二叉搜索树

最新推荐文章于 2025-04-29 16:04:18 发布

原创最新推荐文章于 2025-04-29 16:04:18 发布 · 795 阅读

1 ·

CC 4.0 BY-SA版权

文章标签：

#null #search #delete #insert #tree #算法

数据结构专栏收录该内容

12 篇文章

订阅专栏

本文介绍了一个二叉搜索树的实现过程，包括插入、删除、遍历等操作，并提供了完整的源代码示例。文章还讨论了搜索树删除元素时的各种情况及指针调整问题。

写一个二叉搜索树花了不少时间，第一次写还真费劲，感受：1、从搜索树删除一个元素需要考虑的情况真多，每一种情况都要考虑好指针的调整；2、遍历二叉树，递归版本真不好理解，真不知道真么出来的，非递归版本比较好理解。

下面是代码

BinaryTree.h

//二叉搜索树 #include<stack> template<class T> struct Node{ T data; Node *pleft; Node *pright; Node *pparent; }; template<class T> class BitTree{ public: BitTree():proot(NULL){} ~BitTree(){} bool isEmpty(); bool Addroot(T& element); //当树为空时，添加一个跟节点 bool Insert(T& element); //插入一个元素 bool Remove(T& element); //删除一个元素 bool get_max_element(T&); //查找最大元素 bool get_min_element(T&); //查找最小元素 Node<T>* search(T&); //搜索一个元素，返回指向所找元素的指针 Node<T>* successor(T&); //后继（节点x的后继是所有大于x的元素中最小的一个）,返回element元素的后继 void InorderTreeWalk(Node<T>* pNode); //中序遍历（从小到大遍历树）（递归和非递归版本） void PreorderTreeWalk(Node<T>* pNode); //前序遍历 void PostorderTreeWalk(Node<T>* pNode); //后续遍历 void FloorTreeWalk(Node<T>* pNode); //分层遍历 int getTreeDepth(Node<T>* pNode); //返回树的深度，第一层为0,如果在Node里加入一个next指针，用链表把树串起来，这样更好实现。 Node<int>* get_proot() { return proot; } //获取根节点 private: Node<T>* proot; //指向跟节点 }; template<class T> bool BitTree<T>::isEmpty() { if(proot == NULL) { cout<<"tree is empty()"<<endl; return false; } else return true; } template<class T> bool BitTree<T>::Addroot(T& element) { Node<T>* pNode = new Node<T>(); pNode->data = element; pNode->pleft = NULL; pNode->pright = NULL; pNode->pparent = NULL; proot = pNode; return true; } template<class T> bool BitTree<T>::get_max_element(T& max) { if(!isEmpty()) return false; Node<T>* ptemp = proot; while(ptemp->pright != NULL) ptemp = ptemp->pright; max = ptemp->data; return true; } template<class T> bool BitTree<T>::get_min_element(T& min) { if(!isEmpty()) return false; Node<T>* ptemp = proot; while(ptemp->pleft != NULL) ptemp = ptemp->pleft; min = ptemp->data; return true; } template<class T> Node<T>* BitTree<T>::search(T& element) { if(!isEmpty()) return NULL; Node<T>* ptemp = proot; bool flag = false; if(ptemp->data != element) flag = true; while(ptemp->data != element && flag == true) { if(element <= ptemp->data && ptemp->pleft != NULL) { ptemp = ptemp->pleft; flag = true; } else if(element > ptemp->data && ptemp->pright != NULL) { ptemp = ptemp->pright; flag = true; } else flag = false; } return ptemp->data == element ? ptemp : NULL; } template<class T> Node<T>* BitTree<T>::successor(T& element) { T Ttemp; get_max_element(Ttemp); //得到最大元素，判断element是否有后继 if(element == Ttemp) { cout<<element<<" have no successor!/n"; return new Node<T>(); } Node<T>* pElement = search(element); if(pElement->pright != NULL) //如果element的右子节点不为空，则element的后继为右子树中的最左子节点 { Node<T>* ptemp1 = pElement->pright; while(ptemp1->pleft != NULL) ptemp1 = ptemp1->pleft; element = ptemp1->data; return ptemp1; } else //如果为空,因为x没有右子树，所以这时，按中序遍历的x下一个结点即后继， { //应该是这样一个子树的根结点y，x的祖先是其左孩子，这样，y就大于其左子树所有结点，并且因为x是y的左子树中最大的结点了 Node<T>* ptemp2 = pElement->pparent; while(ptemp2 != NULL && pElement == ptemp2->pright ) { pElement = ptemp2; ptemp2= ptemp2->pparent; } return ptemp2; } } template<class T> bool BitTree<T>::Insert(T& element) {//作为数最底层的孩子插入，搜寻到需要插入的位置 if(proot == NULL) { Addroot(element); return true; } Node<T>* ptemp = proot; bool flag = false; if(ptemp->pleft != NULL || ptemp->pright != NULL) flag = true; while(flag) { if(ptemp->pleft != NULL && element <= ptemp->data) { ptemp = ptemp->pleft; flag = true; } else if(ptemp->pright != NULL && element > ptemp->data) { ptemp = ptemp->pright; flag = true; } else flag = false; } if(element <= ptemp->data) { ptemp->pleft = new Node<T>(); ptemp->pleft->data = element; ptemp->pleft->pleft = NULL; ptemp->pleft->pright = NULL; ptemp->pleft->pparent = ptemp; } else { ptemp->pright = new Node<T>(); ptemp->pright->data = element; ptemp->pright->pleft = NULL; ptemp->pright->pright = NULL; ptemp->pright->pparent = ptemp; } return true; } template<class T> bool BitTree<T>::Remove(T& element) { //删除节点时，要考虑Node的四个指针的更改问题（pleft,pright,pparent,proot) Node<T>* pElement = search(element); if(pElement == NULL) return false; if(pElement->pleft == NULL && pElement->pright == NULL) {//如果element节点没有孩子 if(pElement->pparent == NULL) //如果树只有一个根节点,注意需要调整proot proot = NULL; else if(pElement->pparent->data <= element) pElement->pparent->pright = NULL; else