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Multiplication of two polynomials using Linked list
  • Difficulty Level : Medium
  • Last Updated : 29 Dec, 2020

Given two polynomials in the form of linked list. The task is to find the multiplication of both polynomials.

Examples: 

Input: Poly1: 3x^2 + 5x^1 + 6, Poly2: 6x^1 + 8
Output: 18x^3 + 54x^2 + 76x^1 + 48
On multiplying each element of 1st polynomial with 
elements of 2nd polynomial, we get
18x^3 + 24x^2 + 30x^2 + 40x^1 + 36x^1 + 48
On adding values with same power of x,
18x^3 + 54x^2 + 76x^1 + 48

Input: Poly1: 3x^3 + 6x^1 - 9, Poly2: 9x^3 - 8x^2 + 7x^1 + 2
Output: 27x^6 - 24x^5 + 75x^4 - 123x^3 + 114x^2 - 51x^1 - 18

Approach: 

  1. In this approach we will multiply the 2nd polynomial with each term of 1st polynomial.
  2. Store the multiplied value in a new linked list.
  3. Then we will add the coefficients of elements having the same power in resultant polynomial.

Below is the implementation of the above approach: 

C++




// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Node structure containing powerer
// and coefficient of variable
struct Node {
    int coeff, power;
    Node* next;
};
 
// Function add a new node at the end of list
Node* addnode(Node* start, int coeff, int power)
{
    // Create a new node
    Node* newnode = new Node;
    newnode->coeff = coeff;
    newnode->power = power;
    newnode->next = NULL;
 
    // If linked list is empty
    if (start == NULL)
        return newnode;
 
    // If linked list has nodes
    Node* ptr = start;
    while (ptr->next != NULL)
        ptr = ptr->next;
    ptr->next = newnode;
 
    return start;
}
 
// Functionn To Display The Linked list
void printList(struct Node* ptr)
{
    while (ptr->next != NULL) {
        cout << ptr->coeff << "x^" << ptr->power ;
       if( ptr->next!=NULL && ptr->next->coeff >=0)
          cout << "+";
 
        ptr = ptr->next;
    }
    cout << ptr->coeff << "\n";
}
 
// Function to add coefficients of
// two elements having same powerer
void removeDuplicates(Node* start)
{
    Node *ptr1, *ptr2, *dup;
    ptr1 = start;
 
    /* Pick elements one by one */
    while (ptr1 != NULL && ptr1->next != NULL) {
        ptr2 = ptr1;
 
        // Compare the picked element
        // with rest of the elements
        while (ptr2->next != NULL) {
 
            // If powerer of two elements are same
            if (ptr1->power == ptr2->next->power) {
 
                // Add their coefficients and put it in 1st element
                ptr1->coeff = ptr1->coeff + ptr2->next->coeff;
                dup = ptr2->next;
                ptr2->next = ptr2->next->next;
 
                // remove the 2nd element
                delete (dup);
            }
            else
                ptr2 = ptr2->next;
        }
        ptr1 = ptr1->next;
    }
}
 
// Function two Multiply two polynomial Numbers
Node* multiply(Node* poly1, Node* poly2,
               Node* poly3)
{
 
    // Create two pointer and store the
    // address of 1st and 2nd polynomials
    Node *ptr1, *ptr2;
    ptr1 = poly1;
    ptr2 = poly2;
    while (ptr1 != NULL) {
        while (ptr2 != NULL) {
            int coeff, power;
 
            // Multiply the coefficient of both
            // polynomials and store it in coeff
            coeff = ptr1->coeff * ptr2->coeff;
 
            // Add the powerer of both polynomials
            // and store it in power
            power = ptr1->power + ptr2->power;
 
            // Invoke addnode function to create
            // a newnode by passing three parameters
            poly3 = addnode(poly3, coeff, power);
 
            // move the pointer of 2nd polynomial
            // two get its next term
            ptr2 = ptr2->next;
        }
 
        // Move the 2nd pointer to the
        // starting point of 2nd polynomial
        ptr2 = poly2;
 
        // move the pointer of 1st polynomial
        ptr1 = ptr1->next;
    }
 
    // this function will be invoke to add
    // the coefficient of the elements
    // having same powerer from the resultant linked list
    removeDuplicates(poly3);
    return poly3;
}
 
// Driver Code
int main()
{
 
    Node *poly1 = NULL, *poly2 = NULL, *poly3 = NULL;
 
