Algorithm Part I:Priority Queues

1.binary heap实现

BinaryHeap.h

#ifndef BINARYHEAP_H
#define BINARYHEAP_H

class BinaryHeap
{
    public:
        BinaryHeap(int N);
        bool isEmpty();
        void exchange(int i,int j);
        void insert(int key);
        int delMax();
        int getMax();
        virtual ~BinaryHeap();
    protected:
    private:
        int N;
        int * data;
        void swim(int key);
        void sink(int key);
};

#endif // BINARYHEAP_H

BinaryHeap.cpp

#include "BinaryHeap.h"
#include <stdlib.h>

BinaryHeap::BinaryHeap(int N)
{
    this->N = 0;
    this->data = (int *)malloc(sizeof(int)*(N+1));
}

BinaryHeap::~BinaryHeap()
{
}

bool BinaryHeap::isEmpty()
{
    return N == 0;
}

void BinaryHeap::exchange(int i,int j)
{
    int temp = this->data[i];
    this->data[i] = this->data[j];
    this->data[j] = temp;
}

void BinaryHeap::swim(int key)
{
    while(key > 1 && data[key/2] < data[key])
    {
        exchange(key/2,key);
        key = key/2;
    }
}

void BinaryHeap::insert(int key)
{
    N++;
    data[N] = key;
    swim(N);
}

void BinaryHeap::sink(int key)
{
    while(key*2 <= N)
    {
        int j = key*2;
        if(j < N && data[j] < data[j+1])
            j++;
        if(data[key] >= data[j])
            break;
        else
        {
            exchange(key,j);
            key = j;
        }
    }
}

int BinaryHeap::delMax()
{
    int max = data[1];
    exchange(1,N-1);
    N--;
    sink(1);
    return max;
}

int BinaryHeap::getMax()
{
    return data[1];
}

main.c

#include <iostream>
#include "BinaryHeap.h"

using namespace std;

int main()
{
    BinaryHeap * bp = new BinaryHeap(10);
    bp->insert(3);
    bp->insert(2);
    bp->insert(1);
    bp->insert(5);
    bp->insert(8);
    bp->insert(7);
    cout << bp->getMax() << "\n";
    bp->delMax();
    cout << bp->getMax() << "\n";
    char c;
    cin >> c;
    return 0;
}

各操作时间复杂度的分析：

2.堆排序

堆排序的主要步骤：

（1）建堆

（2）依次移除最大元素，将它放到数组的尾端。

3.各种排序算法的分析

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