数据结构-堆（程序）

用程序实现：

（1）根据一个数组建立大根堆（最大堆）；

（2）插入数据，向上调整为大根堆；

（3）删除根节点数据，重新调整为大根堆；

（4）堆排序

程序如下：

#include<iostream>
#include<assert.h>
//#include"List.h"
#include<string>
//#include"Stack.h"
//#include"Tree.h"

#define MAX 100
using namespace std;

//根据数据创建堆
void CreateHeap(int *heap, int length);
//向下调整堆中元素
void AdjustDownHeap(int *heap, int i, int length);
//向上调整堆中元素
void AdjustUpHeap(int *heap, int i, int length);
//向堆中插入元素
int InsertHeap(int *heap, int length, int x);
//删除元素，每次只能删除根节点
int DeleteHeap(int *heap, int length);
//堆排序
void SortHeap(int *heap, int length);
int main()
{
	int heap[7] = {4,5,6,9,8,7};
	printf("根据所给数组元素创建大根堆：");
	CreateHeap(heap,6);
	for (int i = 0; i < 6;i++)
	{
		printf("%d ",heap[i]);
	}
	printf("\n");
	printf("插入元素10，向上调整：");
	InsertHeap(heap,6,10);
	for (int i = 0; i < 7; i++)
	{
		printf("%d ", heap[i]);
	}
	printf("\n");
	printf("删除根节点，调整为大根堆：");
	DeleteHeap(heap, 7);
	for (int i = 0; i < 6; i++)
	{
		printf("%d ", heap[i]);
	}
	printf("\n");
	printf("根据大根堆进行堆排序：");
	SortHeap(heap, 6);
	for (int i = 0; i < 6; i++)
	{
		printf("%d ", heap[i]);
	}
	printf("\n");
	return 0;
}

//根据数据创建堆，用数组创建堆
void CreateHeap(int *heap,int length)
{
	//向下调整创建大根堆
	for (int i = length / 2-1; i >= 0;i--)
	{
		AdjustDownHeap(heap, i, length);
	}
}

//向下调整堆中元素
void AdjustDownHeap(int *heap,int i,int length)
{
	int temp = 0;
	int nChild;
	while ((2 * i + 1)<length)
	{
		nChild = 2 * i + 1;
		//当存在左右儿子节点时，判断左儿子节点和右儿子节点大小关系
		if (heap[nChild]<heap[nChild + 1] && nChild+1<length)
		{
			nChild++;
		}
		if (heap[i]<heap[nChild])
		{
			temp = heap[i];
			heap[i] = heap[nChild];
			heap[nChild] = temp;
			i = nChild;
		}
		else
		{
			break;
		}
	}
}

//向堆中插入元素，将元素插入到堆最后位置，再向上调整
int InsertHeap(int *heap,int length,int x)
{
	int i = length;
	int temp = 0;
	heap[length] = x;
	while (i>0)
	{
		if (heap[i]>heap[(i-1)/2])
		{
			temp = heap[i];
			heap[i] = heap[(i - 1) / 2];
			heap[(i - 1) / 2] = temp;
			i = (i-1) / 2;
		}
		else
		{
			break;
		}
	}
	//返回插入位置
	return i;
}
//删除元素，只能删除根节点；将根节点换成堆最后一个元素，删除根节点，然后再向下调整使之变成大根堆
int DeleteHeap(int *heap, int length)
{
	int topNum = heap[0];
	heap[0] = heap[length-1];
	AdjustDownHeap(heap,0,length-1);
	//返回根节点元素
	return topNum;
}
//堆排序
void SortHeap(int *heap, int length)
{
	int index = length - 1;
	int temp = 0;
	int num = 0;
	while (index > 0)
	{
		temp = heap[0];
		heap[0] = heap[index];
		heap[index] = temp;
		AdjustDownHeap(heap, 0, index);
		index--;
	}

}