自主编程实现二叉树

在计算机科学中，二叉树是每个节点最多有两个子树的树结构。通常子树被称作“左子树”（left subtree）和“右子树”（right subtree）。二叉树常被用于实现二叉查找树和二叉堆。

二叉树的每个结点至多只有二棵子树(不存在度大于2的结点)，二叉树的子树有左右之分，次序不能颠倒。二叉树的第i层至多有2^{i-1}个结点；深度为k的二叉树至多有2^k-1个结点；对任何一棵二叉树T，如果其终端结点数为n_0，度为2的结点数为n_2，则n_0=n_2+1。

一棵深度为k，且有2^k-1个节点称之为满二叉树；深度为k，有n个节点的二叉树，当且仅当其每一个节点都与深度为k的满二叉树中，序号为1至n的节点对应时，称之为完全二叉树。

下面是顺序存储方式的二叉树实现代码：

#include <iostream>using namespace std ;class Tree{char* m_pTree;int m_nSize;     //数组大小 public:Tree(int size, char* pRoot);//创建树~Tree();//销毁树char SearchNode(int nodeindex);//根据索引寻找结点bool AddNode(int nodeindex, int direction, char* pNode);//添加结点bool DeleteNode(int nodeindex);//删除结点void TreeTraverse();};Tree::Tree(int size,char *pRoot)  //构造函数{    m_nSize = size ;m_pTree = new char[size] ;for(int i=0;i<size;i++){   m_pTree[i] = ' ' ;    //将二叉树数组所有内容赋为' '  代表空}m_pTree[0] = *pRoot ;}Tree::~Tree()    //析构函数{delete []m_pTree;m_pTree = NULL;}char Tree::SearchNode(int nodeindex)  //寻找数据  传入参数为节点位置{if(nodeindex < 0 || nodeindex >= m_nSize){return NULL;}if(m_pTree[nodeindex] == ' '){return NULL;}return m_pTree[nodeindex];}bool Tree::AddNode(int nodeindex, int direction, char* pNode)   //添加数据  nodeindex为父结点位置{if(nodeindex < 0 || nodeindex >= m_nSize){return false;}if(m_pTree[nodeindex] == 0){return false;}if(direction == 0)   //左子树{if(nodeindex*2+1 >= m_nSize){return false;}if(m_pTree[nodeindex*2+1] != ' ')   //该位置已有数据{return false;}m_pTree[nodeindex*2+1] = *pNode;    //在该位置赋值}if(direction == 1)   //右子树{if(nodeindex*2+2 >= m_nSize){return false;}if(m_pTree[nodeindex*2+2] != ' '){return false;}m_pTree[nodeindex*2+2] = *pNode;}return true;}bool Tree::DeleteNode(int nodeindex)  //删除结点{if(nodeindex < 0 || nodeindex >= m_nSize){return false;}if(m_pTree[nodeindex] == ' ')   //该位置为空 无数据{return false;}//char Node = m_pTree[nodeindex];  //cout<<Node << endl ;      //打印删除的结点数据m_pTree[nodeindex] = ' ';       //位置赋空return true;}void Tree::TreeTraverse()       //打印二叉树内容{for(int i = 0; i < m_nSize; i++){cout<<m_pTree[i]<<"  ";}cout<<endl ;}int main(){      char Node = 'a' ;  Tree * mTree = new Tree(20,&Node) ;      char node1 = 'b';  char node2 = 'c';  mTree->AddNode(0, 0, &node1);  mTree->AddNode(0, 1, &node2);  mTree->TreeTraverse() ;  cout<<mTree->SearchNode(2)<<endl ;  mTree->DeleteNode(2);  mTree->TreeTraverse() ;  return 0 ;}

       

  

