Adding two polynomials using Linked List using map
Last Updated :
26 Oct, 2023
Given two polynomial numbers represented by a linked list. Write a function to perform their algebraic sum. Examples:
Input: 1st number = 5x^2 + 4x^1 + 2x^0 2nd number = 5x^1 + 5x^0 Output: 5x^2 + 9x^1 + 7x^0
Approach: The implementation uses map data structure so that all coefficients of same power value are added together and kept in key-value pairs inside a map. Below is the implementation of the above approach:
CPP
// C++ program for addition of two polynomials
// represented as linked lists
#include <bits/stdc++.h>
using namespace std;
// Structure of Node used
struct Node {
// Coefficient of the polynomial
int coeff;
// Power of the polynomial
int pow;
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;
}
}
// Display Linked list
void show(struct Node* node)
{
if (node == NULL)
return;
while (node->next != NULL) {
printf("%dx^%d", node->coeff, node->pow);
node = node->next;
if (node->next != NULL)
printf(" + ");
}
}
/* Function to print the required sum of a
polynomial p1 and p2 as specified in output */
void addPolynomial(Node* p1, Node* p2)
{
map<int, int> mp;
Node* temp1 = p1;
Node* temp2 = p2;
while (temp1 != NULL) {
// Add coefficients of same power value
// map contains (powervalue, coeff) pair
mp[temp1->pow] += temp1->coeff;
temp1 = temp1->next;
}
while (temp2 != NULL) {
mp[temp2->pow] += temp2->coeff;
temp2 = temp2->next;
}
// Started from the end because higher power should
// come first and there should be "+" symbol in between
// so iterate up to second element and print last out of
// the loop.
for (auto it = (mp.rbegin()); it != prev(mp.rend());
++it)
cout << it->second << "x^" << it->first << " + ";
cout << mp.begin()->second << "x^" << mp.begin()->first;
}
// Driver function
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));
printf("\nAdded polynomial: ");
// Function add two polynomial numbers
addPolynomial(poly1, poly2);
return 0;
}
// Java program for addition of two polynomials
// represented as linked lists
import java.util.*;
// Structure of Node used
class Node {
// Coefficient of the polynomial
int coeff;
// Power of the polynomial
int pow;
Node next;
Node(int coeff, int pow) {
this.coeff = coeff;
this.pow = pow;
this.next = null;
}
}
// Display Linked list
class LinkedList {
Node head;
// Function to create new node
void create_node(int x, int y) {
Node node = new Node(x, y);
if (head == null) {
head = node;
}
else {
Node temp = head;
while (temp.next != null) {
temp = temp.next;
}
temp.next = node;
}
}
void show() {
Node node = head;
while (node != null) {
System.out.print(node.coeff + "x^" + node.pow);
node = node.next;
if (node != null) {
System.out.print(" + ");
}
}
}
}
class Main {
// Function to print the required sum of a
// polynomial p1 and p2 as specified in output
static void addPolynomial(Node p1, Node p2) {
Map<Integer, Integer> mp = new TreeMap<>(Collections.reverseOrder());
Node temp1 = p1;
Node temp2 = p2;
while (temp1 != null) {
// Add coefficients of same power value
// map contains (powervalue, coeff) pair
mp.put(temp1.pow, mp.getOrDefault(temp1.pow, 0) + temp1.coeff);
temp1 = temp1.next;
}
while (temp2 != null) {
mp.put(temp2.pow, mp.getOrDefault(temp2.pow, 0) + temp2.coeff);
temp2 = temp2.next;
}
// Started from the end because higher power should
// come first and there should be "+" symbol in between
// so iterate up to second element and print last out of
// the loop.
