二叉树的常见操作

数据结构中树这一块儿一直是个难点和考点，刚好前几天在面实习生，面试过程中问到了二叉树并让写出代码，就想自己再写一遍二叉树的常见操作，目的为了留着以后用起来方便，于是乎，拿起书本又看了一遍，写下这些代码，编译环境是VS2012。

在Btree.h中的有下列声明和定义：

typedef struct BtNode//二叉树的数据结构
{
char data;
struct BtNode*lchild,*rchild;
}BtNode,*BTree;

void CreateBTree(BTree& Bt);//二叉树的创建

void PreOrder(BTree &Bt);//二叉树前序遍历

void PreOrderNon(BTree &Bt);//二叉树前序非递归遍历

void MidOrder(BTree &Bt);//二叉树中序遍历

void MidOrderNon(BTree &Bt);//二叉树非递归中序遍历

void LastOrder(BTree &Bt);//二叉树后序遍历

void LastOrderNon(BTree &Bt);//二叉树非递归后序遍历

void LevelOrder(BTree &Bt);//二叉树层次遍历

BtNode * CommonParent1(BtNode *root,BtNode *bt1,BtNode *bt2);//求最近公共父节点

int Depth(BTree &Bt);//二叉树的深度

int leafCount(BTree &Bt);//二叉树叶子节点的个数

void Exchagechild(BTree &Bt);//交换二叉树的左右孩子

bool IsBalanceTree(BTree &Bt);//是否为平衡二叉树

void DestroyTree(BtNode *Bt);//二叉树的销毁

在BTree.cpp中有一下函数实现：

#include<iostream>#include"Btree.h"#include<stack>#include<queue>using namespace std;//先序创建二叉树void CreateBTree(BTree &Bt){char ch;cin>>ch;if(ch == '#')   Bt=NULL;else{Bt = new BtNode;Bt->data = ch;CreateBTree(Bt->lchild);//递归创建左子树CreateBTree(Bt->rchild);//递归创建右子树}}//递归先序遍历void PreOrder(BTree &Bt){if(Bt == NULL) return ;cout<<Bt->data<<" ";PreOrder(Bt->lchild);PreOrder(Bt->rchild);}//非递归先序遍历void PreOrderNon(BTree &Bt){if (Bt == NULL) return ;stack<BTree> s;BTree p = Bt;while(!s.empty() || p != NULL){if( p != NULL){cout<<p->data<<" ";s.push(p);p = p->lchild;}if(!s.empty()){p = s.top();s.pop();p = p->rchild;}}}//递归中序遍历void MidOrder(BTree &Bt){if (Bt == NULL) return ;MidOrder(Bt->lchild);cout<<Bt->data<<" ";MidOrder(Bt->rchild);}//非递归中序遍历void MidOrderNon(BTree &Bt){if(Bt == NULL) return ;BTree p = Bt;stack<BTree> s;while( p != NULL || !s.empty() ){while( p != NULL){s.push(p);p = p->lchild;}if(!s.empty()){p = s.top();s.pop();cout<<p->data<<" ";p = p->rchild;}}}//递归后序遍历void LastOrder(BTree &Bt){if(Bt== NULL) return ;LastOrder(Bt->lchild);LastOrder(Bt->rchild);cout<<Bt->data<<" ";}//非递归后序遍历void LastOrderNon(BTree &Bt){if(Bt == NULL) return ;stack<BTree> s;BTree p = Bt;BTree visted = NULL;while(p != NULL || !s.empty()){while(p != NULL){s.push(p);p = p->lchild;}p = s.top();if(p->rchild == NULL || p->rchild == visted){cout<<p->data<<" ";visted = p;s.pop();p = NULL;}else{p = p->rchild;}}}//层次遍历void LevelOrder(BTree &Bt){queue<BTree> q;BTree temp = NULL;if(Bt != NULL) q.push(Bt);while(!q.empty()){temp = q.front();q.pop();cout<<temp->data<< " ";if(temp->lchild != NULL){q.push(temp->lchild);}if(temp->rchild != NULL){q.push(temp->rchild);}}}//求公共父节点,已知两个子节点BtNode * CommonParent(BtNode *root,BtNode *bt1,BtNode *bt2){if(root == NULL) return NULL;if(bt1 == root || bt2 == root) return root;BtNode *left = CommonParent(root->lchild,bt1,bt2);BtNode*right = CommonParent(root->rchild,bt1,bt2);if(left && right )return root;return left ?left:right;}//二叉树深度int Depth(BTree &Bt){if(Bt == NULL ) return 0;int len1 = Depth(Bt->lchild);int len2 = Depth(Bt->rchild);return len1>len2?len1+1:len2+1;}//叶子节点总数int leafCount(BTree &Bt){if(Bt == NULL) return 0;if(Bt->lchild== NULL && Bt->rchild == NULL){return 1;}return leafCount(Bt->lchild)+leafCount(Bt->rchild);}//交换左右孩子void Exchagechild(BTree &Bt){if(Bt == NULL) return ;BTree temp = NULL;if(Bt->lchild || Bt->rchild){temp = Bt->lchild;Bt->lchild = Bt->rchild;Bt->rchild = temp;Exchagechild(Bt->lchild);Exchagechild(Bt->rchild);}}//是否是平衡二叉树bool IsBalanceTree(BTree &Bt){if(Bt == NULL)return true;int ldepth = Depth(Bt->lchild);int rdepth = Depth(Bt->rchild);int  dis = ldepth-rdepth;if(dis >1 || dis <-1)  return false;return IsBalanceTree(Bt->lchild) && IsBalanceTree(Bt->rchild);}//销毁树void DestroyTree(BtNode *Bt){if(Bt == NULL)return ;DestroyTree(Bt->lchild);DestroyTree(Bt->rchild);delete Bt;}int main(){BTree T;CreateBTree(T);cout<<"PreOrder:";PreOrder(T);cout<<endl;cout<<"MidOrder:";MidOrder(T);cout<<endl;cout<<"LastOrder:";LastOrder(T);cout<<endl;cout<<"PreOrderNon:";PreOrderNon(T);cout<<endl;cout<<"LevelOrder:";LevelOrder(T);cout<<endl;cout<<"leafCount:";cout<<leafCount(T)<<endl;cout<<"Depth:";cout<<Depth(T)<<endl;cout<<"Exchangechild:";Exchagechild(T);PreOrder(T);cout<<endl;cout<<"MidOrderNon:";MidOrderNon(T);cout<<endl;cout<<"LastOrderNon:";LastOrderNon(T);cout<<endl;cout<<"IsBalanceTree:";if(IsBalanceTree(T))cout<<"IsBanlanceTree"<<endl;elsecout<<"IsNotBanlanceTree"<<endl;cout<<"CommonParent:";cout<<(CommonParent(T,T->lchild->lchild,T->rchild->rchild))->data;cout<<endl;return 0;}