Adding two polynomials using Linked List using map

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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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:

// 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; 
} 

Output:

1st Number: 5x^2 + 4x^1 + 2x^0
2nd Number: 5x^1 + 5x^0
Added polynomial: 5x^2 + 9x^1 + 7x^0

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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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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