左式堆

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零路径长：从X到一个不具有两个儿子的结点的最短路径的长。

性质：

任一结点的零路径长比他的诸儿子结点的零路径长的最小值多1

父节点属性值小于子节点属性值；

堆中的任何节点，其左儿子的零路径长>=右儿子的零路径长；的二叉树。

下面是左式堆的类型声明：

 1 template <typename Comparable> 2 class LeftistHeap 3 { 4 public: 5     LeftistHeap(); 6     LeftistHeap(const LeftistHeap & rhs); 7     ~LeftistHeap(); 8  9     bool isEmpty() const;10     const Comparable & findMin() const;11 12     void insert(const Comparable & x);13     void deleteMin();14     void deleteMin(Comparable & minItem);15     void makeEmpty();16     void merge(LeftistHeap & rhs);17 18     const LeftistHeap & operator=(const LeftistHeap & rhs);19 20 private:21     struct LeftistNode22     {23         Comparable element;24         LeftistNode *left;25         LeftistNode *right;26         int npl;27 28         LeftistNode(const Comparable & theElement,LeftistNode *lt = NULL,LeftistNode *rt = NULL,int np=0)29             :element(theElement),left(lt),right(rt),npl(np)30         {31         }32     };33     LeftistNode *root;34     LeftistNode * merge(LeftistHeap *h1,LeftistHeap *h2);35     LeftistNode * merge1(LeftistHeap *h1,LeftistHeap *h2);36 37     void swapChildren(LeftistHeap *t);38     void reclaimMemory(LeftistHeap *t);39     LeftistNode * clone(LeftistHeap *t) const;40 }

合并左式堆的驱动实例：

void merge(LeftistHeap & rhs){    if(this == &rhs)        return;    root = merge(root,rhs.root );    rhs.root = NULL;}LeftistNode * merge(LeftistNode * h1,LeftistNode *h2){    if(h1 == NULL)        return h2;    if(h2 == NULL)        return h1;    if(h1->element < h2->element)        return mergel(h1,h2);    else        return mergel(h2,h1);}

合并左式堆的实例：

 1 LeftistNode * mergel(LeftistNode *h1,LeftistNode *h2) 2 { 3     if(h1->left == NULL) 4         h1->left = h2; 5     else 6     { 7         h1->right = merge(h1->right,h2); 8         if(h1->left->npl < h1->right->npl) 9             swapChildren(h1);10         h1->npl = h1->right->npl + 1;11     }12     return h1;13 }

左式堆的插入操作：

1 void insert(const Comparable & x)2 {3     root = merge(new LeftListNode(x),root);4 }

左式堆的deleteMin操作：

 1  void deleteMin() 2  { 3      if(isEmpty()) 4          throw UnderflowException(); 5      LeftistNode * oldRoot = root; 6      root = merge(root->left,root->right); 7      delete oldRoot; 8  } 9  void deleteMin(Comparable & minItem)10  {11     minItem = findMin();12     deleteMin();13  }