pElement->pparent->pleft = NULL; delete pElement; pElement = NULL; } else if( pElement->pleft != NULL && pElement->pright != NULL ) { //如果element节点有两个子女，则删除其后继y（y没有左子女，《算法导论 P155 习题12.2-5》） Node<T>* psuccessor = successor(element); pElement->data = psuccessor->data; if(psuccessor->pleft == NULL && psuccessor->pright == NULL) {//如果后继没有子女 if(psuccessor->pparent->data <= psuccessor->data) psuccessor->pparent->pright = NULL; else psuccessor->pparent->pleft = NULL; } else if(psuccessor->pparent->data <= psuccessor->pright->data) {//如果后继的右孩子小于后继的父节点 psuccessor->pparent->pright = psuccessor->pright; psuccessor->pright->pparent = psuccessor->pparent; } else {//如果后继的右孩子大于后继的父节点 psuccessor->pparent->pleft = psuccessor->pright; psuccessor->pright->pparent = psuccessor->pparent; } delete psuccessor; psuccessor = NULL; } else {//如果element节点有一个孩子 if(pElement->pparent == NULL) {//如果element为跟节点，注意需要调整proot if(pElement->pleft != NULL) { pElement->pleft->pparent = NULL; proot = pElement->pleft; } else { pElement->pright->pparent = NULL; proot = pElement->pright; } } else if(pElement->pright != NULL ) {//如果是右孩子 if(pElement->pright->data > pElement->pparent->data) pElement->pparent->pright = pElement->pright; else pElement->pparent->pleft = pElement->pright; pElement->pright->pparent = pElement->pparent; } else {//如果是左孩子 if(pElement->pleft->data > pElement->pparent->data) pElement->pparent->pright = pElement->pleft; else pElement->pparent->pleft = pElement->pleft; pElement->pleft->pparent = pElement->pparent; } delete pElement; pElement = NULL; } return true; } //中序遍历（递归版本） template<class T> void BitTree<T>::InorderTreeWalk(Node<T>* pNode) { if(pNode == NULL) return ; if(pNode != NULL) { InorderTreeWalk(pNode->pleft); cout<<pNode->data<<" "; InorderTreeWalk(pNode->pright); } } ////中序遍历（非递归版本） //template<class T> //void BitTree<T>::InorderTreeWalk(Node<T>* pNode) //{ // stack<Node<T>*> stk; // while(pNode != NULL || stk.size() != 0) // { // while(pNode != NULL) // { // stk.push(pNode); // pNode = pNode->pleft; //遍历左子树 // } // if(stk.size() != 0) // { // pNode = stk.top(); // stk.pop(); // cout<<pNode->data<<" "; //打印中序遍历 // pNode = pNode->pright; // // } // } //} ////前序遍历（递归版本） //template<class T> //void BitTree<T>::PreorderTreeWalk(Node<T>* pNode) //{ // if(pNode == NULL) // return ; // if(pNode != NULL) // { // cout<<pNode->data<<" "; // PreorderTreeWalk(pNode->pleft); // PreorderTreeWalk(pNode->pright); // } //} //前序遍历（非递归版本） template<class T> void BitTree<T>::PreorderTreeWalk(Node<T>* pNode) { stack<Node<T>*> stk; while(pNode != NULL || stk.size() != 0) { while(pNode != NULL) { stk.push(pNode); cout<<pNode->data<<" "; //打印前序遍历 pNode = pNode->pleft; //遍历左子树 } if(stk.size() != 0) { pNode = stk.top(); stk.pop(); pNode = pNode->pright; } } } ////后序遍历（递归版本） //template<class T> //void BitTree<T>::PostorderTreeWalk(Node<T>* pNode) //{ // if(pNode == NULL) // return ; // if(pNode != NULL) // { // PostorderTreeWalk(pNode->pleft); // PostorderTreeWalk(pNode->pright); // cout<<pNode->data<<" "; // } //} //后序遍历（非递归版本） template<class T> void BitTree<T>::PostorderTreeWalk(Node<T>* pNode) { Node<T>* tp = NULL; stack<Node<T>*> stk; while(pNode != NULL || stk.size() != 0) { while(pNode != NULL) { stk.push(pNode); pNode = pNode->pleft; //遍历左子树 } if(stk.size() != 0) pNode = stk.top(); if(pNode->pright == NULL || pNode->pright == tp) { cout<<pNode->data<<" "; stk.pop(); tp = pNode; //tp记住上一次遍历的位置 pNode = NULL; } else pNode = pNode->pright; } } //分层遍历 template<class T> void BitTree<T>::FloorTreeWalk(Node<T>* pNode) //参考《编程之美 P256》 { if(pNode == NULL) return; vector<Node<int>*> vec; vec.push_back(pNode); int cur = 0; int last = 1; while(cur < vec.size()) { last = vec.size(); //新的一行访问开始，重新定位last于当前行最后一个节点的下一个节点 while(cur<last) { cout<<vec[cur]->data<<" "; // if(vec[cur]->pleft) //当前访问节点的左节点不为空则压入 vec.push_back(vec[cur]->pleft); if(vec[cur]->pright) //当前访问节点的右节点不为空则压入 vec.push_back(vec[cur]->pright); cur++; } cout<<endl; } } template<class T> int BitTree<T>::getTreeDepth(Node<T>* pNode) //返回树的深度，第一层为0 { //通过分层遍历的方法，统计层数 if(pNode == NULL) return -1; vector<Node<int>*> vec; vec.push_back(pNode); int cur = 0; int last = 1; int depth = -1; while(cur < vec.size()) { last = vec.size(); ++depth; while(cur<last) { if(vec[cur]->pleft) vec.push_back(vec[cur]->pleft); if(vec[cur]->pright) vec.push_back(vec[cur]->pright); cur++; } } return depth; }