boolean first = true;
for (Map.Entry<Integer, Integer> entry : mp.entrySet()) {
int pow = entry.getKey();
int coeff = entry.getValue();
if (first) {
System.out.print(coeff + "x^" + pow);
first = false;
} else {
System.out.print(" + " + coeff + "x^" + pow);
}
}
}
// Driver function
public static void main(String[] args) {
LinkedList poly1 = new LinkedList();
LinkedList poly2 = new LinkedList();
// Create first list of 5x^2 + 4x^1 + 2x^0
poly1.create_node(5, 2);
poly1.create_node(4, 1);
poly1.create_node(2, 0);
// Create second list of 5x^1 + 5x^0
poly2.create_node(5, 1);
poly2.create_node(5, 0);
System.out.print("1st Number: ");
poly1.show();
System.out.print("\n2nd Number: ");
poly2.show();
System.out.print("\nAdded polynomial: ");
// Function add two polynomial numbers
addPolynomial(poly1.head, poly2.head);
}
}
// This code is contributed by Prajwal Kandekar
# Python program for addition of two polynomials
# represented as linked lists
# Structure of Node used
class Node:
# Coefficient of the polynomial
def __init__(self, coeff, pow):
self.coeff = coeff
# Power of the polynomial
self.pow = pow
self.next = None
# Function to create new node
def create_node(x, y):
r = Node(x, y)
r.next = None
return r
# Display Linked list
def show(node):
if node is None:
return
while node.next is not None:
print(f"{node.coeff}x^{node.pow}", end="")
print(" + ", end="")
node = node.next
if node.next is not None:
print(" ", end="")
print(f"{node.coeff}x^{node.pow}")
# Function to print the required sum of a
# polynomial p1 and p2 as specified in output
def addPolynomial(p1, p2):
mp = {}
temp1 = p1
temp2 = p2
while temp1 is not None:
# Add coefficients of same power value
# map contains (powervalue, coeff) pair
mp[temp1.pow] = mp.get(temp1.pow, 0) + temp1.coeff
temp1 = temp1.next
while temp2 is not None:
mp[temp2.pow] = mp.get(temp2.pow, 0) + temp2.coeff
temp2 = temp2.next
# Started from the end because higher power should
# come first and there should be "+" symbol in between
# so iterate up to second element and print last out of
# the loop.
for power in sorted(mp.keys(), reverse=True):
print(f"{mp[power]}x^{power}", end="")
if power != sorted(mp.keys(), reverse=True)[-1]:
print(" + ", end="")
# Driver function
if __name__ == "__main__":
poly1 = None
poly2 = None
poly = None
# Create first list of 5x^2 + 4x^1 + 2x^0
poly1 = create_node(5, 2)
poly1.next = create_node(4, 1)
poly1.next.next = create_node(2, 0)
# Create second list of 5x^1 + 5x^0
poly2 = create_node(5, 1)
poly2.next = create_node(5, 0)
print("1st Number: ", end="")
show(poly1)
print("2nd Number: ", end="")
show(poly2)
print("Added polynomial: ", end="")
# Function to add two polynomial numbers
addPolynomial(poly1, poly2)
using System;
using System.Collections.Generic;
using System.Linq;
// Structure of Node used
public class Node
{
// Coefficient of the polynomial
public int coeff;
// Power of the polynomial
public int pow;
public Node next;
}
public class PolynomialAddition
{
// Function to create a new node
public static Node CreateNode(int x, int y)
{
Node r = new Node();
r.coeff = x;
r.pow = y;
r.next = null;
return r;
}
// Display Linked list
public static void Show(Node node)
{
if (node == null)
return;
while (node.next != null)
{
Console.Write($"{node.coeff}x^{node.pow}");
node = node.next;
if (node.next != null)
Console.Write(" + ");
}
}
/* Function to print the required sum of a
polynomial p1 and p2 as specified in output */
public static void AddPolynomial(Node p1, Node p2)
{
Dictionary<int, int> mp = new Dictionary<int, int>();
Node temp1 = p1;
Node temp2 = p2;
while (temp1 != null)
{
// Add coefficients of the same power value
if (!mp.ContainsKey(temp1.pow))
mp[temp1.pow] = temp1.coeff;
else
mp[temp1.pow] += temp1.coeff;
temp1 = temp1.next;
}
while (temp2 != null)
{
if (!mp.ContainsKey(temp2.pow))
mp[temp2.pow] = temp2.coeff;
else
mp[temp2.pow] += temp2.coeff;
temp2 = temp2.next;
}
// Started from the end because higher power should
// come first and there should be "+" symbol in between
// so iterate up to the second element and print the last out of the loop.
