Adding two polynomials using Linked List
Last Updated :
13 Sep, 2024
Given two polynomial numbers represented by a linked list. The task is to add these lists meaning the coefficients with the same variable powers will be added.
Note: Given polynomials are sorted in decreasing order of power.
Example:
Input:
head1: [[5, 2], [4, 1], [2, 0]]
head2: [[5, 1], [5, 0]]
Output: [[5, 2], [9, 1], [7, 0]]
Explanation:
Input:
head1: [[5, 3], [4, 2], [2, 0]]
head2: [[5, 1], [-5, 0]]
Output: [[5, 3], [4, 2], [5, 1], [-3, 0]]
Explanation: head1 can be represented as 5x^3 + 4x^2 + 2 , head2 can be represented as 5x - 5, add both the polynomials to get 5x^3 + 4x^2 + 5x - 3
[Expected Approach - 1] Using Recursion - O(m+n) Time and O(max(m,n)) Space:
The idea is to recursively check the heads of both lists. If one of the heads is NULL, then return the other head. Otherwise, compare the power of both nodes. If the power of one list is greater than the other, then recursively find the next node of the greater power list. Otherwise, store the sum of coefficients in one list, and return its head.
Below is the implementation of the above approach:
C++
// C++ program to add two polynomials
#include <bits/stdc++.h>
using namespace std;
class Node {
public:
int coeff;
int pow;
Node* next;
Node(int c, int p) {
coeff = c;
pow = p;
next = nullptr;
}
};
Node* addPolynomial(Node* head1, Node* head2) {
// if any list is empty, then return
// the other list.
if (head1 == nullptr) return head2;
if (head2 == nullptr) return head1;
// If head1.pow is greater, then recursively find
// its next node, and return head1.
if (head1->pow > head2->pow) {
Node* nextPtr = addPolynomial(head1->next, head2);
head1->next = nextPtr;
return head1;
}
// If head2.pow is greater, then recusrively find its
// next node, and return head2.
else if (head1->pow < head2->pow) {
Node* nextPtr = addPolynomial(head1, head2->next);
head2->next = nextPtr;
return head2;
}
// else store the sum of head1.coeff and head2.coeff in
// head1->coeff, then find its next node and return head1.
Node* nextPtr = addPolynomial(head1->next, head2->next);
head1->coeff += head2->coeff;
head1->next = nextPtr;
return head1;
}
void printList(Node* head) {
Node* curr = head;
while (curr != nullptr) {
cout << curr->coeff << "," << curr->pow <<" ";
curr = curr->next;
}
cout<<endl;
}
int main() {
// 1st polynomial: 5x^2+4x^1+2x^0
Node* head1 = new Node(5,2);
head1->next = new Node(4,1);
head1->next->next = new Node(2,0);
// 2nd polynomial: -5x^1-5x^0
Node* head2 = new Node(-5,1);
head2->next = new Node(-5,0);
Node* head = addPolynomial(head1, head2);
printList(head);
}
// C program to add two polynomials
#include <stdio.h>
#include <stdlib.h>
struct Node {
int coeff;
int pow;
struct Node* next;
};
struct Node* createNode(int c, int p);
struct Node* addPolynomial(struct Node* head1, struct Node* head2) {
// if any list is empty, then return
// the other list.
if (head1 == NULL) return head2;
if (head2 == NULL) return head1;
// If head1.pow is greater, then recursively find
// its next node, and return head1.
if (head1->pow > head2->pow) {
struct Node* nextPtr =
addPolynomial(head1->next, head2);
head1->next = nextPtr;
return head1;
}
// If head2.pow is greater, then recursively find its
// next node, and return head2.
else if (head1->pow < head2->pow) {
struct Node* nextPtr =
addPolynomial(head1, head2->next);
head2->next = nextPtr;
return head2;
}
// else store the sum of head1.coeff and head2.coeff in
// head1->coeff, then find its next node and return head1.
