Data Structures CSCI 132, Fall 2018 Lecture 13 Queues as Linked Lists, Polynomial Arithmetic

1. Data StructuresCSCI 132, Fall 2018Lecture 13Queues as Linked Lists, Polynomial Arithmetic

2. Queues as Linked Lists front entry 1 entry 2 entry 3 class Queue { public: Queue(); bool empty() const; Error_code append (const Queue_entry &item); Error_code serve( ); Error_code retrieve(Queue_entry &item) const; ~Queue(); Queue(const Queue &original); void operator =(const Queue &original); protected: Node *front, *rear; }; rear

3. append( ) implementation Error_code Queue :: append(const Queue_entry &item) { }

4. append( ) implementation Error_code Queue :: append(const Queue_entry &item) { Node *new_rear = new Node(item); }

5. Implementing serve( ) Error_code Queue :: serve( ) { }

6. coeff exponent p 3 2 4 1 -1 0 Polynomial Arithmetic p = 3x2 + 4x -1 q = x3 - 2x2 - 4x + 7 r = p + q = x3 + x2 + 6 Rules: Order elements from highest exponent to lowest. Terms with coefficient of zero are not included. No two terms have the same exponent.

7. The Term struct struct Term { int degree; double coefficient; Term (int exponent = 0, double scalar = 0); }; Term :: Term(int exponent, double scalar) /* Post: The Term is initialized with the given coefficient and exponent, or with default parameter values of 0. */ { degree = exponent; coefficient = scalar; }

8. The Polynomial class typedef Term Queue_entry; class Polynomial: private Extended_queue { // Use private inheritance. public: void read( ); void print( ) const; void equals_sum(Polynomial p, Polynomial q); void equals_difference(Polynomial p, Polynomial q); void equals_product(Polynomial p, Polynomial q); Error_code equals_quotient(Polynomial p, Polynomial q); int degree( ) const; private: void mult_term(Polynomial p, Term t); };

9. Polynomial addition void Polynomial :: equals_sum(Polynomial p, Polynomial q) { clear( ); while (!p.empty( ) || !q.empty( )) { Term p_term, q_term; if (p.degree( ) > q.degree( )) { p.serve_and_retrieve(p_term); append(p_term); } else if (q.degree( ) > p.degree( )) { q.serve_and_retrieve(q_term); append(q_term); } else { p.serve_and_retrieve(p_term); q.serve_and_retrieve(q_term); if (p_term.coefficient + q_term.coefficient != 0) { Term answer_term(p_term.degree, p_term.coefficient + q_term.coefficient); append(answer_term); } } } }

10. The degree( ) function int Polynomial :: degree( ) const { if (empty( )) { return -1; } Term lead; retrieve(lead); return lead.degree; }