# 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^0Output: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 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.