最小堆和最大堆的原理是一样的，学会其中一个另一个自然也会了。

接下来我们以最小堆为例：

堆的抽象模型就是二叉树，最小堆的意思是任一个节点的值都比此节点的子节点的值要小。

例子

上述数组所表示的堆是如下：

c++代码实现

#include <bits/stdc++.h>

using namespace std;


typedef struct minHeap
{   
    int *arr;//存储堆的数组指针
    int size;//元素的数目
    int cap;//堆的容量
}MinHeap;

MinHeap *createMinHeap(int cap)
{
    MinHeap *h = new MinHeap;
    h->arr = new int[cap];
    h->cap = cap;
    h->size = 0;
    return h;
}

void swap(int *a,int *b)
{
    int tmp = *a;
    *a = *b;
    *b = tmp;
}

//往堆中插值
void insertKey(MinHeap *h,int key)
{
    if(h->size == h->cap)
    {
        cout << "堆已满" << endl;
        return;
    }
    h->size++;
    int i = h->size-1;
    h->arr[i] = key;
    //(i-1)/2 是 索引为i的节点的父节点的索引
    while(i != 0 && h->arr[(i-1)/2] > h->arr[i])
    {
        swap(&h->arr[i],&h->arr[(i-1)/2]);
        i = (i-1)/2;
    }
}

//将索引为i的值减小为new_key
void decreaseKey(MinHeap *h,int i,int new_key)
{
    if(i > h->size-1)
        return;
    h->arr[i] = new_key;
    while(i != 0 && h->arr[(i-1)/2] > h->arr[i])
    {
        swap(&h->arr[i],&h->arr[(i-1)/2]);
        i = (i-1)/2;
    }
}

void MinHeapify(MinHeap *h,int index)
{
    int l = 2*index+1;//左节点的索引
    int r = 2*index+2;//右节点的索引
    int smallest = index;
    if(h->arr[smallest] > h->arr[l] && l < h->size)
        smallest = l;
    if(h->arr[smallest] > h->arr[r] && r < h->size)
        smallest = r;
    if(smallest != index)
    {
        swap(&h->arr[index],&h->arr[smallest]);
        MinHeapify(h,smallest);
    }
}

//获取最小值,并删除
int extractMin(MinHeap *h)
{
    if(h->size <= 0)
        return INT_MAX;
    if(h->size == 1)
    {
        h->size--;
        return h->arr[0];
    }

    int min = h->arr[0];
    h->arr[0] = h->arr[h->size-1];
    h->size--;
    MinHeapify(h,0);
    return min;
}
//获取最小值
int getMin(MinHeap *h)
{
    return h->arr[0];
}

int main(void)
{

    MinHeap *h = createMinHeap(7);
    insertKey(h,1);
    insertKey(h,2);
    insertKey(h,3);
    insertKey(h,7);
    insertKey(h,9);
    insertKey(h,8);
    insertKey(h,10);
    cout << extractMin(h) <<endl;
    cout << getMin(h) <<endl;
    decreaseKey(h,2, 0);
    cout << getMin(h)<< endl;;

    return 0;
}