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
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 usedstruct Node { // Coefficient of the polynomial int coeff; // Power of the polynomial int pow; Node* next;}; // Function to create new nodevoid 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 listvoid 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 functionint 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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