• Difficulty Level : Medium
• Last Updated : 30 Jun, 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

 `// C++ program for addition of two polynomials``// using Linked Lists``#include ``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

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

Simple and concise version of the above approach:

We will maintain a prev pointer that will point to the last node of resultant liked list. We will be modifying the same given nodes rather than creating new ones .The below code will provide you with more insight.

Thank you Nakshatra Chhillar for suggesting this simplification and contributing the code :

## C++

 `#include ``using` `namespace` `std;` `/* Link list Node */``struct` `Node {``    ``int` `coeff;``    ``int` `pow``;``    ``struct` `Node* next;` `    ``Node(``int` `c, ``int` `p)``    ``{``        ``coeff = c;``        ``pow` `= p;``        ``next = NULL;``    ``}``};``void` `append(``struct` `Node** head_ref, ``struct` `Node** tail_ref,``            ``int` `new_data, ``int` `new_data1)``{``    ``struct` `Node* new_node = ``new` `Node(new_data, new_data1);` `    ``if` `(*head_ref == NULL)``        ``*head_ref = new_node;``    ``else``        ``(*tail_ref)->next = new_node;``    ``*tail_ref = new_node;``}``void` `printList(``struct` `Node* head)``{``    ``struct` `Node* temp = head;` `    ``while` `(temp != NULL) {``        ``printf``(``"%d %d "``, temp->coeff, temp->``pow``);``        ``temp = temp->next;``    ``}``}``Node* addPolynomial(Node* p1, Node* p2);``void` `create_node(``int` `x, ``int` `y, ``struct` `Node** temp)``{``    ``struct` `Node *r, *z;``    ``z = *temp;``    ``if` `(z == NULL) {``        ``r = ``new` `Node(x, y);``        ``*temp = r;``        ``r->next = NULL;``    ``}``    ``else` `{``        ``r->next = ``new` `Node(x, y);``        ``r = r->next;``        ``r->next = NULL;``    ``}``}` `/* Structure of Node used``struct Node``{``    ``int coeff;``    ``int pow;``    ``struct Node* next;` `    ``Node(int c, int p){``        ``coeff = c;``        ``pow = p;``        ``next = NULL;``    ``}` `};``*/``// 1st Number: 5x^2+4x^1+2x^0``// 2nd Number: -5x^1-5x^0``class` `Solution {``public``:``    ``/* The below method print the required sum of polynomial``    ``p1 and p2 as specified in output  */``    ``Node* addPolynomial(Node* p1, Node* p2)``    ``{``        ``Node* res = ``new` `Node(``            ``0, 0); ``// dummy node ...head of resultant list``        ``Node* prev``            ``= res; ``// pointer to last node of resultant list``        ``// like Merge procedure :``        ``while` `(p1 != NULL and p2 != NULL) {``            ``if` `(p1->``pow` `< p2->``pow``) {``                ``prev->next = p2;``                ``prev = p2;``                ``p2 = p2->next;``            ``}``            ``else` `if` `(p1->``pow` `> p2->``pow``) {``                ``prev->next = p1;``                ``prev = p1;``                ``p1 = p1->next;``            ``}``            ``else` `{``                ``p1->coeff = p1->coeff + p2->coeff;``                ``prev->next = p1;``                ``prev = p1;``                ``p1 = p1->next;``                ``p2 = p2->next;``            ``}``        ``}``        ``if` `(p1 != NULL) {``            ``prev->next = p1;``        ``}``        ``if` `(p2 != NULL) {``            ``prev->next = p2;``        ``}``        ``return` `res->next;``    ``}``};` `int` `main()``{``    ``struct` `Node *poly1 = NULL, *poly2 = NULL, *poly = NULL;``    ``struct` `Node *tail1 = NULL, *tail2 = NULL;``    ``// 1st Number: 5x^2+4x^1+2x^0``    ``append(&poly1, &tail1, 5, 2);``    ``append(&poly1, &tail1, 4, 1);``    ``append(&poly1, &tail1, 2, 0);``    ``// 2nd Number: -5x^1-5x^0``    ``append(&poly2, &tail2, -5, 1);``    ``append(&poly2, &tail2, -5, 0);``    ``Solution obj;``    ``Node* sum = obj.addPolynomial(poly1, poly2);``    ``for` `(Node* ptr = sum; ptr; ptr = ptr->next) {``        ``// printing polynomial``        ``cout << ptr->coeff << ``"x^"` `<< ptr->``pow``;``        ``if` `(ptr->next)``            ``cout << ``" + "``;``    ``}``    ``cout << endl;``}``// contributed by Nakshatra Chhillar`

Output

`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.

Space Complexity: O(1) no extra nodes have been created Recursive Method :

Algorithm :

1. If both the numbers are null then return
2. else if compare the power, if same then  add the coefficients and recursively call  addPolynomials on the next elements of both the numbers.
3. 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.
4. 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``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<<``" "``<coeff +  head2->coeff<<``"x^"``<power<<``" "``;``    ``addPolynomials(head1->next,head2->next);``  ``}``  ``else` `if``(head1->power > head2->power){``    ``cout<<``" "``<coeff<<``"x^"``<power<<``" "``;``    ``addPolynomials(head1->next,head2);``  ``}``  ``else``{``    ``cout<<``" "``<coeff<<``"x^"``<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"``<coeff<<``"x"``<<``"^"``<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<

## Javascript

 ``

Output

```Linked List
5x^2 4x^1
6x^2 4x^1