Priority Queue Using Heap

#include “Event.cpp” 
#include “Heap.cpp” 
#define PQMAX 30 

class PriorityQueue {
    public: 
        PriorityQueue() {
            heap = new Heap (PQMAX);
        }; 

        ~PriorityQueue() {
            delete heap; 
        };

        Event* remove() {

            if (!heap->isEmpty()) {
                Event* e;
                heap -> deleteMin(e);
                return e;
            }

            std::cout << "remove - queue is empty" << std::endl;
            return (Event*)NULL;
        };

        int insert (Event* e) {

            if (!heap->isFull()) {
                heap->insert(e);
                return 1;
            }

            std::cout << "insert queue is full" << std::endl;
        };

        int length() {
            return heap->getSize();
        }   

Equivalence Relations

A binary relation R over a set S is called equivalence relation if it has the following properties. 1. Reflexivity: \(\forall x \in S, x R x\)
2. Symmetry: \(\forall x \land y \in S, x R y \land y R x\) 3. Transitivity: \(\forall x, y, z \in S\) if \(x R y \land y R z\) then \(x R z\)