Adding two polynomials using Linked List

Difficulty Level : Medium
Last Updated : 10 Jul, 2021

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

Addition-of-two-polynomial

CPP

// 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->coeff >= 0) {
            if (node->next != NULL)
                printf("+");
        }
    }
}
 
// Driver code
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;
}

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.

Recursive Method :

Algorithm :

If both the numbers are null then return
else if compare the power, if same then add the coefficients and recursively call addPolynomials on the next elements of both the numbers.
else if the power of first number is greater then print the current element of first number and recursively call addPolynomial on the next element of the first number and current element of the second number.
else print the current element of the second number and recursively call addPolynomial on the current element of first number and next element of second number.

C++

//Program to add two polynomials represented in linkedlist using recursion
#include<iostream>
using namespace std;
 
class Node{
public:
  int coeff,power;
  Node *next;
  Node(int coeff, int power){
    this->coeff = coeff;
    this->power = power;
    this->next = NULL;
  }
};
 
void addPolynomials(Node *head1, Node *head2){
 
  if(head1==NULL && head2==NULL)
    return;
  else if(head1->power == head2->power){
    cout<<" "<<head1->coeff +  head2->coeff<<"x^"<<head1->power<<" ";
    addPolynomials(head1->next,head2->next);
  }
  else if(head1->power > head2->power){
    cout<<" "<<head1->coeff<<"x^"<<head1->power<<" ";
    addPolynomials(head1->next,head2);
  }
  else{
    cout<<" "<<head2->coeff<<"x^"<<head2->power<<" ";
    addPolynomials(head1,head2->next);
  }
}
 
void insert(Node *head, int coeff, int power){
  Node *new_node = new Node(coeff,power);
  while(head->next!=NULL){
    head = head->next;
  }
  head->next = new_node;
}
 
void printList(Node *head){
  cout<<"Linked List"<<endl;
  while(head!=NULL){
    cout<<" "<<head->coeff<<"x"<<"^"<<head->power;
    head = head->next;
  }
}
 
int main(){
 
  Node *head=new Node(5,2);
  insert(head,4,1);
  Node *head2 = new Node(6,2);
  insert(head2,4,1);
  printList(head);
  cout<<endl;
  printList(head2);
  cout<<endl<<"Addition:"<<endl;
  addPolynomials(head,head2);
 
 
  return 0;
}
 
//This code is contributed by Akshita Patel

Output

Linked List
 5x^2 4x^1
Linked List
 6x^2 4x^1
Addition:
 11x^2  8x^1

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

Related Article: Add two polynomial numbers using Arrays
This article is contributed by Akash Gupta and Akshita Patel. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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