    // Creation of 1st Polynomial: 3x^2 + 5x^1 + 6
    poly1 = addnode(poly1, 3, 3);
    poly1 = addnode(poly1, 6, 1);
    poly1 = addnode(poly1, -9, 0);
 
    // Creation of 2nd polynomial: 6x^1 + 8
    poly2 = addnode(poly2, 9, 3);
    poly2 = addnode(poly2, -8, 2);
    poly2 = addnode(poly2, 7, 1);
    poly2 = addnode(poly2, 2, 0);
 
    // Displaying 1st polynomial
    cout << "1st Polynomial:- ";
    printList(poly1);
 
    // Displaying 2nd polynomial
    cout << "2nd Polynomial:- ";
    printList(poly2);
 
    // calling multiply function
    poly3 = multiply(poly1, poly2, poly3);
 
    // Displaying Resultant Polynomial
    cout << "Resultant Polynomial:- ";
    printList(poly3);
 
    return 0;
}

Java




// Java implementation of above approach
import java.util.*;
class GFG
{
 
// Node structure containing powerer
// and coefficient of variable
static class Node {
    int coeff, power;
    Node next;
};
 
// Function add a new node at the end of list
static Node addnode(Node start, int coeff, int power)
{
    // Create a new node
    Node newnode = new Node();
    newnode.coeff = coeff;
    newnode.power = power;
    newnode.next = null;
 
    // If linked list is empty
    if (start == null)
        return newnode;
 
    // If linked list has nodes
    Node ptr = start;
    while (ptr.next != null)
        ptr = ptr.next;
    ptr.next = newnode;
 
    return start;
}
 
// Functionn To Display The Linked list
static void printList( Node ptr)
{
    while (ptr.next != null) {
        System.out.print( ptr.coeff + "x^" + ptr.power + " + ");
 
        ptr = ptr.next;
    }
    System.out.print( ptr.coeff  +"\n");
}
 
// Function to add coefficients of
// two elements having same powerer
static void removeDuplicates(Node start)
{
    Node ptr1, ptr2, dup;
    ptr1 = start;
 
    /* Pick elements one by one */
    while (ptr1 != null && ptr1.next != null) {
        ptr2 = ptr1;
 
        // Compare the picked element
        // with rest of the elements
        while (ptr2.next != null) {
 
            // If powerer of two elements are same
            if (ptr1.power == ptr2.next.power) {
 
                // Add their coefficients and put it in 1st element
                ptr1.coeff = ptr1.coeff + ptr2.next.coeff;
                dup = ptr2.next;
                ptr2.next = ptr2.next.next;
 
            }
            else
                ptr2 = ptr2.next;
        }
        ptr1 = ptr1.next;
    }
}
 
// Function two Multiply two polynomial Numbers
static Node multiply(Node poly1, Node poly2,
            Node poly3)
{
 
    // Create two pointer and store the
    // address of 1st and 2nd polynomials
    Node ptr1, ptr2;
    ptr1 = poly1;
    ptr2 = poly2;
    while (ptr1 != null) {
        while (ptr2 != null) {
            int coeff, power;
 
            // Multiply the coefficient of both
            // polynomials and store it in coeff
            coeff = ptr1.coeff * ptr2.coeff;
 
            // Add the powerer of both polynomials
            // and store it in power
            power = ptr1.power + ptr2.power;
 
            // Invoke addnode function to create
            // a newnode by passing three parameters
            poly3 = addnode(poly3, coeff, power);
 
            // move the pointer of 2nd polynomial
            // two get its next term
            ptr2 = ptr2.next;
        }
 
        // Move the 2nd pointer to the
        // starting point of 2nd polynomial
        ptr2 = poly2;
 
        // move the pointer of 1st polynomial
        ptr1 = ptr1.next;
    }
 
    // this function will be invoke to add
    // the coefficient of the elements
    // having same powerer from the resultant linked list
    removeDuplicates(poly3);
    return poly3;
}
 
// Driver Code
public static void main(String args[])
{
 
    Node poly1 = null, poly2 = null, poly3 = null;
 
    // Creation of 1st Polynomial: 3x^2 + 5x^1 + 6
    poly1 = addnode(poly1, 3, 2);
    poly1 = addnode(poly1, 5, 1);
    poly1 = addnode(poly1, 6, 0);
 
    // Creation of 2nd polynomial: 6x^1 + 8
    poly2 = addnode(poly2, 6, 1);
    poly2 = addnode(poly2, 8, 0);
 
