堆的排序及其基本操作

堆有大根堆和小根堆之分，这里主要实现大根堆，首先利用一个数组建立一个抽象的完全二叉树，例如

arr[]={ 1,2,3,6,5,10};

首先初始化建立一个二叉树，接着给二叉树排序成大根堆

Heap.h

#pragma once
#include<stdio.h>
#include<windows.h>
#include<assert.h>
typedef int HeapDataType;

typedef struct heap
{
	HeapDataType *a;
	size_t size;
	size_t capacity;
}heap;

void HeapInit(heap *hp, HeapDataType *_arr, size_t size)		
{
	assert(_arr&&size>0);
	hp->a = (HeapDataType*)malloc(sizeof(HeapDataType)*size);
	assert(hp->a);
	hp->size = size;
	hp->capacity = hp->size;
	for (size_t i = 0; i < size; i++)
	{
		hp->a[i] = _arr[i];
	}

}



void swap(HeapDataType* x, HeapDataType* y)
{
	HeapDataType tmp = *x;
	*x = *y;
	*y = tmp;
}


//从下往上调整  插入需要
void HeapAdjustUp(heap *hp, int child)
{
	assert(hp);
	int parent = (child - 1) / 2;
	while (child>0)
	{
		if (hp->a[parent] <hp->a[child])
		{
			HeapDataType tmp = hp->a[parent];
			hp->a[parent] = hp->a[child];
			hp->a[child] = tmp;
		}
		else
		{
			break;
		}

		child = parent;
		parent = (child - 1) / 2;

	}

}


//从上往下调整  在父亲节点的两子树中找到最大节点和其交换
void HeapAdjustDown(heap *hp, int root)
{
	assert(hp);
	size_t parent = root;
	size_t child = parent * 2 + 1;
	while (child < hp->size)
	{
		if ((child + 1)<hp->size && hp->a[child] < hp->a[child + 1])		
		{
			child++;
		}
		if (hp->a[parent] < hp->a[child])
		{
			swap(&hp->a[parent], &hp->a[child]);
		}
		parent = child;
		child = parent * 2 + 1;
	}
}


//插入元素
void HeapPush(heap *hp, HeapDataType x)
{
	assert(hp);
	if (hp ->size == hp->capacity)
	{
		hp->capacity *= 2;
		hp->a = realloc(hp->a, hp->capacity * sizeof(HeapDataType));
	}
	
	hp->a[hp->size] = x;
	//从上往下调整
	HeapAdjustUp(hp, hp->size);
	hp->size++;
	
}



//删除元素
void HeapPop(heap *hp)
{
	assert(hp);
	if (hp->size == 0)
	{
		return;
	}
	hp->a[0] = hp->a[hp->size - 1];
	hp->size--;
	HeapAdjustDown(hp, 0);

}



//返回元素个数
size_t Heap_Size(heap *hp)		
{
	assert(hp);
	return hp->size;
}


//返回最大元素
HeapDataType HeapTop(heap *hp)
{
	assert(hp);
	return hp->a[0];
}




//堆排序  必须借助从上往下调整 
void HeapSort(heap *hp)		
{
	assert(hp);
	int root = (hp->size - 1 ) / 2;		//找到最后一个非叶子节点
	while (root >= 0)
	{
		HeapAdjustDown(hp, root);
		root--;
	}
}




void test()
{
	heap hp;
	HeapDataType arr[] = { 1,2,3,6,5,10};
	size_t ret = sizeof(arr) / sizeof(arr[0]);
	HeapInit(&hp, arr, ret);
	HeapSort(&hp);
	HeapPush(&hp, 7);
	HeapPop(&hp);
	
	printf("最大值为: %d ", HeapTop(&hp));
	printf("\n");
	for (size_t i = 0; i < hp.size; i++)
	{
		printf("%d ", hp.a[i]);
	}

}

__________________________________________________________________________________________________________

main.c

#define _CRT_SECURE_NO_WARNINGS 1
#include"Heap.h"
int main()
{
	test();
	system("pause");
	return 0;
}