struct Node* nextPtr =
addPolynomial(head1->next, head2->next);
head1->coeff += head2->coeff;
head1->next = nextPtr;
return head1;
}
void printList(struct Node* head) {
struct Node* curr = head;
while (curr != NULL) {
printf("%d,%d ", curr->coeff, curr->pow);
curr = curr->next;
}
printf("\n");
}
struct Node* createNode(int c, int p) {
struct Node* newNode =
(struct Node*)malloc(sizeof(struct Node));
newNode->coeff = c;
newNode->pow = p;
newNode->next = NULL;
return newNode;
}
int main() {
// 1st polynomial: 5x^2+4x^1+2x^0
struct Node* head1 = createNode(5, 2);
head1->next = createNode(4, 1);
head1->next->next = createNode(2, 0);
// 2nd polynomial: -5x^1-5x^0
struct Node* head2 = createNode(-5, 1);
head2->next = createNode(-5, 0);
struct Node* head = addPolynomial(head1, head2);
printList(head);
return 0;
}
// Java program to add two polynomials
class Node {
int coeff;
int pow;
Node next;
Node(int c, int p) {
coeff = c;
pow = p;
next = null;
}
}
class Main {
static Node addPolynomial(Node head1, Node head2) {
// if any list is empty, then return
// the other list.
if (head1 == null) return head2;
if (head2 == null) return head1;
// If head1.pow is greater, then recursively find
// its next node, and return head1.
if (head1.pow > head2.pow) {
Node nextPtr = addPolynomial(head1.next, head2);
head1.next = nextPtr;
return head1;
}
// If head2.pow is greater, then recursively find its
// next node, and return head2.
else if (head1.pow < head2.pow) {
Node nextPtr = addPolynomial(head1, head2.next);
head2.next = nextPtr;
return head2;
}
// else store the sum of head1.coeff and head2.coeff in
// head1.coeff, then find its next node and return head1.
Node nextPtr = addPolynomial(head1.next, head2.next);
head1.coeff += head2.coeff;
head1.next = nextPtr;
return head1;
}
static void printList(Node head) {
Node curr = head;
while (curr != null) {
System.out.print(curr.coeff + "," + curr.pow + " ");
curr = curr.next;
}
System.out.println();
}
public static void main(String[] args) {
// 1st polynomial: 5x^2+4x^1+2x^0
Node head1 = new Node(5, 2);
head1.next = new Node(4, 1);
head1.next.next = new Node(2, 0);
// 2nd polynomial: -5x^1-5x^0
Node head2 = new Node(-5, 1);
head2.next = new Node(-5, 0);
Node head = addPolynomial(head1, head2);
printList(head);
}
}
# Python program to add two polynomials
class Node:
def __init__(self, c, p):
self.coeff = c
self.pow = p
self.next = None
def add_polynomial(head1, head2):
# if any list is empty, then return
# the other list.
if head1 is None:
return head2
if head2 is None:
return head1
# If head1.pow is greater, then recursively find
# its next node, and return head1.
if head1.pow > head2.pow:
next_ptr = add_polynomial(head1.next, head2)
head1.next = next_ptr
return head1
# If head2.pow is greater, then recursively find its
# next node, and return head2.
elif head1.pow < head2.pow:
next_ptr = add_polynomial(head1, head2.next)
head2.next = next_ptr
return head2
# else store the sum of head1.coeff and head2.coeff in
# head1.coeff, then find its next node and return head1.
next_ptr = add_polynomial(head1.next, head2.next)
head1.coeff += head2.coeff
head1.next = next_ptr
return head1
def print_list(head):
curr = head
while curr is not None:
print(f"{curr.coeff},{curr.pow}", end=" ")
curr = curr.next
print()
if __name__ == "__main__":
# 1st polynomial: 5x^2+4x^1+2x^0
head1 = Node(5, 2)
head1.next = Node(4, 1)
head1.next.next = Node(2, 0)
# 2nd polynomial: -5x^1-5x^0
head2 = Node(-5, 1)
head2.next = Node(-5, 0)
head = add_polynomial(head1, head2)
print_list(head)
// C# program to add two polynomials
class Node {
public int coeff;
public int pow;
public Node next;
public Node(int c, int p) {
coeff = c;
pow = p;
next = null;
}
}
class GfG {
static Node AddPolynomial(Node head1, Node head2) {
// if any list is empty, then return
// the other list.
