堆排序算法(c++实现)

template <class T> void HeapSort(T a[], int n) { //创建一个最大堆 MaxHeap<T> H(1); H.Initialize(a,n,n); T x; for (int i = n-1; i >= 1; i--) { H.DeleteMax(x); a[i+1] = x; } H.Deactivate(); }

 

最大堆:

 

template<class T> class MaxHeap { public: MaxHeap(int MaxHeapSize = 10); ~MaxHeap() {delete [] heap;} int Size() const {return CurrentSize;} T Max() {if (CurrentSize == 0) throw OutOfBounds(); return heap[1];} MaxHeap<T>& Insert(const T& x); MaxHeap<T>& DeleteMax(T& x); void Initialize(T a[], int size, int ArraySize); void Deactivate() {heap = 0;} void Output() const; private: int CurrentSize, MaxSize; T *heap; }; template<class T> MaxHeap<T>::MaxHeap(int MaxHeapSize) { MaxSize = MaxHeapSize; heap = new T[MaxSize+1]; CurrentSize = 0; } template<class T> MaxHeap<T>& MaxHeap<T>::Insert(const T& x) { if (CurrentSize == MaxSize) throw NoMem(); //为x寻找应插入的位置 //i从新的叶节点开始，并沿着树上升 int i = ++CurrentSize; while (i != 1 && x > heap[i/2]) { heap[i] = heap[i/2]; // 将元素下移 i /= 2; // 移向父节点 } heap[i] = x; return *this; } template<class T> MaxHeap<T>& MaxHeap<T>::DeleteMax(T& x) { if (CurrentSize == 0) throw OutOfBounds(); x = heap[1]; T y = heap[CurrentSize--]; //最后一个元素 // 从根开始, 为y寻找合适的位置 int i = 1, // 堆的当前节点 ci = 2; // i的子节点 while (ci <= CurrentSize) { // 使heap[ci] 是i较大的子节点 if (ci < CurrentSize && heap[ci] < heap[ci+1]) ci++; // 能把y放入heap[i]吗? if (y >= heap[ci]) break;//能 //不能 heap[i] = heap[ci]; // 子节点上移 i = ci; // 下移一层 ci *= 2; } heap[i] = y; return *this; } template<class T> void MaxHeap<T>::Initialize(T a[], int size, int ArraySize) { delete [] heap; heap = a; CurrentSize = size; MaxSize = ArraySize; // 产生一个最大堆 for (int i = CurrentSize/2; i >= 1; i--) { T y = heap[i]; // 子树的根 // 寻找放置y的位置 int c = 2*i; // c 的父节点是y的目标位置 while (c <= CurrentSize) { // 使heap[c]是较大的子节点 if (c < CurrentSize && heap[c] < heap[c+1]) c++; // 能把y放入heap[c/2]吗? if (y >= heap[c]) break; // 能 // 不能 heap[c/2] = heap[c]; // 子节点上移 c *= 2; // 下移一层 } heap[c/2] = y; } } template<class T> void MaxHeap<T>::Output() const { cout << "The " << CurrentSize << " elements are"<< endl; for (int i = 1; i <= CurrentSize; i++) cout << heap[i] << ' '; cout << endl; }