二叉排序树（建树、查找、删除）

今天我主要学习了二叉排序树（Binary Search Tree，简称 BST）的基本操作，包括：

• 非递归插入与查找实现

• 递归插入实现

• 节点删除实战

        二叉排序树是一种重要的数据结构，在查找、排序、以及后续平衡树（如 AVL、红黑树）等算法中有广泛应用。下面将所写代码分享给大家。

一、二叉排序树（非递归插入版）

//二叉排序树
typedef struct bitree {int data;struct bitree* lchild, * rchild;
}bitree,*pbitree;// 初始化数组，随机生成数据
void init_arr(int* arr, int arr_len)
{for (int i = 0; i < arr_len; i++){arr[i] = rand() % 100;}
}// 中序遍历（递归实现）
void in_order(pbitree tree)
{if(tree){in_order(tree->lchild);printf("%-3d", tree->data);in_order(tree->rchild);}
}// 二叉排序树插入（非递归写法）
void insert_bst(pbitree &tree, int key)
{pbitree parent = NULL;if (tree == NULL){tree = (pbitree)malloc(sizeof(bitree));tree->lchild = NULL;tree->rchild = NULL;tree->data = key;return;}pbitree p = tree;// 用p来遍历；while (p){parent = p;// p为空前保存父节点if (key == p->data){return;}if (key < p->data){p = p->lchild;}else if (key > p->data){p = p->rchild;}}pbitree pnew = (pbitree)calloc(1, sizeof(bitree));pnew->data = key;if (parent->data > key){parent->lchild = pnew;}else if (parent->data < key){parent->rchild = pnew;}
}// 构建二叉排序树
void creat_bst(pbitree &tree, int* arr, int arr_len)
{for (int i = 0; i < arr_len; i++){insert_bst(tree, arr[i]);}
}// 查找指定关键字
bool search_key(pbitree tree, int key, pbitree &parent)
{while (key != tree->data){if (tree == NULL){return false;}parent = tree;if (key < tree->data){tree = tree->lchild;}else if (key > tree->data){tree = tree->rchild;}}return true;
}int main()
{pbitree tree = NULL;srand(time(NULL));int arr[10] = { 0 };init_arr(arr, 10);creat_bst(tree, arr, 10);// bst->binary search treein_order(tree);pbitree parent = NULL;int key = 0;scanf("%d", &key);bool ret = search_key(tree, key, parent);if (ret){printf("success,and the parent key is&d", parent->data);}return 0;
}

二、二叉排序树（递归插入版）

//递归写法
typedef struct bitree {int data;struct bitree* lchild, * rchild;
}bitree, * pbitree;// 初始化数组
void init_arr(int* arr, int arr_len)
{for (int i = 0; i < arr_len; i++){arr[i] = rand() % 100;}
}// 中序遍历
void in_order(pbitree tree)
{if (tree){in_order(tree->lchild);printf("%-3d", tree->data);in_order(tree->rchild);}
}// 二叉排序树插入（递归写法）
int insert_bst1(pbitree &tree, int key)
{if (tree == NULL){tree = (pbitree)malloc(sizeof(bitree));tree->lchild = tree->rchild = NULL;tree->data = key;return 1;}if (key == tree->data){return 0;}else if (key < tree->data){insert_bst1(tree->lchild, key);}else if (key > tree->data){insert_bst1(tree->rchild, key);}
}// 构建二叉排序树
void creat_bst(pbitree& tree, int* arr, int arr_len)
{for (int i = 0; i < arr_len; i++){insert_bst1(tree, arr[i]);}
}int main()
{pbitree tree = NULL;srand(time(NULL));int arr[10] = { 0 };init_arr(arr, 10);creat_bst(tree, arr, 10);// bst->binary search treein_order(tree);return 0;
}

三、二叉排序树删除操作实战

       实现了 BST 的删除操作，分三种情况处理：
1️⃣ 叶子节点：直接删除。
2️⃣ 只有一个子树：用子树替代当前节点。
3️⃣ 有两个子树：用左子树的最大节点（或右子树最小节点）替代当前节点，再删除该节点。

//二叉排序树 删除实战
typedef struct bitree {int data;struct bitree* lchild, * rchild;
}bitree, * pbitree;// 中序遍历
void in_order(pbitree tree)
{if (tree){in_order(tree->lchild);printf("%-3d", tree->data);in_order(tree->rchild);}
}// 插入（递归写法）
int insert_bst1(pbitree &tree, int key)
{if (tree == NULL){tree = (pbitree)malloc(sizeof(bitree));tree->lchild = tree->rchild = NULL;tree->data = key;return 1;}if (key == tree->data){return 0;}else if (key < tree->data){insert_bst1(tree->lchild, key);}else if (key > tree->data){insert_bst1(tree->rchild, key);}
}// 构建BST
void creat_bst(pbitree& tree, int* arr, int arr_len)
{for (int i = 0; i < arr_len; i++){insert_bst1(tree, arr[i]);}
}// 删除节点
int delete_bitree(pbitree &tree, int key)
{if (tree == NULL){return 0;}if (key < tree->data){delete_bitree(tree->lchild, key);}else if (key > tree->data){delete_bitree(tree->rchild, key);}else{if (tree->lchild == NULL){pbitree tmp = tree;tree = tree->rchild;free(tmp);}else if (tree->rchild == NULL){pbitree tmp = tree;tree = tree->lchild;free(tmp);}else  {// 左子树最大节点替代当前节点pbitree tmp = tree->lchild;while (tmp->rchild != NULL){tmp = tmp->rchild;}tree->data = tmp->data;delete_bitree(tree->lchild,tmp->data);}}
}int main()
{pbitree tree = NULL;srand(time(NULL));int arr[10] = {22,32,13,64,43,56,23,66,2,31};creat_bst(tree, arr, 10);// bst->binary search treein_order(tree);delete_bitree(tree, 32);in_order(tree);return 0;
}