if (head1 == null) return head2;
if (head2 == null) return head1;
Node nextPtr;
// If head1.pow is greater, then recursively find
// its next node, and return head1.
if (head1.pow > head2.pow) {
nextPtr = AddPolynomial(head1.next, head2);
head1.next = nextPtr;
return head1;
}
// If head2.pow is greater, then recursively find its
// next node, and return head2.
else if (head1.pow < head2.pow) {
nextPtr = AddPolynomial(head1, head2.next);
head2.next = nextPtr;
return head2;
}
// else store the sum of head1.coeff and head2.coeff in
// head1.coeff, then find its next node and return head1.
nextPtr = AddPolynomial(head1.next, head2.next);
head1.coeff += head2.coeff;
head1.next = nextPtr;
return head1;
}
static void PrintList(Node head) {
Node curr = head;
while (curr != null) {
System.Console.Write(curr.coeff + "," + curr.pow + " ");
curr = curr.next;
}
System.Console.WriteLine();
}
static void Main(string[] args) {
// 1st polynomial: 5x^2+4x^1+2x^0
Node head1 = new Node(5, 2);
head1.next = new Node(4, 1);
head1.next.next = new Node(2, 0);
// 2nd polynomial: -5x^1-5x^0
Node head2 = new Node(-5, 1);
head2.next = new Node(-5, 0);
Node head = AddPolynomial(head1, head2);
PrintList(head);
}
}
// JavaScript program to add two polynomials
class Node {
constructor(c, p) {
this.coeff = c;
this.pow = p;
this.next = null;
}
}
function addPolynomial(head1, head2) {
// if any list is empty, then return
// the other list.
if (head1 === null) return head2;
if (head2 === null) return head1;
// If head1.pow is greater, then recursively find
// its next node, and return head1.
if (head1.pow > head2.pow) {
let nextPtr = addPolynomial(head1.next, head2);
head1.next = nextPtr;
return head1;
}
// If head2.pow is greater, then recursively find its
// next node, and return head2.
else if (head1.pow < head2.pow) {
let nextPtr = addPolynomial(head1, head2.next);
head2.next = nextPtr;
return head2;
}
// else store the sum of head1.coeff and head2.coeff in
// head1.coeff, then find its next node and return head1.
let nextPtr = addPolynomial(head1.next, head2.next);
head1.coeff += head2.coeff;
head1.next = nextPtr;
return head1;
}
function printList(head) {
let curr = head;
while (curr !== null) {
console.log(curr.coeff+","+curr.pow + " ");
curr = curr.next;
}
console.log();
}
// 1st polynomial: 5x^2+4x^1+2x^0
let head1 = new Node(5, 2);
head1.next = new Node(4, 1);
head1.next.next = new Node(2, 0);
// 2nd polynomial: -5x^1-5x^0
let head2 = new Node(-5, 1);
head2.next = new Node(-5, 0);
let head = addPolynomial(head1, head2);
printList(head);
Time Complexity: O(m+n), where m and n are the number of nodes in both the lists.
Auxiliary Space: O(max(m,n))
[Expected Approach] Using Iterative Method - O(m+n) Time and O(1) Space:
The idea is to create a dummy node which will act as the head of resultant list. Start traversing both the lists, if list1->pow if not equal to list2->pow, then Link the node with greater power to the resultant list. Otherwise, add the sum of list1->coeff + list2->coeff to the resultant list.
