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
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(); } } |
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 |
Javascript
<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 code let 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
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