二叉树的【深/高度】【度为0/1/2的结点数】【遍历】【查找】【销毁】

与二叉树相关问题的求解：包括前中后，层次遍历，树的高度和深度，叶子结点的个数，度为1、2的结点个数，二叉树中数据的查找等相关问题的实现。
具体实现代码：

#include<iostream>using namespace std;struct tree  //存储数据的二叉树的节点；{int data;tree *left,*right;};struct Queue  //层次遍历的时候的队列；{tree *tr;Queue *next;};class Btree{private:static int n;static int m;public:tree *root;Queue *qu;Queue *pHead;Queue *pEnd;int flag;Btree(){root=NULL;qu=NULL;pHead=NULL;pEnd=NULL;flag=0;}void create_Btree(int);void Preorder(tree *);                  //先序遍历void inorder(tree *);                   //中序遍历void Postorder(tree *);                 //后序遍历void Ceng(tree *);                      //层次遍历int Hight_Length(tree *);               //计算树的高度和深度；int count(tree *);                      //计算二叉树的个数;int findleaf(tree *);                   //求二叉树叶子的个数int findnode(tree *);                   //求二叉树中度数为的结点数量；void Destory(tree *);             //销毁二叉树；void Push(tree *);int print_at_level(tree* T, int level);void print_by_level_1(tree* T,int level);int Find1(tree *,int value);int Find2(tree *,int value);tree* Pop();};   int Btree::n=0;int Btree::m=0;int Btree::Find1(tree *trr,int findvalue) //递归查找，需要注意函数的调用；{//当查找的节点不为空;if(trr){//找到则返回该值；if(trr->data==findvalue){flag=1;//递归调用的函数返回不是全部结束，而是结束当前继续执行其他；return findvalue;}//看在左子树还是右子树；if(trr->data > findvalue&& flag==0){Find1(trr->left,findvalue);}if(trr->data < findvalue&& flag==0){Find1(trr->right,findvalue);}}elsereturn -1;}int Btree::Find2(tree *trr,int findvalue)  //查找结点；{//当查找的节点不为空;while(trr){//找到则返回该值；if(trr->data==findvalue){return findvalue;}//看在左子树还是右子树；if(trr->data > findvalue){trr=trr->left;}if(trr->data < findvalue){trr=trr->right;}}return -1;}int Btree::print_at_level(tree*T, int level){ if (!T|| level < 0)  //当根节点为空或者是层次小于时，退出；return 0; if (0 == level)       //当LEVEL为时，t->left,每当减一次，就下一层；{ cout << T->data<< " "; return 1; } return print_at_level(T->left, level - 1) + print_at_level(T->right, level - 1); } void Btree::print_by_level_1(tree*T,int level) //按层打印；{ int i= 0;  for (i= 0; i<level;i++){ if (!print_at_level(T, i)) break; } cout << endl; } void Btree::Push(tree *p){Queue *pp=new Queue;pp->tr=p;pp->next=NULL;if(pHead==NULL){pHead=pp;pEnd=pHead;}else{pEnd->next=pp;pEnd=pp;}}tree* Btree::Pop(){if(!pHead){return NULL;}else{tree *trr=pHead->tr;Queue *temp=pHead;pHead=pHead->next;delete temp;return trr;}}void Btree::Ceng(tree *temp) //层次遍历；{tree *p=temp;while(p!=NULL){cout<<p->data<<" ";if(p->left){Push(p->left);}if(p->right){Push(p->right);}p=Pop();}}void Btree::Destory(tree *p)  //销毁二叉树；{if(NULL==p){return;}else{Destory(p->left);Destory(p->right);delete p;p=NULL;}}int Btree::Hight_Length(tree*p) //返回二叉树的高；{int Hleft,Hright;if(p==NULL)return 0;else{Hright=Hight_Length(p->right);Hleft=Hight_Length(p->left);return 1+(Hright>Hleft? Hright:Hleft);}}void Btree::create_Btree(int x) //循环创建二叉树；{tree *newnode=new tree;newnode->data=x;newnode->right=newnode->left=NULL;if(root==NULL)root=newnode;else{tree *back;tree *current=root;while(current!=NULL){back=current;if(current->data>x)current=current->left;elsecurrent=current->right;}if(back->data>x)back->left=newnode;elseback->right=newnode;}}int Btree::count(tree *p) //统计结点的个数；{if(p==NULL)return 0;elsereturn count(p->left)+count(p->right)+1;     //这是运用了函数嵌套即递归的方法。}void Btree::Preorder(tree *temp)    //这是先序遍历二叉树，采用了递归的方法。{if(temp!=NULL){cout<<temp->data<<" ";Preorder(temp->left);Preorder(temp->right);}}void Btree::inorder(tree *temp)      //这是中序遍历二叉树，采用了递归的方法。{if(temp!=NULL){inorder(temp->left);cout<<temp->data<<" ";inorder(temp->right);}}void Btree::Postorder(tree*temp)    //这是后序遍历二叉树，采用了递归的方法。{if(temp!=NULL){Postorder(temp->left);Postorder(temp->right);cout<<temp->data<<" ";}}int Btree::findleaf(tree *temp) //统计叶子结点；{if(temp==NULL)return 0;else{if(temp->left==NULL&& temp->right==NULL)return n+=1;else{findleaf(temp->left);findleaf(temp->right);}return n;}}int Btree::findnode(tree *temp) //度为1的结点{if(temp==NULL)return 0;else{if(temp->left!=NULL&& temp->right!=NULL){findnode(temp->left);findnode(temp->right);}if(temp->left!=NULL&& temp->right==NULL){m+=1;findnode(temp->left);}if(temp->left==NULL&& temp->right!=NULL){m+=1;findnode(temp->right);}}return m;}void main(){Btree A;// intarray[]={7,4,2,3,15,35,6,45,55,20,1,14,56,57,58};// int k; //15// k=sizeof(array)/sizeof(array[0]);int k;cout<<"please input the number of your data: "<<endl;cin>>k;int *array=new int[k];cout<<"please input "<<k<<"numbers:"<<endl;for(int i=0;i<k;i++)cin>>array[i];cout<<"建立排序二叉树顺序: "<<endl;for(int i=0;i<k;i++){cout<<array[i]<<" ";A.create_Btree(array[i]);}cout<<endl;cout<<"二叉树节点个数："<<A.count(A.root)<<endl;cout<<"二叉树叶子个数："<<A.findleaf(A.root)<<endl;cout<<"二叉树中度数为1的结点的数量为："<<A.findnode(A.root)<<endl;cout<<"二叉树的高度--高度为："<<A.Hight_Length(A.root)<<endl;cout<<"查找数字8的结果是："<<A.Find1(A.root,8)<<endl;A.flag=0;cout<<"查找数字8的结果是："<<A.Find2(A.root,8)<<endl;cout<<endl<<"先序遍历序列: "<<endl;A.Preorder(A.root);cout<<endl<<"中序遍历序列: "<<endl;A.inorder(A.root);cout<<endl<<"后序遍历序列: "<<endl;A.Postorder(A.root);cout<<endl<<"层次遍历序列: "<<endl;A.Ceng(A.root);cout<<endl<<"递归层次遍历序列: "<<endl;A.print_by_level_1(A.root,A.Hight_Length(A.root));cout<<endl;A.Destory(A.root);system("pause");}

二叉树的结构图：

运行结果：