foreach (var item in mp.OrderByDescending(x => x.Key))
Console.Write($"{item.Value}x^{item.Key} + ");
}
// Driver function
public static void Main()
{
Node poly1 = null;
Node poly2 = null;
// Create the first list of 5x^2 + 4x^1 + 2x^0
poly1 = CreateNode(5, 2);
poly1.next = CreateNode(4, 1);
poly1.next.next = CreateNode(2, 0);
// Create the second list of 5x^1 + 5x^0
poly2 = CreateNode(5, 1);
poly2.next = CreateNode(5, 0);
Console.Write("1st Number: ");
Show(poly1);
Console.Write("\n2nd Number: ");
Show(poly2);
Console.Write("\nAdded polynomial: ");
// Function to add two polynomial numbers
AddPolynomial(poly1, poly2);
}
}
class Node {
constructor(coeff, pow) {
this.coeff = coeff;
this.pow = pow;
this.next = null;
}
}
// Function to create a new node
function createNode(x, y, temp) {
let r = new Node(x, y);
if (temp === null) {
temp = r;
} else {
let current = temp;
while (current.next !== null) {
current = current.next;
}
current.next = r;
}
return temp;
}
// Display Linked list
function show(node) {
if (node === null) {
return;
}
while (node.next !== null) {
console.log(`${node.coeff}x^${node.pow}`);
node = node.next;
if (node.next !== null) {
console.log(" + ");
}
}
}
// Function to print the required sum of a polynomial p1 and p2
function addPolynomial(p1, p2) {
let result = null;
let currentResult = null;
let current1 = p1;
let current2 = p2;
while (current1 !== null && current2 !== null) {
if (current1.pow === current2.pow) {
let sumCoeff = current1.coeff + current2.coeff;
if (sumCoeff !== 0) {
result = createNode(sumCoeff, current1.pow, result);
current1 = current1.next;
current2 = current2.next;
}
} else if (current1.pow > current2.pow) {
result = createNode(current1.coeff, current1.pow, result);
current1 = current1.next;
} else {
result = createNode(current2.coeff, current2.pow, result);
current2 = current2.next;
}
}
// Add any remaining terms from p1 and p2
while (current1 !== null) {
result = createNode(current1.coeff, current1.pow, result);
current1 = current1.next;
}
while (current2 !== null) {
result = createNode(current2.coeff, current2.pow, result);
current2 = current2.next;
}
// Reverse the result linked list for correct order
let reversedResult = null;
while (result !== null) {
let next = result.next;
result.next = reversedResult;
reversedResult = result;
result = next;
}
return reversedResult;
}
// Driver function
function main() {
let poly1 = null;
let poly2 = null;
// Create the first list of 5x^2 + 4x^1 + 2x^0
poly1 = createNode(5, 2, poly1);
poly1 = createNode(4, 1, poly1);
poly1 = createNode(2, 0, poly1);
// Create the second list of 5x^1 + 5x^0
poly2 = createNode(5, 1, poly2);
poly2 = createNode(5, 0, poly2);
console.log("1st Number: ");
show(poly1);
console.log("2nd Number: ");
show(poly2);
console.log("Added polynomial: ");
let result = addPolynomial(poly1, poly2);
show(result);
}
main();
Time Complexity: O((m + n)log(m+n)) where m and n are numbers of nodes in first and second lists respectively and we are using a map for adding the coefficients extra log(m+n) factor is added.
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