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Lecture 15, Thu 03/05

Heaps

Heaps

A Heap is a complete binary tree

MaxHeap

MinHeap

Examples

MaxHeap

MinHeap

Heaps are an efficient way to implement a Priority Queue

Heaps represented as an array

Heap Array

Insertion into a binary MaxHeap

Max Heap Insertion

Removing root element of a MaxHeap

Extract Root

Simple implementation of a MaxHeap class

// main.cpp
#include <unistd.h>
#include <iostream>

using namespace std;

class HeapEmptyException {};

class MaxHeap {
private:
    int* heapArray;
    int size;
    const static int CAPACITY = 100;
    void heapify(int index);
public:
    MaxHeap();
    int removeMax() throw (HeapEmptyException);
    void insert(int e);
    int getSize() { return size; }
    void printHeap();
};

void MaxHeap::heapify(int index) {
    int leftChild = 2 * index;
    int rightChild = 2 * index + 1;
    int largestIndex = index;

    if (leftChild <= size && 
    heapArray[leftChild] > heapArray[largestIndex]) {
        largestIndex = leftChild;
    }
    if (rightChild <= size &&
    heapArray[rightChild] > heapArray[largestIndex]) {
        largestIndex = rightChild;
    }
    if (largestIndex != index) {
        int temp = heapArray[index];
        heapArray[index] = heapArray[largestIndex];
        heapArray[largestIndex] = temp;
        heapify(largestIndex);
    }
}

MaxHeap::MaxHeap() {
    size = 0;
    heapArray = new int[CAPACITY];
}

void MaxHeap::insert(int e) {
    size++;
    heapArray[size] = e;
    int temp;
    int index = size;
    while (index > 1 && heapArray[index / 2] < heapArray[index]) {
        // swap parent and current node
        temp = heapArray[index];
        heapArray[index] = heapArray[index / 2];
        heapArray[index / 2] = temp;
        index = index / 2;
    }
}
int MaxHeap::removeMax() throw (HeapEmptyException) {
    if (size <= 0)
        throw HeapEmptyException();

    if (size == 1) {
        size--;
        return heapArray[1];
    }

    int index = 1;
    int max = heapArray[index];
    heapArray[index] = heapArray[size];
    size--;

    heapify(index);
    return max;
}

void MaxHeap::printHeap() {
    for (int i = 1; i <= size; i++) {
        cout << "i = " << i << ": " << heapArray[i] << endl;
    }
}

int main() {
    MaxHeap heap;
    heap.insert(3);
    heap.insert(2);
    heap.insert(1);
    heap.insert(15);
    heap.insert(5);
    heap.insert(4);
    heap.insert(45);
    cout << "---" << endl;
    heap.printHeap();
    cout << "---" << endl;

    cout << heap.getSize() << endl;
    cout << "---" << endl;

    // heapSort
    int times = heap.getSize();
    for (int i = 0; i < times; i++) {
        cout << heap.removeMax() << endl;
    }
}