Polynomials List with Addition

// CSC 2101 Data Structures And Algorithms
// Assignment 1: Adding Polynomials
// 1221417 Zaid Huda

#include "cmath"

class Node {
  public:
    int coef;   // coefficient of x
    int exp;    // degree of x
    Node *next; // pointer to next Node
};

class List {
  private:
    Node *head; // head of List

  public:
    List(){ head = NULL; } // head initilized to NULL (empty list)

    ~List(){
      clear();      // clear the list
      delete head;  // delete head
    }

    Node *first(){
      return head; // return head as first Node (or NULL for empty list)
    }

    void insert(int coef, int exp){
      Node *newNode = new Node;   // temporary Node with new info
      newNode->coef = coef;       // set new coef to argument coef
      newNode->exp = exp;         // set new exp to argument exp
      newNode->next = NULL;       // set next to NULL
      bool added = false;         // temporary boolean to check whether node added in or at the end of the list

      if (head == NULL) head = newNode; // if empty list, set head to new Node
      else {                            // iterate non empty list
        Node *currNode = head;     // set current Node to head
        Node *prevNode = head;     // set previous Node to head
        bool first = true;
        while(currNode){           // check if current Node is last
          if(currNode->exp < exp){ // check if current Node exp less than argument exp, if true
            if(first)              // if first Node
              head = newNode;      // set head to new Node
            else
              prevNode->next = newNode; // set new Node after previous Node
            newNode->next = currNode;   // set current Node after new Node
            added = true;               // set added to true
            break;                      // break the iteration
          }
          first = false;
          prevNode = currNode;       // set previous Node to current Node before continuing the loop
          currNode = currNode->next; // iterate the list
        }
        if(!added){
          prevNode->next = newNode; // if not added, add new Node at the end of list
        }
      }
    }

    void addNode(int coef, int exp){  // add a 'node' with coef and exp
      Node *currNode = head;      // set head as current Node
      bool newNode = true;        // temporary to check 'node' is unique
      while(currNode){            // iterate non empty list
        if(currNode->exp == exp){ // check if nodes has same exp
          currNode->coef += coef; // add coef of same exp
          newNode = false;        // set new as false ('node' is added to list)
          break;
        }
        currNode = currNode->next; // iterate the list
      }
      if(newNode) insert(coef, exp); // if it is new 'node', insert to list
    }

    void addPolynomials(List that){             // add that to this list
      Node *currNode = that.first();            // get first Node to start iteration
      while(currNode){                          // iterate that list
        addNode(currNode->coef, currNode->exp); // add every Node to this
        currNode = currNode->next;
      }
    }

    void display(){
      Node *currNode = head;
      bool first = true;
      while(currNode){
        int coef = currNode->coef, exp = currNode->exp;
        if(coef != 1){
          if (first)  std::cout << coef;
          else        std::cout << std::abs(coef);
        }
        if(exp != 1 && exp != 0) std::cout << "x^" << exp;
        else if(exp == 1) std::cout << 'x';
        if(coef == 1 && exp == 0) std::cout << "1";
        if(currNode->next){
          if(currNode->next->coef < 0) std::cout << " - ";
          else std::cout << " + ";
        }
        first = false;
        currNode = currNode->next;
      }
    }

    void clear(){
      Node *currNode = head;   // set head as current Node
      while(currNode){         // iterating the list
        head = currNode->next; // set head to next Node
        delete currNode;       // delete current Node
        currNode = head;       // set current Node as head
      }
    }
};