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二叉搜索树是常见的数据结构，主要用于快速查找数据。以下是对二叉搜索树操作集的实现，包括插入、删除、查找、找最小值和找最大值的函数。

节点结构定义

typedef struct TNode *Position;typedef Position BinTree;struct TNode {    ElementType Data;    BinTree Left;    BinTree Right;};

插入函数

插入函数将一个元素插入二叉搜索树中，并返回根节点指针。

BinTree Insert(BinTree BST, ElementType X) {    if (!BST) {        BST = (BinTree)malloc(sizeof(struct TNode));        BST->Data = X;        BST->Left = NULL;        BST->Right = NULL;    } else {        if (X < BST->Data) {            BST->Left = Insert(BST->Left, X);        } else if (X > BST->Data) {            BST->Right = Insert(BST->Right, X);        }    }    return BST;}

删除函数

删除函数将一个元素从二叉搜索树中删除，并返回根节点指针。如果元素不存在，输出“Not Found”并返回原树根节点。

BinTree Delete(BinTree BST, ElementType X) {    Position Tmp;    if (!BST) {        printf("Not Found\n");        return BST;    } else if (X < BST->Data) {        BST->Left = Delete(BST->Left, X);    } else if (X > BST->Data) {        BST->Right = Delete(BST->Right, X);    } else {        if (BST->Left && BST->Right) {            Tmp = FindMin(BST->Right);            BST->Data = Tmp->Data;            BST->Right = Delete(BST->Right, BST->Data);        } else {            Tmp = BST;            if (!BST->Left) {                BST = BST->Right;            } else if (!BST->Right) {                BST = BST->Left;            }            free(Tmp);        }    }    return BST;}

查找函数

查找函数返回目标值的节点指针，如果不存在则返回空指针。

Position Find(BinTree BST, ElementType X) {    while (BST) {        if (X > BST->Data) {            BST = BST->Right;        } else if (X < BST->Data) {            BST = BST->Left;        } else {            return BST;        }    }    return NULL;}

找最小值函数

找最小值函数返回二叉搜索树中最小值的节点指针。

Position FindMin(BinTree BST) {    while (BST) {        if (!BST->Left) {            return BST;        } else {            BST = BST->Left;        }    }    return NULL;}

找最大值函数

找最大值函数返回二叉搜索树中最大值的节点指针。

Position FindMax(BinTree BST) {    while (BST) {        if (!BST->Right) {            return BST;        } else {            BST = BST->Right;        }    }    return NULL;}

使用示例

#include 
   
    #include 
    
     typedef int ElementType;typedef struct TNode *Position;typedef Position BinTree;struct TNode {    ElementType Data;    BinTree Left;    BinTree Right;};BinTree Insert(BinTree BST, ElementType X) {    if (!BST) {        BST = (BinTree)malloc(sizeof(struct TNode));        BST->Data = X;        BST->Left = NULL;        BST->Right = NULL;    } else {        if (X < BST->Data) {            BST->Left = Insert(BST->Left, X);        } else if (X > BST->Data) {            BST->Right = Insert(BST->Right, X);        }    }    return BST;}BinTree Delete(BinTree BST, ElementType X) {    Position Tmp;    if (!BST) {        printf("Not Found\n");        return BST;    } else if (X < BST->Data) {        BST->Left = Delete(BST->Left, X);    } else if (X > BST->Data) {        BST->Right = Delete(BST->Right, X);    } else {        if (BST->Left && BST->Right) {            Tmp = FindMin(BST->Right);            BST->Data = Tmp->Data;            BST->Right = Delete(BST->Right, BST->Data);        } else {            Tmp = BST;            if (!BST->Left) {                BST = BST->Right;            } else if (!BST->Right) {                BST = BST->Left;            }            free(Tmp);        }    }    return BST;}Position Find(BinTree BST, ElementType X) {    while (BST) {        if (X > BST->Data) {            BST = BST->Right;        } else if (X < BST->Data) {            BST = BST->Left;        } else {            return BST;        }    }    return NULL;}Position FindMin(BinTree BST) {    while (BST) {        if (!BST->Left) {            return BST;        } else {            BST = BST->Left;        }    }    return NULL;}Position FindMax(BinTree BST) {    while (BST) {        if (!BST->Right) {            return BST;        } else {            BST = BST->Right;        }    }    return NULL;}int main() {    BinTree BST, MinP, MaxP, Tmp;    ElementType X;    int N, i;    BST = NULL;    scanf("%d", &N);    for (i = 0; i < N; i++) {        scanf("%d", &X);        BST = Insert(BST, X);    }    printf("preorder: ");    preorderTraversal(BST);    printf("\n");    MinP = FindMin(BST);    MaxP = FindMax(BST);    for (i = 0; i < N; i++) {        X = ...;        Tmp = Find(BST, X);        if (Tmp == NULL) {            printf("%d is not found\n", X);        } else {            if (Tmp == MinP) {                printf("%d is the smallest key\n", Tmp->Data);            }            if (Tmp == MaxP) {                printf("%d is the largest key\n", Tmp->Data);            }        }    }    scanf("%d", &N);    for (i = 0; i < N; i++) {        X = ...;        Tmp = Insert(BST, X);        ...    }    ...}
    
   

功能说明

这些函数按照二叉搜索树的性质实现，确保插入、删除和查找的效率。

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