Below is the implementation of the above approach:
C++
// C++ program to add two polynomials
#include <bits/stdc++.h>
using namespace std;
class Node {
public:
int coeff;
int pow;
Node* next;
Node(int c, int p) {
coeff = c;
pow = p;
next = nullptr;
}
};
Node* addPolynomial(Node* head1, Node* head2) {
Node* dummy = new Node(0, 0);
// Node to append other nodes to the end
// of list
Node* prev = dummy;
Node* curr1 = head1, *curr2 = head2;
while (curr1 != nullptr && curr2 != nullptr) {
// if curr2.pow > curr1.pow, then
// append curr2 to list
if (curr1->pow < curr2->pow) {
prev->next = curr2;
prev = curr2;
curr2 = curr2->next;
}
// if curr1.pow > curr2.pow, then
// append curr2 to list
else if (curr1->pow > curr2->pow) {
prev->next = curr1;
prev = curr1;
curr1 = curr1->next;
}
// else, add the sum of curr1->coeff and
// curr2->coeff to curr1->coeff, and append
// curr1 to the list
else {
curr1->coeff = curr1->coeff + curr2->coeff;
prev->next = curr1;
prev = curr1;
curr1 = curr1->next;
curr2 = curr2->next;
}
}
// if curr1 if not null, then append the rest
// to the list
if (curr1 != nullptr) {
prev->next = curr1;
}
// if curr2 if not null, then append the rest
// to the list
if (curr2 != NULL) {
prev->next = curr2;
}
return dummy->next;
}
void printList(Node* head) {
Node* curr = head;
while (curr != nullptr) {
cout << curr->coeff << "," << curr->pow << " ";
curr = curr->next;
}
cout<<endl;
}
int main() {
// 1st polynomial: 5x^2+4x^1+2x^0
Node* head1 = new Node(5,2);
head1->next = new Node(4,1);
head1->next->next = new Node(2,0);
// 2nd polynomial: -5x^1-5x^0
Node* head2 = new Node(-5,1);
head2->next = new Node(-5,0);
Node* head = addPolynomial(head1, head2);
printList(head);
}
// C program to add two polynomials
#include <stdio.h>
#include <stdlib.h>
struct Node {
int coeff;
int pow;
struct Node* next;
};
struct Node* createNode(int c, int p);
struct Node* addPolynomial(struct Node* head1, struct Node* head2) {
struct Node* dummy = createNode(0, 0);
// Node to append other nodes to the end
// of list
struct Node* prev = dummy;
struct Node *curr1 = head1, *curr2 = head2;
while (curr1 != NULL && curr2 != NULL) {
// if curr2.pow > curr1.pow, then
// append curr2 to list
if (curr1->pow < curr2->pow) {
prev->next = curr2;
prev = curr2;
curr2 = curr2->next;
}
// if curr1.pow > curr2.pow, then
// append curr2 to list
else if (curr1->pow > curr2->pow) {
prev->next = curr1;
prev = curr1;
curr1 = curr1->next;
}
// else, add the sum of curr1->coeff and
// curr2->coeff to curr1->coeff, and append
// curr1 to the list
else {
curr1->coeff = curr1->coeff + curr2->coeff;
prev->next = curr1;
prev = curr1;
curr1 = curr1->next;
curr2 = curr2->next;
}
}
// if curr1 is not null, then append the rest
// to the list
if (curr1 != NULL) {
prev->next = curr1;
}
// if curr2 is not null, then append the rest
// to the list
if (curr2 != NULL) {
prev->next = curr2;
}
return dummy->next;
}
void printList(struct Node* head) {
struct Node* curr = head;
while (curr != NULL) {
printf("%d,%d ", curr->coeff, curr->pow);
curr = curr->next;
}
printf("\n");
}
struct Node* createNode(int c, int p) {
struct Node* newNode =
(struct Node*)malloc(sizeof(struct Node));
newNode->coeff = c;
newNode->pow = p;
newNode->next = NULL;
return newNode;
}
int main() {
// 1st polynomial: 5x^2+4x^1+2x^0
