二叉树相关功能的实现

一.本篇博客的主要内容

1.二叉树的前序遍历递归创建

2.拷贝二叉树（赋值运算符重载和拷贝构造函数）

3.二叉树的前序遍历

4.二叉树的中序遍历

5.二叉树的后序遍历

6.二叉树的层序遍历

7.二叉树的所有结点个数

8.二叉树的叶子结点个数

9.求第k层的结点个数

10.求二叉树的高度（深度）

11.在二叉树中查找某个元素，并返回元素结点位置

12.查找某个结点的双亲结点，并返回双亲结点位置

13.查找左右孩子，并返回孩子的结点位置

14.销毁二叉树

给出二叉树形象图：

注意：算法代码的实现是在类中封装起来的。下面给出代码

#define _CRT_SECURE_NO_WARNINGS 1#include<iostream>#include<queue>using namespace std;//二叉树的结点template<class T>struct BinTreeNode{BinTreeNode<T> *_pLeft;BinTreeNode<T>* _pRight;T _data;BinTreeNode(const T& data):_pLeft(NULL), _pRight(NULL), _data(data){}};template<class T>class Bintree//二叉树的封装{typedef BinTreeNode<T> Node;typedef BinTreeNode<T> *_PNode;public:Bintree(){_pRoot = NULL;}Bintree(const T *array, size_t size,const T& invalid)//前序遍历创建二叉树{size_t index = 0;//索引下标_CreatBinTree(_pRoot, array, size,index,invalid);}Bintree(const Bintree<T>& bt)//拷贝构造函数{_pRoot = _CopyBinTree(bt._pRoot);}Bintree<T>& operator=(const Bintree<T>& bt)//赋值运算符重载{if (this != &bt){_DestroyBinTree(_pRoot);_pRoot = _CopyBinTree(bt._pRoot);}return *this;}void _DestroyBinTree(_PNode& pRoot)//销毁二叉树{if (pRoot){_DestroyBinTree(pRoot->_pLeft);_DestroyBinTree(pRoot->_pRight);delete pRoot;pRoot = NULL;}}void PreOrder()//前序遍历{_PreOrder(_pRoot);cout << endl;}void InOrder()//中序遍历{_InOrder(_pRoot);cout << endl;}void PostORder()//后续遍历{_PostORder(_pRoot);cout << endl;}void LevelOrder()//层序遍历{_LevelOrder(_pRoot);}size_t Size()//结点个数{return _Size(_pRoot);}size_t GetLeafCount()//求叶子结点的个数{return _GetLeafCount(_pRoot);}size_t GetkLeveCount(size_t K)//求第K层的结点的个数，自己完成{return _GetkLeveCount(_pRoot, K);}size_t Height()//求二叉树的高度{return _Height(_pRoot);}_PNode Find(const T& data)//查找某个结点{return _Find(_pRoot,data);}_PNode FindParent(_PNode _Node)//查找双亲结点{return _FindParent(_pRoot,_Node);}_PNode Findlchild(_PNode _Node)//查找左孩子{_Findlchild( _Node);}_PNode FindRchild(_PNode _Node)//查找左孩子{_FindRchild( _Node);}~Bintree()//析构函数{_DestroyBinTree(_pRoot);}private://创建二叉树的算法代码void _CreatBinTree(_PNode& pRoot, const T* array, size_t size,size_t& index, const T& invalid){//创建跟结点+左子树+右子数if (index < size &&'#' != array[index]){pRoot = new Node(array[index]);_CreatBinTree(pRoot->_pLeft, array, size, ++index, invalid);_CreatBinTree(pRoot->_pRight, array, size, ++index, invalid);}}_PNode _CopyBinTree(_PNode pRoot)//拷贝树的算法代码{_PNode pNewRoot = NULL;if (pRoot){//拷贝根节点pNewRoot = new Node(pRoot->_data);//拷贝根节点的左子树if (pRoot->_pLeft)pNewRoot->_pLeft=_CopyBinTree(pRoot->_pLeft);//拷贝右子数if (pRoot->_pRight)pNewRoot->_pRight = _CopyBinTree(pRoot->_pRight);}return pNewRoot;}void _PreOrder(_PNode pRoot)//前序遍历算法代码{if (pRoot){cout << pRoot->_data <<"   ";_PreOrder(pRoot->_pLeft);_PreOrder(pRoot->_pRight);}}void _InOrder(_PNode pRoot)//中序遍历算法代码{if (pRoot){_InOrder(pRoot->_pLeft);cout << pRoot->_data << "   ";_InOrder(pRoot->_pRight);}}void _PostORder(_PNode pRoot)//后续遍历算法代码{if (pRoot){_PostORder(pRoot->_pLeft);_PostORder(pRoot->_pRight);cout << pRoot->_data << "   ";}}void _LevelOrder(_PNode pRoot)//层序遍历算法代码{queue<_PNode> q;if (pRoot == NULL){return;}q.push(pRoot);while (!q.empty()){_PNode pCur = q.front();//得到第一个cout << pCur->_data << "   ";q.pop();if (pCur->_pLeft)q.push(pCur->_pLeft);if (pCur->_pRight)q.push(pCur->_pRight);}}size_t _Size(_PNode pRoot)//所以的结点的个数{if (NULL == pRoot)return 0;return _Size(pRoot->_pLeft) + _Size(pRoot->_pRight) + 1;}size_t _GetLeafCount(_PNode  pRoot)//求叶子结点的个数{if (NULL==pRoot)return 0;else if (NULL == pRoot->_pLeft&&NULL==pRoot->_pRight)return 1;elsereturn _GetLeafCount(pRoot->_pLeft) + _GetLeafCount(pRoot->_pRight);}size_t _GetkLeveCount(_PNode pRoot, size_t  K)//求第k层的结点个数{if(NULL == pRoot || K < 1)return 0;if (1 == K)return 1;return _GetkLeveCount(pRoot->_pLeft, K - 1) + _GetkLeveCount(pRoot->_pRight, K - 1);}size_t _Height(_PNode pRoot)//数的高度{if (NULL == pRoot)return 0;else if(NULL == pRoot->_pLeft&&NULL == pRoot->_pRight)return 1;else{size_t leftHight = _Height(pRoot->_pLeft);size_t RightHight = _Height(pRoot->_pRight);return leftHight > RightHight ? leftHight+1 : RightHight+1;}}_PNode _Find(_PNode pRoot,const T& data)//查找指定的元素{if (NULL == pRoot)return NULL;if (pRoot->_data == data)return pRoot;_PNode pRet;if (pRet = _Find(pRoot->_pLeft, data))      return pRet;elsereturn _Find(pRoot->_pRight, data);}_PNode _FindParent(_PNode pRoot,_PNode _Node)//找结点的双亲{if (NULL == Root || NULL == _Node || pRoot == _Node)return NULL;if (pRoot->_pLeft == _Node || pRoot->_pRight == _Node)return pRoot;_PNode Parent;if (Parent = _FindParent(pRoot->_pLeft, _Node))return Parent;return _FindParent(pRoot->_pRight, _Node);}_PNode _Findlchild(_PNode pRoot)//找左孩子{return (NULL == pRoot) ? NULL : _Findlchild(pRoot->_pLeft);}_PNode _FindRchild(_PNode pRoot)//找右孩子{return (NULL == pRoot) ? NULL : _Findlchild(pRoot->_pRight);}private:_PNode _pRoot;};void test()//测试函数{char *pStr = "ABD##E##CF###";Bintree<char> bt(pStr, strlen(pStr), '#');cout << "前序遍历二叉树:";bt.PreOrder();cout << endl;cout << "层序遍历二叉树:";bt.LevelOrder();cout << endl;cout <<"二叉树所有结点个数:"<< bt.Size()<<endl;cout <<"二叉树叶子结点的个数:" <<bt.GetLeafCount()<<endl;cout << "二叉树的高度："<<bt.Height()<<endl;BinTreeNode<char> *p = bt.Find('B');cout <<"查找到了B:"<< p->_data << endl;;cout << "第3层的结点个数：" << bt.GetkLeveCount(3) << endl;;}int main(){test();system("pause");return 0;}

给出部分测试图：