面试题之重构二叉树

重构二叉树

• 引言

好久没写代码了，手有点生了。。。博客如有不好之处，还请指出，谢谢大家一直对我的关注。相信自己，相信未来。有句话说得好，不怕贼偷就怕贼惦记，举一反三，人生中的种种问题也是如此，不怕我们解决，就怕我们一直惦记着它。愿我们各种前进，各种加油。

• 题目

知道二叉树中序遍历和先序遍历的结果，然后重构二叉树。

• 思路

本人思路是如果不写程序，把此题当问答题，本人是可以解答的，但是如果写程序怎么办呢？

本人思路有两步：

1）根据中序遍历，对二叉树中的关键字建立哈希表，目的就是通过关键字可以得到其在中序遍历中的位置；空间复杂度O（n），时间复杂度也是O（n）；前提是二叉树中的关键字是不重复的；

2）利用第一步的结果，把关键字在中序遍历中的位置作为关键字的value值，新建一个二叉树，新建的过程是把先序遍历中的每个关键字从前往后依次插入，时间复杂度为O（n*log n）；

说个例子吧，还好理解些，如下

重建二叉树后，如下

• 实验

程序截图如下

• 代码

binary_tree.h

#include <iostream>#include <utility>#include <string>#include <cmath>using namespace std;template<typename T>class btnode{public:T key;btnode * Lchild;btnode * Rchild; // function:make functionbtnode( );};template<typename T>btnode<T>::btnode(){key = -1;Lchild = NULL;Rchild = NULL;};template<typename T>class tree{private:// function:insert data to node from string to treevoid tree<T>::_data_into_node(T data,btnode<T>* &Tree,int *hash,int hash_length);public:// var:R id the root of the treebtnode<T> * R;// function:make functiontree();// function:make tree void _maketree(T * data,size_t s);// function:insert key into treevoid tree<T>::_insert(btnode<T> * *bt,T d);// function:visit node pvoid _visit(btnode<T> * p);// fucntion:preorder visit treevoid _preOrderTraver(btnode<T> * p);// fucntion:inorder visit treevoid _inOrderTraver(btnode<T> * p);// fucntion:postorder visit treevoid tree<T>::_postOrderTraver(btnode<T> * p);// function:whether is balanced binary treestd::pair<size_t,bool> _IsBalancedBinaryTree(btnode<T> *p);// function: string to treebtnode<T> * tree<T>::_data_to_tree(T * _preorder,int plength,T * _inorder,int ilength);};// function:make functiontemplate<typename T>tree<T>::tree(){this->R = NULL;};// function:make tree// input:an array of data and its length// output: a binary treetemplate<typename T>void tree<T>::_maketree(T * data,size_t s){for(size_t i= 0;i<s;i++){this->_insert(&(this->R),data[i]);}};// function:insert key into treetemplate<typename T>void tree<T>::_insert(btnode<T> * *bt,T d){if((*bt) == NULL){(*bt) = new btnode<T>;(*bt) -> key = d;}else{btnode<T> * p = *bt ;if(d < p->key){this->_insert(&(p->Lchild),d);}else if(d>p->key){this->_insert(&(p->Rchild),d);}else{cout<<d<<" has been inserted"<<endl;}}};// function:visit node ptemplate<typename T>void tree<T>::_visit(btnode<T> * p){if(p != NULL){cout<<"key="<<p->key<<endl;}else{cout<<"node point null"<<endl;}};// fucntion:preorder visit treetemplate<typename T>void tree<T>::_preOrderTraver(btnode<T> * p){if(p != NULL ){this->_visit(p);this->_preOrderTraver(p->Lchild);this->_preOrderTraver(p->Rchild);}};// fucntion:inorder visit treetemplate<typename T>void tree<T>::_inOrderTraver(btnode<T> * p){if(p != NULL ){this->_inOrderTraver(p->Lchild);this->_visit(p);this->_inOrderTraver(p->Rchild);}};// fucntion:postorder visit treetemplate<typename T>void tree<T>::_postOrderTraver(btnode<T> * p){if(p != NULL ){this->_postOrderTraver(p->Lchild);this->_postOrderTraver(p->Rchild);this->_visit(p);}};// function:whether is balanced binary treetemplate<typename T>std::pair<size_t,bool> tree<T>::_IsBalancedBinaryTree(btnode<T> *p){if( p == NULL )return std::make_pair(0,true);else {std::pair<size_t,bool> r = this -> _IsBalancedBinaryTree(p->Rchild);std::pair<size_t,bool> l = this -> _IsBalancedBinaryTree(p->Lchild);int h = (int)(r.first) - (int)(l.first);h = abs(h);if(h>1)return std::make_pair(max(r.first,l.first)+1,false);else return std::make_pair(max(r.first,l.first)+1,r.second && l.second);}};// function: string to treetemplate<typename T>btnode<T> * tree<T>::_data_to_tree(T * _preorder,int plength,T * _inorder,int ilength){if( plength > 0 && ilength > 0 ){btnode<T> * p = NULL;int * hash = new int[ilength];T zero = 0; for(int i=0;i<ilength;i++){hash[ abs(_inorder[i] - zero) % ilength ] = i;}for(int i=0;i<plength;i++){//function:insert data into tree_data_into_node(_preorder[i],p,hash,ilength);}cout<<"inorder"<<endl;this->_inOrderTraver(p);cout<<"preprder"<<endl;this->_preOrderTraver(p);return p;}else{cout<<"exception of function :<string to tree> input"<<endl;}};// function:insert data to node from string to treetemplate<typename T>void tree<T>::_data_into_node(T data,btnode<T>* &Tree,int *hash,int hash_length){// insure all data is rightif( hash != NULL || hash_length <= 0 ){if( Tree == NULL ){Tree = new btnode<T>() ;Tree -> key = data ;}else {T zero =0;btnode<T> * p =Tree;while(p != NULL){if(hash[abs(data-zero)%hash_length] < hash[abs(p->key - zero)%hash_length]){if(p->Lchild == NULL){p->Lchild = new btnode<T>();(p->Lchild)->key = data;break;}elsep = p->Lchild;}else{if(p->Rchild == NULL){p->Rchild = new btnode<T>();(p->Rchild)->key =data;break;}else{p = p->Rchild;}}}}}else{cout<<"exception of function <_data_into_node> input"<<endl;}};

test.cpp

 

#include<iostream>#include "binary_tree.h"using namespace std;// function: mainint main(){tree<char> * T = new tree<char>(); char* P = "abdcef";char* I = "dbaecf";T->_data_to_tree(P,6,I,6);system("pause");return 0;}