    // Displaying 1st polynomial
    System.out.print("1st Polynomial:- ");
    printList(poly1);
 
    // Displaying 2nd polynomial
    System.out.print("2nd Polynomial:- ");
    printList(poly2);
 
    // calling multiply function
    poly3 = multiply(poly1, poly2, poly3);
 
    // Displaying Resultant Polynomial
    System.out.print( "Resultant Polynomial:- ");
    printList(poly3);
 
}
 
 
}
// This code is contributed by Arnab Kundu

Python3




# Python3 implementation of the above approach
  
# Node structure containing powerer
# and coefficient of variable
class Node:  
    def __init__(self):      
        self.coeff = None
        self.power = None
        self.next = None
  
# Function add a new node at the end of list
def addnode(start, coeff, power):
 
    # Create a new node
    newnode = Node();
    newnode.coeff = coeff;
    newnode.power = power;
    newnode.next = None;
  
    # If linked list is empty
    if (start == None):
        return newnode;
  
    # If linked list has nodes
    ptr = start;
    while (ptr.next != None):
        ptr = ptr.next;
    ptr.next = newnode;
    return start;
  
# Functionn To Display The Linked list
def printList(ptr):
 
    while (ptr.next != None):
        print(str(ptr.coeff) + 'x^' + str(ptr.power), end = '')
        if( ptr.next != None and ptr.next.coeff >= 0):
            print('+', end = '')
        ptr = ptr.next
    print(ptr.coeff)
      
# Function to add coefficients of
# two elements having same powerer
def removeDuplicates(start):
    ptr2 = None
    dup = None
    ptr1 = start;
  
    # Pick elements one by one
    while (ptr1 != None and ptr1.next != None):
        ptr2 = ptr1;
  
        # Compare the picked element
        # with rest of the elements
        while (ptr2.next != None):
  
            # If powerer of two elements are same
            if (ptr1.power == ptr2.next.power):
  
                # Add their coefficients and put it in 1st element
                ptr1.coeff = ptr1.coeff + ptr2.next.coeff;
                dup = ptr2.next;
                ptr2.next = ptr2.next.next;
             
            else:
                ptr2 = ptr2.next;
         
        ptr1 = ptr1.next;
     
# Function two Multiply two polynomial Numbers
def multiply(poly1, Npoly2, poly3):
  
    # Create two pointer and store the
    # address of 1st and 2nd polynomials
    ptr1 = poly1;
    ptr2 = poly2;
     
    while (ptr1 != None):
        while (ptr2 != None):
  
            # Multiply the coefficient of both
            # polynomials and store it in coeff
            coeff = ptr1.coeff * ptr2.coeff;
  
            # Add the powerer of both polynomials
            # and store it in power
            power = ptr1.power + ptr2.power;
  
            # Invoke addnode function to create
            # a newnode by passing three parameters
            poly3 = addnode(poly3, coeff, power);
  
            # move the pointer of 2nd polynomial
            # two get its next term
            ptr2 = ptr2.next;
          
        # Move the 2nd pointer to the
        # starting point of 2nd polynomial
        ptr2 = poly2;
  
        # move the pointer of 1st polynomial
        ptr1 = ptr1.next;
      
    # this function will be invoke to add
    # the coefficient of the elements
    # having same powerer from the resultant linked list
    removeDuplicates(poly3);
    return poly3;
  
# Driver Code
if __name__=='__main__':
    poly1 = None
    poly2 = None
    poly3 = None;
  
    # Creation of 1st Polynomial: 3x^2 + 5x^1 + 6
    poly1 = addnode(poly1, 3, 3);
    poly1 = addnode(poly1, 6, 1);
    poly1 = addnode(poly1, -9, 0);
  
    # Creation of 2nd polynomial: 6x^1 + 8
    poly2 = addnode(poly2, 9, 3);
    poly2 = addnode(poly2, -8, 2);
    poly2 = addnode(poly2, 7, 1);
    poly2 = addnode(poly2, 2, 0);
  
    # Displaying 1st polynomial
    print("1st Polynomial:- ", end = '');
    printList(poly1);
  
    # Displaying 2nd polynomial
    print("2nd Polynomial:- ", end = '');
    printList(poly2);
  
    # calling multiply function
    poly3 = multiply(poly1, poly2, poly3);
  
    # Displaying Resultant Polynomial
    print("Resultant Polynomial:- ", end = '');
    printList(poly3);
  
# This code is contributed by rutvik_56

C#




// C# implementation of above approach
using System;
 
class GFG
{
 
// Node structure containing powerer
// and coefficient of variable
public class Node
{
    public int coeff, power;
    public Node next;
};
 
