排序算法——堆排序（C++）

堆排序分为大根堆和小根堆。

堆排思想：（采用树的概念来组织数据结构，在这里我是根据小根堆对数据进行排序）

①首先我们Insertheap一组数据，在插入的过程中采用向上调整（Shiftup）,每次将插入的最小值放在堆顶（heap[0]）.

②然后我们Removeheap创建好的堆，将heap[0]节点剔除作为返回值，每次都将最后一个叶子节点赋值到heap[0]，然后在执行向下调整（ShiftDown），查找到根节点以下最小的节点，重新创建小跟堆。

#include<iostream>
#include<assert.h>
using namespace std;
#define DEFAULT_SIZE 10
//堆排
class BigHeap
{
public:
    BigHeap(int sz = DEFAULT_SIZE)
    {
        capacity = sz > DEFAULT_SIZE ? sz : DEFAULT_SIZE;
        heap = new int[capacity];
        cursize = 0;
    }
    ~BigHeap()
    {
        delete[]heap;
        heap = NULL;
        capacity = cursize = 0;
    }
public:
    void Insert(int& x)
    {
        if (cursize >= capacity)
            return;
        heap[cursize] = x;
        ShiftUp(cursize);
        cursize++;
    }
    int RemoveHeap()
    {
        assert(cursize != 0);
        int key = heap[0];
        heap[0] = heap[cursize - 1];
        cursize--;
        ShiftDown(0);
        return key;
    }
public:
    void ShiftUp(int pos)
    {
        int i = (pos - 1) / 2;
        int j = pos;
        int tmp = heap[j];
        while (j > 0)
        {
            if (tmp < heap[i])
            {
                heap[j] = heap[i];
                j = i;
                i = (j - 1) / 2;
            }
            else
                break;
        }
        heap[j] = tmp;
    }
    void ShiftDown(int pos)
    {
        int i = pos;
        int j = i * 2 + 1; //父的左子树节点
        int tmp = heap[i];
        while (j < cursize)
        {
            if (j + 1 < cursize && heap[j] > heap[j + 1])
                j++;
            if (heap[j] < tmp)
            {
                heap[i] = heap[j];
                i = j;
                j = i * 2 + 1;
            }
            else
                break;
        }
        heap[i] = tmp;
    }
private:
    int* heap;
    int cursize;
    int capacity;
};

void HeapSort(int* a, int n)
{
    BigHeap small(n);
    for (int i = 0; i < n; i++)
        small.Insert(a[i]);
    for (int i = 0; i < n; i++)
    {
        a[i] = small.RemoveHeap();
    }
}
int main()
{
    int arr[] = { 23,12,11,2,5,16,26,37,59,29 };
    int n = sizeof(arr) / sizeof(int);
    HeapSort(arr, n);
    for (int i = 0; i < n; i++)
    {
        cout << arr[i] << " ";
    }
    cout << endl;
    
    return 0;
}