二叉查找树 算法导论笔记

---------概念和定理---------

二叉查找树的属性：对于一个二叉查找树t而言，其根结点root的key值比所有的左子树都小，比所有的右子树都大。（包括“等于"的情况）

定理1：设x为一个n个结节点的二叉搜索树的根，调用INORDER-TREE-WALK（x）中序遍历的时间复杂度为@(n)。

定理2：二叉查找树上的下述操作时间复杂度均为O（h），h为树的高度：查询、最小值、最大值、后继、前驱。

定理3：二叉查找树上的插入和删除的时间复杂度也为O（h），h为树的高度。

源代码如下：

#include <iostream>using namespace std;typedef int DataType;typedef struct BSTreeNode{DataType data;BSTreeNode * left, * right;BSTreeNode * pnt;}BSTreeNode, *BSTree;void InorderTreeWalk(BSTree t){if(t!=NULL)  //终止的条件为，到达空的指针 {InorderTreeWalk(t->left);cout<<t->data;InorderTreeWalk(t->right);}}BSTree TreeSearch(BSTree t,DataType data){if(t==NULL||t->data == data)return t;else if (t->data > data)return TreeSearch(t->right, data);elsereturn TreeSearch(t->left, data);} BSTree IterativeTreeSearch(BSTree t,DataType data){if(t==NULL||t->data == data)return t;else if (t->data<data)t = t->left;elset = t->right;}BSTree TreeMinimum(BSTree t){while(t->left!=NULL)t = t->left;return t;}BSTree TreeMaximum(BSTree t){while(t->right = NULL) t = t->right;return t;}BSTree TreeSuccessor(BSTree t){BSTree f;if(t->right!=NULL)return TreeMinimum(t->right);f = t->pnt;while(f!=NULL&&t==f->right){t = f;f = f->pnt;} return f;}BSTree TreePredecessor(BSTree t){BSTree f;if(t->left!=NULL)return TreeMaximum(t->left);f = t->pnt;while(f!=NULL&&t == f->left){t = f;f = f->pnt;}return f;}void TreeInsert(BSTree &t, BSTree z){BSTree f=NULL;  // 父结点 BSTree x = t;while(x!=NULL){f=x;if(z->data<x->data)x=x->left;elsex=x->right;}z->pnt = f;if(f==NULL)t = z; else if (z->data<f->data)f->left = z;else f->right = z;}void Transplant(BSTree t, BSTree u, BSTree v){if(u->pnt==NULL)t = v;else if(u==u->pnt->left){u->pnt->left= v;} elseu->pnt->right= v;if(v!=NULL)v->pnt = u->pnt;}void TreeDelete(BSTree t,BSTree z){BSTree y;if(z->left==NULL)Transplant(t,z,z->right);else if(z->right==NULL)Transplant(t,z,z->left);else {y = TreeMinimum(z->right);if (y->pnt == z)Transplant(t,y,y->right);y->right = z->right;y->right->pnt= y;Transplant(t,z,y);y->left = z->left;y->left->pnt= y;}}int main(){return 0;}