下面是链表存储方式的二叉树实现代码：

#include <iostream>using namespace std ;class Node ;class Tree{Node * m_pRoot;public:Tree();//创建树~Tree();//销毁树Node * SearchNode(int nodeindex);//根据索引寻找结点bool AddNode(int nodeindex, int direction, Node* pNode);//添加结点bool DeleteNode(int nodeindex, Node* pNode);//删除结点void PreorderTraversal();//前序遍历void InorderTraversal();//中序遍历void PostorderTraversal();//后序遍历};class Node {public:Node();Node* SearchNode(int nodeindex);void DeleteNode();void PreorderTraversal();//前序遍历void InorderTraversal();//中序遍历void PostorderTraversal();//后序遍历int index;char data;Node* pLChild;Node* pRChild;Node* pParent;};Tree::Tree()//初始化这棵树{m_pRoot = new Node();}Tree::~Tree(){//DeleteNode(0, NULL);m_pRoot->DeleteNode();}Node* Tree::SearchNode(int nodeIndex){return m_pRoot->SearchNode(nodeIndex);}bool Tree::AddNode(int nodeIndex, int direction, Node* pNode)    //添加结点{Node* temp = SearchNode(nodeIndex);  //根据索引寻找结点if(temp == NULL){return false;}Node* node = new Node();if(node == NULL){return false;}node->index = pNode->index;node->data = pNode->data;node->pParent = temp;if(direction == 0){temp->pLChild = node;}else if(direction == 1){temp->pRChild = node;}return true;}bool Tree::DeleteNode(int nodeIndex, Node* pNode)  //删除结点{Node* temp = SearchNode(nodeIndex);if(temp == NULL){return false;}if(pNode != NULL){pNode->data = temp->data;}temp->DeleteNode();return true;}void Tree::PreorderTraversal()    //前序遍历{m_pRoot->PreorderTraversal();}void Tree::InorderTraversal()    //中序遍历{m_pRoot->InorderTraversal();}void Tree::PostorderTraversal()    //后序遍历{m_pRoot->PostorderTraversal();}Node::Node()     //结点构造函数{index = 0;data = ' ';pLChild = NULL;pRChild = NULL;pParent = NULL;}Node* Node::SearchNode(int nodeindex)   {if(this->index == nodeindex){return this;}Node *temp;if(this->pLChild != NULL){if(this->pLChild->index == nodeindex){return this->pLChild;}else {temp = this->pLChild->SearchNode(nodeindex);if(temp != NULL){return temp;}}}if(this->pRChild != NULL){if(this->pRChild->index == nodeindex){return this->pRChild;}else {temp = this->pRChild->SearchNode(nodeindex);if(temp != NULL){return temp;}}}return NULL;}void Node::DeleteNode(){if(this->pLChild != NULL){this->pLChild->DeleteNode();}if(this->pRChild != NULL){this->pRChild->DeleteNode();}if(this->pParent != NULL){if(this->pParent->pLChild == this){this->pParent->pLChild = NULL;}if(this->pParent->pRChild == this){this->pParent->pRChild = NULL;}}delete this;}void Node::PreorderTraversal(){cout<<this->index<<"    "<<this->data<<endl;if(this->pLChild != NULL){this->pLChild->PreorderTraversal();}if(this->pRChild != NULL){this->pRChild->PreorderTraversal();}}void Node::InorderTraversal(){if(this->pLChild != NULL){this->pLChild->InorderTraversal();}cout<<this->index<<"    "<<this->data<<endl;if(this->pRChild != NULL){this->pRChild->InorderTraversal();}}void Node::PostorderTraversal(){if(this->pLChild != NULL){this->pLChild->PostorderTraversal();}if(this->pRChild != NULL){this->pRChild->PostorderTraversal();}cout<<this->index<<"    "<<this->data<<endl;}int main(){Tree *tree = new Tree();Node* node1 = new Node;node1->index = 1;node1->data = 'a';Node* node2 = new Node;node2->index = 2;node2->data = 'b';Node* node3 = new Node;node3->index = 3;node3->data = 'c';tree->AddNode(0, 0, node1);tree->AddNode(0, 1, node2);tree->AddNode(1, 0, node3);//tree->DeleteNode(2, NULL);//tree->PreorderTraversal();//tree->InorderTraversal();tree->PostorderTraversal();delete tree;return 0;}