数据结构-二叉堆

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二叉堆：堆是一颗完全二叉树，即除了底层外都被填满，底层从左到右填入的二叉树，注意不是满二叉树；

堆的特性：最大堆，堆顶元素始终为最大值，任一节点的左右儿子则均小于该节点，最小堆则相反

堆由于其特性可以以数组实现并且不大量浪费空间；

当该节点为位置为i时，其左儿子位置为2i，右儿子为2i+1;

root节点应在下标为1的位置；

这里实现了最大堆

/***********************************************     >  Filename: Heap.cpp     >  Author:   Pyt     >  Create:   2017-08-04 16:19:49************************************************/#include <iostream>#include <vector>using namespace std;template<typename T>class Heap{public:    Heap();    explicit Heap(const vector<T> &t);    T top() const;    void push(const T &t);    void pop();    bool empty() const;private:    vector<T> tree;    size_t cursize;    void buildHeap();    void percolateDown(int hole);};/***默认构造****/template<typename T>Heap<T>::Heap() : tree(100), cursize(0){}/****vector建堆****/template<typename T>Heap<T>::Heap(const vector<T> &t) : tree(t.size()+10), cursize(t.size()){    for(int i=0; i<t.size(); i++)      tree[i+1] = t[i];    buildHeap();}/***返回堆顶元素****/template<typename T>T Heap<T>::top() const{    if(!empty())      return tree[1];}/****插入元素*****/template<typename T>void Heap<T>::push(const T &t){    if(cursize == tree.size()-1)      tree.resize(tree.size()*2);    size_t hole = ++cursize;    for(; hole>1 && tree[hole/2]<t; hole /= 2)      tree[hole] = tree[hole/2];    tree[hole] = t;}/****删除堆顶元素****/template<typename T>void Heap<T>::pop(){    if(empty())      return ;    T tmp = tree[cursize--];    tree[1] = tmp;    percolateDown(1);}/***判空****/template<typename T>bool Heap<T>::empty() const{    return cursize == 0;}/****私有函数将无序数组建堆****/template<typename T>void Heap<T>::buildHeap(){    for(int i=cursize/2; i>=1; i--)      percolateDown(i);}/***私有函数下滤*****/template<typename T>void Heap<T>::percolateDown(int hole){    T tmp = tree[hole];    int child;    for( ; hole*2 <= cursize; hole = child)    {        child = hole*2;        if(child!=cursize && tree[child+1]>tree[child])          child++;        if(tree[child] > tmp)          tree[hole] = tree[child];        else          break;    }    tree[hole] = tmp;}int main(){    vector<int> a = {5, 2, 1, 7, 4, 3, 9, 8};    Heap<int> q(a);    Heap<int> p;    p = q;    while(!p.empty())    {        cout << p.top() << endl;        p.pop();    }    cout << p.empty() << endl;}

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