// Function add a new node at the end of list
static Node addnode(Node start, int coeff, int power)
{
    // Create a new node
    Node newnode = new Node();
    newnode.coeff = coeff;
    newnode.power = power;
    newnode.next = null;
 
    // If linked list is empty
    if (start == null)
        return newnode;
 
    // If linked list has nodes
    Node ptr = start;
    while (ptr.next != null)
        ptr = ptr.next;
    ptr.next = newnode;
 
    return start;
}
 
// Functionn To Display The Linked list
static void printList( Node ptr)
{
    while (ptr.next != null)
    {
        Console.Write( ptr.coeff + "x^" + ptr.power + " + ");
 
        ptr = ptr.next;
    }
    Console.Write( ptr.coeff +"\n");
}
 
// Function to add coefficients of
// two elements having same powerer
static void removeDuplicates(Node start)
{
    Node ptr1, ptr2, dup;
    ptr1 = start;
 
    /* Pick elements one by one */
    while (ptr1 != null && ptr1.next != null)
    {
        ptr2 = ptr1;
 
        // Compare the picked element
        // with rest of the elements
        while (ptr2.next != null)
        {
 
            // If powerer of two elements are same
            if (ptr1.power == ptr2.next.power)
            {
 
                // Add their coefficients and put it in 1st element
                ptr1.coeff = ptr1.coeff + ptr2.next.coeff;
                dup = ptr2.next;
                ptr2.next = ptr2.next.next;
 
            }
            else
                ptr2 = ptr2.next;
        }
        ptr1 = ptr1.next;
    }
}
 
// Function two Multiply two polynomial Numbers
static Node multiply(Node poly1, Node poly2,
            Node poly3)
{
 
    // Create two pointer and store the
    // address of 1st and 2nd polynomials
    Node ptr1, ptr2;
    ptr1 = poly1;
    ptr2 = poly2;
    while (ptr1 != null)
    {
        while (ptr2 != null)
        {
            int coeff, power;
 
            // Multiply the coefficient of both
            // polynomials and store it in coeff
            coeff = ptr1.coeff * ptr2.coeff;
 
            // Add the powerer of both polynomials
            // and store it in power
            power = ptr1.power + ptr2.power;
 
            // Invoke addnode function to create
            // a newnode by passing three parameters
            poly3 = addnode(poly3, coeff, power);
 
            // move the pointer of 2nd polynomial
            // two get its next term
            ptr2 = ptr2.next;
        }
 
        // Move the 2nd pointer to the
        // starting point of 2nd polynomial
        ptr2 = poly2;
 
        // move the pointer of 1st polynomial
        ptr1 = ptr1.next;
    }
 
    // this function will be invoke to add
    // the coefficient of the elements
    // having same powerer from the resultant linked list
    removeDuplicates(poly3);
    return poly3;
}
 
// Driver Code
public static void Main(String []args)
{
 
    Node poly1 = null, poly2 = null, poly3 = null;
 
    // Creation of 1st Polynomial: 3x^2 + 5x^1 + 6
    poly1 = addnode(poly1, 3, 2);
    poly1 = addnode(poly1, 5, 1);
    poly1 = addnode(poly1, 6, 0);
 
    // Creation of 2nd polynomial: 6x^1 + 8
    poly2 = addnode(poly2, 6, 1);
    poly2 = addnode(poly2, 8, 0);
 
    // Displaying 1st polynomial
    Console.Write("1st Polynomial:- ");
    printList(poly1);
 
    // Displaying 2nd polynomial
    Console.Write("2nd Polynomial:- ");
    printList(poly2);
 
    // calling multiply function
    poly3 = multiply(poly1, poly2, poly3);
 
    // Displaying Resultant Polynomial
    Console.Write( "Resultant Polynomial:- ");
    printList(poly3);
}
}
 
// This code has been contributed by 29AjayKumar
Output
1st Polynomial:- 3x^3+6x^1-9
2nd Polynomial:- 9x^3-8x^2+7x^1+2
Resultant Polynomial:- 27x^6-24x^5+75x^4-123x^3+114x^2-51x^1-18

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