20120919-二叉樹 數據結構《數據結構與算法分析》

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二叉查找樹類的框架：

 1 template <typename Comparable>
 2 class BinarySearchTree  3 {  4 public:  5  BinarySearchTree();  6     BinarySearchTree(const BinarySearchTree & rhs)  7     ~BinarySearchTree();  8 
 9     const Comparable & findMin() const; 10     const Comparable & findMax() const; 11 
12     bool contains(const Comparable & x ) const; 13     bool isEmpty() const; 14     void printTree() const; 15 
16     void makeEmpty(); 17     void insert(const Comparable & x); 18     void remove(const Comparable & x); 19 
20     const BinarySearchTree & operator = (const BinarySearchTree & rhs); 21 
22 private: 23     struct BinaryNode 24  { 25  Comparable element; 26         BinaryNode *left; 27         BinaryNode *right; 28 
29         BinaryNode(const  Comparable & theElement,BinaryNode *lt,BinaryNode *rt):element(theElement),left(lt),right(rt){} 30  }; 31 
32     BinaryNode *root; 33 
34     void insert (const Comparable & x,BinaryNode * & t) const; 35     void remove (const Comparable & x ,BinaryNode * & t) const; 36     BinaryNode * findMin(BinaryNode *t) const; 37     BinaryNode * findMax(BinaryNode *t) const; 38     bool contains( const Comparable & x,BinaryNode * t) const; 39     void makeEmpty( BinaryNode * & t); 40     void printTree(BinaryNode *t) const; 41     BinaryNode * clone(BinaryNode *t) const; 42 };

contains    insert   remove三種操做遞歸列表：

bool contains (const Comparable & x) const { return contains(x,root) } void insert(const Comparable & x) { insert (x,root); } void remove(const Comparable & x) { remove(x,root); }

二叉查找樹的contains操做：

 1 bool contains(const Comparable & x,BinaryNode * t) const
 2 {  3     if( t == NUll )  4         return false;  5     else if ( x < t->element )  6         return contains(x,t->left );  7     else if (t->element < t)  8         return contains(x,t->right);  9     else
10         return true; 11 }

 

使用函數對象 實現 二叉查找樹：

template <typename Object,typename Comparator = less<Object>>
class BinarySearchTree { public: private: BinaryNode * root; Comparable isLessThan; bool contains( const Object & x,BinaryNode *t ) const { if(t == NULL) return false; else if (isLessThan(x,t->element)) return contains(x,t->left); else if (isLessThan(t->element,x)) return contains(x,t->right); else
                return true; } };

findMin方法的遞歸實現：

1 BinaryNode * findMin( BinaryNode * t) const
2 { 3     if( t == NULL) 4         return NULL; 5     if(t->left == NULL) 6         return t; 7     return findMin(t->left); 8 }

findMax方法的遞歸實現：

1 BinaryNode * findMax(BinaryNode * t) const
2 { 3     if(t != NULL) 4         while( t ->right !=NULL) 5             t = t->right; 6     return t; 7 }

二叉查找樹插入操做：

 1 void insert( const Comparable & x,BinaryNode * & t )  2 {  3     if( t== NULL)  4         t = new BinaryNode(x,NULL,NULL);  5     else if (x<t->element)  6         insert(x,t->left);  7     else if (t->element < x)  8         insert(x,t->right);  9     else
10  ; 11 }

二叉查找樹 刪除操做:

 1 void remove (const Comparable & x,BinaryNode * & t)  2 {  3     if( t == NULL)  4         return;  5     if( x <  t->element)  6         remove( x,t->left);  7     else if ( t->element < x)  8         remove(x,t->right);  9     else if (t->left != NULL && t->right!=NULL ) 10  { 11         t->element = findMin( t->right)->element; 12         remove(t->element , t->right); 13  } 14     else
15  { 16         BinaryNode *oldNode = t; 17         t = ( t->left !=NULL) ? t->left : t->right; 18  delete oldNode; 19  } 20 }

析構函數遞歸實現makeEmpty

~BinarySearchTree() { makEmpty(); } void makeEmpty(BinaryNode * & t) { if( t != NULL) { makeEmpty(t->left); makeEmpty(t->right); delete t; } t = NULL; }

operator= 遞歸實現clone：

 1 const BinarySearchTree & operator=( const BianrySearchTree & rhs)  2 {  3     if(this != &rhs)  4  {  5  makeEmpty();  6         root = clone(rhs.root);  7  }  8     return *this;  9 } 10 
11 BinaryNode * clone( BinaryNode * t) const
12 { 13     if( t == NULL) 14         return NULL; 15     return new BinaryNode ( t->element,clone(t->left),clone(t->right)); 16 }