下面是左式堆的应用实例：

  1 #ifndef LeftistHeap_h__  2 #define LeftistHeap_h__  3 #define    NULL    0  4 // ******************公共操作*********************  5 // void insert( x )       --> 插入x  6 // deleteMin( minItem )   --> 删除最小元素  7 // Comparable findMin( )  --> 返回最小元素  8 // bool isEmpty( )        --> 为空返回true，否则返回false  9 // void makeEmpty( )      --> 清空 10 // void merge( rhs )      --> 合并rhs到本堆中 11 // ******************说明******************************** 12 //    代码根据数据结构与算法分析中的代码编写 13 template <typename Comparable> 14 class LeftistHeap 15 { 16 public: 17     LeftistHeap():root(NULL) 18     {} 19     LeftistHeap(const LeftistHeap &rhs) 20     { 21         *this = rhs; 22     } 23     ~LeftistHeap() 24     { 25         makeEmtpy(); 26     } 27     //插入x元素 28     void insert(const Comparable &x) 29     { 30         root = merge(new LeftistNode(x), root); 31     }; 32     //为空返回true，否则返回false 33     bool isEmpty() const 34     { 35         return root == NULL; 36     } 37     //找到最小元素并返回其值 38     const Comparable& findMin() const 39     { 40         if(!isEmpty()) 41             return root->element; 42     } 43     //删除最小元素 44     void deleteMin() 45     { 46         if(isEmpty()) 47             return; 48         LeftistNode* oldroot = root; 49         root = merge(root->left, root->right); 50         delete oldroot; 51     } 52     //删除最小元素，并将其值赋予minItem 53     void deleteMin(Comparable &minItem) 54     { 55         minItem = findMin(); 56         deleteMin(); 57     } 58     //清空 59     void makeEmtpy() 60     { 61         reclaimMemory(root); 62         root = NULL; 63     } 64     //将另一个堆合并到本堆中 65     void merge(LeftistHeap &rhs) 66     { 67         if(this == &rhs) 68             return; 69         root = merge(root, rhs.root); 70         rhs.root = NULL; 71     } 72     const LeftistHeap& operator=(const LeftistHeap &rhs) 73     { 74         if(this != &rhs) 75         { 76             makeEmtpy(); 77             root = clone(rhs.root); 78         } 79         return *this; 80     } 81 private: 82     struct LeftistNode 83     { 84         Comparable    element; 85         LeftistNode    *left; 86         LeftistNode    *right; 87         int            npl; 88         LeftistNode(const Comparable &e, LeftistNode *l = NULL, 89             LeftistNode *r = NULL, int n = 0) 90             :element(e), left(l), right(r), npl(n) 91         {} 92     }; 93     LeftistNode *root; 94     //处理非一般情况，并递归调用merge1 95     LeftistNode* merge(LeftistNode *h1, LeftistNode *h2) 96     { 97         if(h1 == NULL) 98             return h2; 99         if(h2 == NULL)100             return h1;101         if(h1->element < h2->element)102             merge1(h1, h2);103         else104             merge1(h2, h1);105     }106     //合并两个节点107     //h1是具有最小元素的根节点108     LeftistNode* merge1(LeftistNode *h1, LeftistNode *h2)109     {110         if(h1->left == NULL)111             h1->left = h2;112         else113         {114             h1->right = merge(h1->right, h2);115             if(h1->left->npl < h1->right->npl)116                 swapChildren(h1);117             h1->npl = h1->right->npl + 1;118         }119         return h1;120     }121     void swapChildren(LeftistNode *t)122     {123         LeftistNode *tmp = t->left;124         t->left = t->right;125         t->right = tmp;126     }127     void reclaimMemory(LeftistNode *t)128     {129         if(t != NULL)130         {131             reclaimMemory(t->left);132             reclaimMemory(t->right);133             delete t;134         }135     }136     LeftistNode *clone(LeftistNode *t) const137     {138         if(t == NULL)139             return NULL;140         else141             return new LeftistNode(t->element, clone(t->left), clone(t->right));142     }143 };144 #endif // LeftistHeap_h__

 1 #include "LeftistHeap.h" 2 #include <cstdlib> 3 #include <ctime> 4 #include <iostream> 5 using namespace std; 6 int main() 7 { 8     LeftistHeap<int> leftistHeapA, leftistHeapB, leftistHeapC; 9     srand((unsigned)time(0));  10     for(int i=0; i< 1000; i++)  11     {  12         int t = rand();   13         leftistHeapA.insert(t);14     }15     for(int i=0; i< 1000; i++)  16     {  17         int t = rand();   18         leftistHeapB.insert(t);19     }20     leftistHeapA.merge(leftistHeapB);21     leftistHeapA.merge(leftistHeapC);22     int t;23     while(leftistHeapA.isEmpty() == false)24     {25         leftistHeapA.deleteMin(t);26         cout<<t<<" ";27     }28     cout<<endl;29     getchar();30     return 0;31 }

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