Adding two polynomials using Linked List - GeeksforGeeks

07 Apr, 2022
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
 
 
CPP
Java
// C++ program for addition of two polynomials// using Linked Lists#include <bits/stdc++.h>using namespace std; // Node structure containing power and coefficient of// variablestruct Node {    int coeff;    int pow;    struct Node* next;}; // Function to create new nodevoid 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 numbersvoid 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 listvoid 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 codeint 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;}
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 Nodesclass Node {    int coeff;    int pow;    Node next;    Node(int a, int b)    {        coeff = a;        pow = b;        next = null;    }} //Linked List main classclass 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();    }}
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 returnelse 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.
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++
Javascript
//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
<script> // JavaScript Program to add two polynomials// represented in linkedlist using recursion class Node{  constructor(coeff, power){        this.coeff = coeff;        this.power = power;        this.next = null;  }} function addPolynomials(head1, head2){  document.write(head1.power, head2.power)   if(head1==null && head2==null)    return;  else if(head1.power == head2.power){    document.write(` ${head1.coeff + head2.coeff}x^${head1.power} `);    addPolynomials(head1.next, head2.next);  }  else if(head1.power > head2.power){    document.write(` ${head1.coeff}x^${head1.power} `);    addPolynomials(head1.next, head2);  }  else{    document.write(` ${head2.coeff}x^${head2.power} `);    addPolynomials(head1, head2.next);  }} function insert(head, coeff, power){  let new_node = new Node(coeff,power);  while(head.next!=null){    head = head.next;  }  head.next = new_node;} function printList(head){  document.write("Linked List","</br>");  while(head != null){    document.write(` ${head.coeff}x^${head.power}`);    head = head.next;  }} // driver codelet head = new Node(5,2);insert(head,4,1);let head2 = new Node(6,2);insert(head2,4,1);printList(head);document.write("</br>");printList(head2);document.write("</br>");document.write("Addition:");document.write("</br>");addPolynomials(head,head2); // This code is contributed by shinjanpatra </script>
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.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
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