一個堆的c++實現

關於堆的描述可以參考：

http://www.cs.auckland.ac.nz/~jmor159/PLDS210/heaps.html

我的實現沒有用二叉樹，而是用數組。上文提到，由於堆是一種complete樹（complete，和完全樹略有區別），即子節點的上層是完全樹，而子節點從左向右嚴格排列，這種資料結構可以用數組很好類比。從第一層第一個節點為1開始，從左至右從上到下依次儲存。則，對於某個索引為i的節點，其左子節點和右子節點的索引分別為：

i * 2， i * 2 + 1

C++代碼：

#include <iostream>using namespace std;template<class T>class doubleHeap{public:    doubleHeap(        int _size,        int _type // 1 : max heap 2 : min heap        );    void extractTop(T &top);    void deleteTop();    bool addElement(T _new_element);    bool empty();    bool full();    void printHeap(int root, int level); // for debugprivate:    void swap(int i, int j);    int leftChild(int i);    int rightChild(int i);    int parent(int i);    bool comp(int i, int j); // if the nodes should exchangeprivate:    T *data;    int max_size;    int size;    int type;};template<class T>doubleHeap<T>::doubleHeap(int _size, int _type){    max_size = 10;    if(_size >= 10)        max_size = _size;    data = new T[max_size];    size = 0;    type = 1; // default max heap    if(_type == 1 || type == 2)        type = _type;}template<class T>void doubleHeap<T>::extractTop(T &top){    if(size == 0)        return;    top = data[0];}template<class T>void doubleHeap<T>::deleteTop(){    if(size == 0)        return;    data[0] = data[size - 1];    size --;    int cur = 0; // start from the root    int lChildIndex;    int rChildIndex;    // begin exchanging the node and check if it's been a heap    while(true)    {        if(cur >= size) // the heap is null            break;        rChildIndex = rightChild(cur);        lChildIndex = leftChild(cur);        if(lChildIndex >= size) // right child and left child has been a null            break;        else if(rChildIndex >= size) // rightChild null, left not        {            if(comp(cur, lChildIndex))            {                swap(cur, lChildIndex);                cur = lChildIndex;            }            else                break; // has been a heap        }        else // left and right are not null        {            if(comp(cur, rChildIndex) || comp(cur, lChildIndex))            {                if(comp(lChildIndex, rChildIndex))                {                    swap(cur, rChildIndex);                    cur = rChildIndex;                }                else                {                    swap(cur, lChildIndex);                    cur = lChildIndex;                }            }            else                break;        }    }}template<class T>bool doubleHeap<T>::addElement(T _new_element){    data[size] = _new_element;    size ++;    int cur = size - 1;    int parentIndex;    while(true)    {        if(cur == 0)            break;        parentIndex = parent(cur);        if(comp(parentIndex, cur))        {            swap(cur, parentIndex);            cur = parentIndex;        }        else            break;    }}template<class T>bool doubleHeap<T>::empty(){    return size == 0;}template<class T>bool doubleHeap<T>::full(){    return max_size == size;}template<class T>void doubleHeap<T>::swap(int i, int j){    T ex;    ex = data[i];    data[i] = data[j];    data[j] = ex;}template<class T>int doubleHeap<T>::leftChild(int i){    return 2 * (i + 1) - 1;}template<class T>int doubleHeap<T>::rightChild(int i){    return 2 * (i + 1);}template<class T>int doubleHeap<T>::parent(int i){    return (i + i) / 2 - 1;}template<class T>bool doubleHeap<T>::comp(int i, int j){    if(type == 1) // max heap    {        return data[i] < data[j];    }    else // min heap    {        return data[i] > data[j];    }}template<class T>void doubleHeap<T>::printHeap(int root, int level){    int i;    if(root >= size)        return;    printHeap(leftChild(root), level + 1);    for(i = 0; i < level; i ++)        cout << "\t";    cout << data[root] << endl;    printHeap(rightChild(root), level + 1);}int main(){    int a[] = {1, 10, 6, 23, 7, 8, 90, 12, 45, 76, 33, 25, 3, 17, 70, 10};    int i, aLen = 16, e;    doubleHeap<int> maxHeap(100, 1);    for(i = 0; i < aLen; i ++)    {        maxHeap.addElement(a[i]);    }    maxHeap.printHeap(0, 0);    // heap sort    while(!maxHeap.empty())    {        maxHeap.extractTop(e);        cout << e << " ";        maxHeap.deleteTop();    }    return 0;}

輸出：

                                1                        17                45                        12        76                        10                33                        1090                        8                25                        7        70                        6                23                        390 76 70 45 33 25 23 17 12 10 10 8 7 6 3 1