Java Program For Adding Two Polynomials Using Linked List

Given two polynomial numbers represented by a linked list. Write a function that add these lists means add the coefficients who have same variable powers.
Example:  

Input:
     1st number = 5x2 + 4x1 + 2x0
     2nd number = -5x1 - 5x0
Output:
        5x2-1x1-3x0
Input:
     1st number = 5x3 + 4x2 + 2x0
     2nd number = 5x^1 - 5x^0
Output:
        5x3 + 4x2 + 5x1 - 3x0

Java

import java.io.*;
import java.util.Scanner;
class Polynomial
{
    public static Node addPolynomial(Node p1,
                                     Node p2)
    {
        Node a = p1, b = p2,
             newHead = new Node(0, 0),
             c = newHead;

        while (a != null || b != null)
        {
            if (a == null)
            {
                c.next = b;
                break;
            }
            else if (b == null)
            {
                c.next = a;
                break;
            }

            else if (a.pow == b.pow)
            {
                c.next = new Node(a.coeff +
                                  b.coeff, a.pow);
                a = a.next;
                b = b.next;
            }

            else if (a.pow > b.pow)
            {
                c.next = new Node(a.coeff,
                                  a.pow);
                a = a.next;
            }

            else if (a.pow < b.pow)
            {
                c.next = new Node(b.coeff,
                                  b.pow);
                b = b.next;
            }
            c = c.next;
        }
        return newHead.next;
    }
}

// Utilities for Linked List
// Nodes
class Node
{
    int coeff;
    int pow;
    Node next;
    Node(int a, int b)
    {
        coeff = a;
        pow = b;
        next = null;
    }
}

// Linked List main class
class LinkedList
{
    public static void main(String args[])
    {
        Node start1 = null, cur1 = null,
             start2 = null, cur2 = null;
        int[] list1_coeff = {5, 4, 2};
        int[] list1_pow = {2, 1, 0};
        int n = list1_coeff.length;

        int i = 0;
        while (n-- > 0)
        {
            int a = list1_coeff[i];
            int b = list1_pow[i];
            Node ptr = new Node(a, b);
            if (start1 == null)
            {
                start1 = ptr;
                cur1 = ptr;
            }
            else
            {
                cur1.next = ptr;
                cur1 = ptr;
            }
            i++;
        }

        int[] list2_coeff = {-5, -5};
        int[] list2_pow = {1, 0};
        n = list2_coeff.length;

        i = 0;
        while (n-- > 0)
        {
            int a = list2_coeff[i];
            int b = list2_pow[i];

            Node ptr = new Node(a, b);

            if (start2 == null)
            {
                start2 = ptr;
                cur2 = ptr;
            }
            else
            {
                cur2.next = ptr;
                cur2 = ptr;
            }
            i++;
        }

        Polynomial obj = new Polynomial();
        Node sum = obj.addPolynomial(start1,
                                     start2);
        Node trav = sum;
        while (trav != null)
        {
            System.out.print(trav.coeff +
                             "x^" + trav.pow);
            if (trav.next != null)
                System.out.print(" + ");
            trav = trav.next;
        }
        System.out.println();
    }
}

Output:

1st Number: 5x^2+4x^1+2x^0
2nd Number: -5x^1-5x^0
Added polynomial: 5x^2-1x^1-3x^0

Time Complexity: O(m + n) where m and n are number of nodes in first and second lists respectively.
Auxiliary Space: O(max(m,n) as it is using extra space for resultant linked list.

Please refer complete article on Adding two polynomials using Linked List for more details!