struct Node* head1 = createNode(5, 2);
head1->next = createNode(4, 1);
head1->next->next = createNode(2, 0);
// 2nd polynomial: -5x^1-5x^0
struct Node* head2 = createNode(-5, 1);
head2->next = createNode(-5, 0);
struct Node* head = addPolynomial(head1, head2);
printList(head);
return 0;
}
// Java program to add two polynomials
class Node {
int coeff;
int pow;
Node next;
Node(int c, int p) {
coeff = c;
pow = p;
next = null;
}
}
class GfG {
static Node addPolynomial(Node head1, Node head2) {
Node dummy = new Node(0, 0);
// Node to append other nodes to the end
// of list
Node prev = dummy;
Node curr1 = head1, curr2 = head2;
while (curr1 != null && curr2 != null) {
// if curr2.pow > curr1.pow, then
// append curr2 to list
if (curr1.pow < curr2.pow) {
prev.next = curr2;
prev = curr2;
curr2 = curr2.next;
}
// if curr1.pow > curr2.pow, then
// append curr2 to list
else if (curr1.pow > curr2.pow) {
prev.next = curr1;
prev = curr1;
curr1 = curr1.next;
}
// else, add the sum of curr1.coeff and
// curr2.coeff to curr1.coeff, and append
// curr1 to the list
else {
curr1.coeff = curr1.coeff + curr2.coeff;
prev.next = curr1;
prev = curr1;
curr1 = curr1.next;
curr2 = curr2.next;
}
}
// if curr1 if not null, then append the rest
// to the list
if (curr1 != null) {
prev.next = curr1;
}
// if curr2 if not null, then append the rest
// to the list
if (curr2 != null) {
prev.next = curr2;
}
return dummy.next;
}
static void printList(Node head) {
Node curr = head;
while (curr != null) {
System.out.print(curr.coeff + "," + curr.pow + " ");
curr = curr.next;
}
System.out.println();
}
public static void main(String[] args) {
// 1st polynomial: 5x^2+4x^1+2x^0
Node head1 = new Node(5, 2);
head1.next = new Node(4, 1);
head1.next.next = new Node(2, 0);
// 2nd polynomial: -5x^1-5x^0
Node head2 = new Node(-5, 1);
head2.next = new Node(-5, 0);
Node head = addPolynomial(head1, head2);
printList(head);
}
}
# Python program to add two polynomials
class Node:
def __init__(self, c, p):
self.coeff = c
self.pow = p
self.next = None
def add_polynomial(head1, head2):
dummy = Node(0, 0)
# Node to append other nodes to the end
# of list
prev = dummy
curr1, curr2 = head1, head2
while curr1 is not None and curr2 is not None:
# if curr2.pow > curr1.pow, then
# append curr2 to list
if curr1.pow < curr2.pow:
prev.next = curr2
prev = curr2
curr2 = curr2.next
# if curr1.pow > curr2.pow, then
# append curr1 to list
elif curr1.pow > curr2.pow:
prev.next = curr1
prev = curr1
curr1 = curr1.next
# else, add the sum of curr1.coeff and
# curr2.coeff to curr1.coeff, and append
# curr1 to the list
else:
curr1.coeff = curr1.coeff + curr2.coeff
prev.next = curr1
prev = curr1
curr1 = curr1.next
curr2 = curr2.next
# if curr1 if not None, then append the rest
# to the list
if curr1 is not None:
prev.next = curr1
# if curr2 if not None, then append the rest
# to the list
if curr2 is not None:
prev.next = curr2
return dummy.next
def print_list(head):
curr = head
while curr is not None:
print(f"{curr.coeff},{curr.pow}", end=" ")
curr = curr.next
print()
if __name__ == "__main__":
# 1st polynomial: 5x^2+4x^1+2x^0
head1 = Node(5, 2)
head1.next = Node(4, 1)
head1.next.next = Node(2, 0)
# 2nd polynomial: -5x^1-5x^0
head2 = Node(-5, 1)
head2.next = Node(-5, 0)
head = add_polynomial(head1, head2)
print_list(head)
