二叉排序树插入，删除（附详细注释）

BinarySortTreeADT.h/**二叉排序树(Binary Sort Tree)又称二叉查找(搜索)树(Binary Search Tree)。*其定义为：二叉排序树或者是空树，或者是满足如下性质的二叉树：*①若它的左子树非空，则左子树上所有结点的值均小于根结点的值；*②若它的右子树非空，则右子树上所有结点的值均大于根结点的值；*③左、右子树本身又各是一棵二叉排序树。*上述性质简称二叉排序树性质(BST性质)，故二叉排序树实际上是满足BST性质的二叉树。*/#ifndef _BINARYSORTTREEADT_H#define _BINARYSORTTREEADT_H/* 声明结点的值的类型 */typedef int KeyType;/* 声明结点类型 */typedef struct CBSTNode { KeyType m_ktKey; struct CBSTNode * m_pCBSTNLeft; struct CBSTNode * m_pCBSTNRight;}CBSTNode, *PCBSTNode, *CBSTree;/* 向二叉排序树中加入一个结点 */extern int InsertNode(CBSTree *, KeyType);/* 通过值查找并删除一个结点 */extern int DelNode(CBSTree *, KeyType);/* 通过值查找结点并返回结点的指针（设为常量指针） */extern const CBSTNode * SearchNode(CBSTree *, KeyType);/* 中序遍历二叉排序树的结点 */extern void PrintAllNodeMid(CBSTree);/* 后序方式释放结点 */extern void FreeBSTree(CBSTree);#endifBinarySortTreeADT.cpp#include "BinarySortTreeADT.h"#include <stdlib.h>#include <stdio.h>/* 向二叉排序树中加入一个结点 */int InsertNode(CBSTree * tree, KeyType key){ PCBSTNode p = NULL, parent = NULL; PCBSTNode pNewNode = (PCBSTNode)malloc(sizeof(CBSTNode)); if (NULL == pNewNode) { return -1; } /* 新建结点赋值，特别是左右子结点指针要赋值为NULL */ pNewNode->m_ktKey = key; pNewNode->m_pCBSTNLeft = NULL; pNewNode->m_pCBSTNRight = NULL; /* 二叉排序树是空树 */ if (NULL == *tree) { *tree = pNewNode; return 0; } else { p = *tree; /* 寻找插入位置 */ while (NULL != p) { /* key值已在二叉排序树中 */ if (p->m_ktKey == key) { return 0; } else { parent = p; p = (p->m_ktKey < key) ? p->m_pCBSTNRight : p->m_pCBSTNLeft; } } if (parent->m_ktKey < key) { parent->m_pCBSTNRight = pNewNode; } else { parent->m_pCBSTNLeft = pNewNode; } return 0; }}/* 通过值查找并删除一个结点 */int DelNode(CBSTree * tree, KeyType key){ PCBSTNode p = NULL, q = NULL, parent = NULL, child = NULL; p = *tree; /* parent为NULL表示根结点的父亲为NULL */ while (NULL != p) { if (p->m_ktKey == key) { break; } else { parent = p; p = (p->m_ktKey < key) ? p->m_pCBSTNRight : p->m_pCBSTNLeft; } } /* p为NULL时，表示没有找到结点值为key的结点 */ if (NULL == p) { return 0; } /* p, q现在都是保存了待删结点指针 */ q = p; /* 待删结点有两个儿子结点，进行一下转化 */ if (NULL != p->m_pCBSTNLeft && NULL != p->m_pCBSTNRight) { parent = p; p = p->m_pCBSTNRight; while (NULL != p->m_pCBSTNLeft) { parent = p; p = p->m_pCBSTNLeft; } /* p中保存了待删结点右子树中最左下的结点指针， parent中就保存了该结点父亲指针 */ child = p->m_pCBSTNRight; } /* parent保存待删结点的父亲结点指针， child保存了待删结点的儿子结点指针（待删结点至多只有一个儿子，有两个会转化为0个或1个右结点）*/ /* 待删结点是根结点 */ if (NULL == parent) { *tree = child; } else { /*待删结点是父亲结点的左儿子*/ if (parent->m_pCBSTNLeft == p) { parent->m_pCBSTNLeft = child; } else { parent->m_pCBSTNRight = child; } /*待删结点有两个儿子结点，转化后需要交换两个结点值 */ if (p != q) { q->m_ktKey = p->m_ktKey; } } free(p); return 0;}/* 通过值查找结点并返回结点的指针（设为常量指针） */const CBSTNode * SearchNode(CBSTree * tree, KeyType key){ PCBSTNode p = *tree; while (NULL != p) { if (p->m_ktKey == key) { break; } else { p = (p->m_ktKey < key) ? p->m_pCBSTNRight : p->m_pCBSTNLeft; } } return p;}/* 中序遍历二叉排序树的结点 */void PrintAllNodeMid(CBSTree tree){ if (NULL != tree) { PrintAllNodeMid(tree->m_pCBSTNLeft); printf("%d is accessed./n", tree->m_ktKey); PrintAllNodeMid(tree->m_pCBSTNRight); }}/* 后序方式释放结点 */void FreeBSTree(CBSTree tree){ if (NULL != tree) { FreeBSTree(tree->m_pCBSTNLeft); FreeBSTree(tree->m_pCBSTNRight); printf("%d is free./n", tree->m_ktKey); free(tree); }}BinarySortTreeADT.h/**二叉排序树(Binary Sort Tree)又称</span></p></div><br /><hr><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap/5.2.1/css/bootstrap.min.css" integrity="sha512-siwe/oXMhSjGCwLn+scraPOWrJxHlUgMBMZXdPe2Tnk3I0x3ESCoLz7WZ5NTH6SZrywMY+PB1cjyqJ5jAluCOg==" crossorigin="anonymous" referrerpolicy="no-referrer" /> <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-icons/1.9.1/font/bootstrap-icons.min.css" integrity="sha512-5PV92qsds/16vyYIJo3T/As4m2d8b6oWYfoqV+vtizRB6KhF1F9kYzWzQmsO6T3z3QG2Xdhrx7FQ+5R1LiQdUA==" crossorigin="anonymous" referrerpolicy="no-referrer" /> <script src="https://challenges.cloudflare.com/turnstile/v0/api.js?onload=_turnstileCb" defer></script> <br /> <main class="form-signin" 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