测试代码test.cpp

#include<iostream> #include<vector> #include "BinaryTree.h" using namespace std; int main() { BitTree<int> tree; int a[18] = {15,-1,10,12,-19,14,-13,-5,21,9, 21,3,6,-6,17,-30,23,-8}; const int sz = sizeof(a)/sizeof(int); for(int i=0;i<sz;++i) tree.Insert(a[i]); int max=-1,min=-1; tree.get_max_element(max); tree.get_min_element(min); cout<<"max = "<<max<<" ; min = "<<min<<endl; cout<<( tree.search(a[3])?"have founded!/n" :"have not founded!/n" ); Node<int>* psNode = tree.successor(a[1]); cout<< "tree.successor(a[1]) = "<<psNode->data<<endl; psNode = tree.successor(a[5]); cout<< "tree.successor(a[5]) = "<<psNode->data<<endl; Node<int>* pNode = tree.get_proot(); cout<<"中序遍历 :"; tree.InorderTreeWalk(pNode); cout<<endl<<"前序遍历 :"; tree.PreorderTreeWalk(pNode); cout<<endl<<"后序遍历 :"; tree.PostorderTreeWalk(pNode); cout<<endl<<"分层遍历 :/n"; tree.FloorTreeWalk(pNode); cout<<"the depth of tree is: "<<tree.getTreeDepth(pNode)<<endl; //清空树 int b[18] = {15,-1,10,12,-19,14,-13,-5,21,9, 21,3,6,-6,17,-30,23,-8}; for(int i=0;i<sz;++i) { if(tree.Remove(b[i])) { cout<<"中序遍历: "; pNode = tree.get_proot(); tree.InorderTreeWalk(pNode); cout<<endl; } } return 0; }