// C# program to add two polynomials
class Node {
public int coeff;
public int pow;
public Node next;
public Node(int c, int p) {
coeff = c;
pow = p;
next = null;
}
}
class GfG {
static Node AddPolynomial(Node head1, Node head2) {
Node dummy = new Node(0, 0);
// Node to append other nodes to the end
// of list
Node prev = dummy;
Node curr1 = head1, curr2 = head2;
while (curr1 != null && curr2 != null) {
// if curr2.pow > curr1.pow, then
// append curr2 to list
if (curr1.pow < curr2.pow) {
prev.next = curr2;
prev = curr2;
curr2 = curr2.next;
}
// if curr1.pow > curr2.pow, then
// append curr1 to list
else if (curr1.pow > curr2.pow) {
prev.next = curr1;
prev = curr1;
curr1 = curr1.next;
}
// else, add the sum of curr1.coeff and
// curr2.coeff to curr1.coeff, and append
// curr1 to the list
else {
curr1.coeff = curr1.coeff + curr2.coeff;
prev.next = curr1;
prev = curr1;
curr1 = curr1.next;
curr2 = curr2.next;
}
}
// if curr1 if not null, then append the rest
// to the list
if (curr1 != null) {
prev.next = curr1;
}
// if curr2 if not null, then append the rest
// to the list
if (curr2 != null) {
prev.next = curr2;
}
return dummy.next;
}
static void PrintList(Node head) {
Node curr = head;
while (curr != null) {
System.Console.Write(curr.coeff + "," + curr.pow + " ");
curr = curr.next;
}
System.Console.WriteLine();
}
static void Main(string[] args) {
// 1st polynomial: 5x^2+4x^1+2x^0
Node head1 = new Node(5, 2);
head1.next = new Node(4, 1);
head1.next.next = new Node(2, 0);
// 2nd polynomial: -5x^1-5x^0
Node head2 = new Node(-5, 1);
head2.next = new Node(-5, 0);
Node head = AddPolynomial(head1, head2);
PrintList(head);
}
}
// JavaScript program to add two polynomials
class Node {
constructor(c, p) {
this.coeff = c;
this.pow = p;
this.next = null;
}
}
function addPolynomial(head1, head2) {
let dummy = new Node(0, 0);
// Node to append other nodes to the end
// of list
let prev = dummy;
let curr1 = head1, curr2 = head2;
while (curr1 !== null && curr2 !== null) {
// if curr2.pow > curr1.pow, then
// append curr2 to list
if (curr1.pow < curr2.pow) {
prev.next = curr2;
prev = curr2;
curr2 = curr2.next;
}
// if curr1.pow > curr2.pow, then
// append curr1 to list
else if (curr1.pow > curr2.pow) {
prev.next = curr1;
prev = curr1;
curr1 = curr1.next;
}
// else, add the sum of curr1.coeff and
// curr2.coeff to curr1.coeff, and append
// curr1 to the list
else {
curr1.coeff = curr1.coeff + curr2.coeff;
prev.next = curr1;
prev = curr1;
curr1 = curr1.next;
curr2 = curr2.next;
}
}
// if curr1 if not null, then append the rest
// to the list
if (curr1 !== null) {
prev.next = curr1;
}
// if curr2 if not null, then append the rest
// to the list
if (curr2 !== null) {
prev.next = curr2;
}
return dummy.next;
}
function printList(head) {
let curr = head;
while (curr !== null) {
console.log(curr.coeff+","+curr.pow + " ");
curr = curr.next;
}
console.log();
}
// 1st polynomial: 5x^2+4x^1+2x^0
let head1 = new Node(5, 2);
head1.next = new Node(4, 1);
head1.next.next = new Node(2, 0);
// 2nd polynomial: -5x^1-5x^0
let head2 = new Node(-5, 1);
head2.next = new Node(-5, 0);
let head = addPolynomial(head1, head2);
printList(head);
Time Complexity: O(m + n) where m and n are number of nodes in first and second lists respectively.
Auxiliary Space: O(1)
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