

using namespace std;

// Node structure containing power and coefficient of variable

struct Node

{

    int coeff;

    int pow;

    struct Node *next;

};

             

// Function to create new node

void create_node(int x, int y, struct Node **temp)

{

    struct Node *r, *z;

    z = *temp;

    if(z == NULL)

    {

        r =(struct Node*)malloc(sizeof(struct Node));

        r->coeff = x;

        r->pow = y;

        *temp = r;

        r->next = (struct Node*)malloc(sizeof(struct Node));

        r = r->next;

        r->next = NULL;

    }

    else

    {

        r->coeff = x;

        r->pow = y;

        r->next = (struct Node*)malloc(sizeof(struct Node));

        r = r->next;

        r->next = NULL;

    }

}

// Function Adding two polynomial numbers

void polyadd(struct Node *poly1, struct Node *poly2, struct Node *poly)

{

while(poly1->next && poly2->next)

    {

        // If power of 1st polynomial is greater then 2nd, then store 1st as it is

        // and move its pointer

        if(poly1->pow > poly2->pow)

        {

            poly->pow = poly1->pow;

            poly->coeff = poly1->coeff;

            poly1 = poly1->next;

        }

         

        // If power of 2nd polynomial is greater then 1st, then store 2nd as it is

        // and move its pointer

        else if(poly1->pow < poly2->pow)

        {

            poly->pow = poly2->pow;

            poly->coeff = poly2->coeff;

            poly2 = poly2->next;

        }

         

        // If power of both polynomial numbers is same then add their coefficients

        else

        {

            poly->pow = poly1->pow;

            poly->coeff = poly1->coeff+poly2->coeff;

            poly1 = poly1->next;

            poly2 = poly2->next;

        }

         

        // Dynamically create new node

        poly->next = (struct Node *)malloc(sizeof(struct Node));

        poly = poly->next;

        poly->next = NULL;

    }

while(poly1->next || poly2->next)

    {

        if(poly1->next)

        {

            poly->pow = poly1->pow;

            poly->coeff = poly1->coeff;

            poly1 = poly1->next;

        }

        if(poly2->next)

        {

            poly->pow = poly2->pow;

            poly->coeff = poly2->coeff;

            poly2 = poly2->next;

        }

        poly->next = (struct Node *)malloc(sizeof(struct Node));

        poly = poly->next;

        poly->next = NULL;

    }

}

// Display Linked list

void show(struct Node *node)

{

while(node->next != NULL)

    {

    printf("%dx^%d", node->coeff, node->pow);

    node = node->next;

    if(node->next != NULL)

        printf(" + ");

    }

}

// Driver program

int main()

{

    struct Node *poly1 = NULL, *poly2 = NULL, *poly = NULL;

     

    // Create first list of 5x^2 + 4x^1 + 2x^0

    create_node(5,2,&poly1);

    create_node(4,1,&poly1);

    create_node(2,0,&poly1);

     

    // Create second list of 5x^1 + 5x^0

    create_node(5,1,&poly2);

    create_node(5,0,&poly2);

     

    printf("1st Number: ");

    show(poly1);

     

    printf("\n2nd Number: ");

    show(poly2);

     

    poly = (struct Node *)malloc(sizeof(struct Node));

     

    // Function add two polynomial numbers

    polyadd(poly1, poly2, poly);

     

    // Display resultant List

    printf("\nAdded polynomial: ");

    show(poly);

return 0;

}

Output:

1st Number: 5x^2 + 4x^1 + 2x^0
2nd Number: 5x^1 + 5x^0
Added polynomial: 5x^2 + 9x^1 + 7x^0

Time Complexity: O(m + n) where m and n are number of nodes in first and second lists respectively.

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