构造一颗二叉排序树的目的，其实并不是为了排序，而是为了提高查找和插入删除关键字的速度。不管怎么说，在一个有序数据集上的查找，速度总是要快于无序数据集的，而二叉排序树这种非线性的结构，也有利于插入和删除的实现。

二叉排序树的查找：

先查找其根节点，如果根节点的数据与data值相等，则返回该根节点；

否则， 如果data值大于根节点，则查询其右子树；

如果小于根节点，则查询其左子树。

pnode search(pnode root,int data)
{
    pnode temp = root;
    while(temp != NULL)    
        {
            if(temp->data == data)
                return temp;
            else if(data < temp->data)
                temp = temp->left;
            else
                temp = temp->right;
        }
    return NULL;
}

 

二叉排序树的删除：

二叉排序树的查找与删除_子树

pnode max_left_tree(pnode root)
{
    pnode temp = root->left;//该结点的左子树
    while (temp != NULL && temp->right != NULL)
    {
        temp = temp->right;
    }
    return temp;
}
pnode min_right_tree(pnode root)
{
    pnode temp = root->right;//该结点的右子树
    while (temp != NULL && temp->left != NULL)
    {
        temp = temp->left;
    }
    return temp;
}
void cut_link_from_tree(pnode node)
{
    if (node->left == NULL && node->right == NULL)
    {
        if (node->parent->left == node)
            node->parent->left = NULL;
        else if(node->parent->right == node)
            node->parent->right = NULL;
    }
    else
    {
        if (node->left != NULL)
            node->parent->right = node->left;
        else if (node->right != NULL)
            node->parent->left = node->right;
    }
}

pnode del_tree(pnode root, int data)
{
    pnode res = search_tree(root, data);//查找到要删除的结点
    pnode replace = NULL;
    if (res == NULL)
    {
        printf("not has this data \n ");
        return root;
    }
    //用该结点的左子数里的最大值或右子树的最小值来代替它
    if (res->left != NULL)
    {
        replace = max_left_tree(res);
    }
    else if(res->right != NULL)
    {
        replace = min_right_tree(res);
    }
    else//若该删除的结点左子树和右子树都为空，则其为叶子结点，直接删除即可
    {
        if (res == root)
            return NULL;
        else
        {
            cut_link_from_tree(res);
            free(res);
            return root;
        }
    }
    cut_link_from_tree(replace);
    res->data = replace->data;//将数据替换即可
    free(replace);
}

完整代码： 

#include<stdio.h>
#include<stdlib.h>
#include<string.h>

//构造结点
typedef struct _node {
  int data;
  struct _node *parent;
  struct _node *left;
  struct _node *right;
}node,*pnode;
//申请一个结点
pnode construct_node(int data) {
  pnode temp = (pnode)malloc(sizeof(node));
  temp->data = data;
  temp->left = temp->right = temp->parent = NULL;
  return temp;
}
//添加结点(构建二插排序树)
pnode add_node(pnode root, pnode newnode) {
  if (root == NULL)
    return newnode;
  pnode temp = root;
  while (temp != NULL)
  {
    if (newnode->data < temp->data)
    {
      if (temp->left == NULL)
      {
        temp->left = newnode; 
        newnode->parent = temp;
        return root;
      }
      else
        temp = temp->left;
    }
    else
    {
      if (temp->right == NULL)
      {
        temp->right = newnode;
        newnode->parent = temp;
        return root;
      }
      else
        temp = temp->right;
    }

  }
}
//访问根结点
void visit(pnode temp)
{
  printf("%d  ", temp->data);
}
//中序遍历（左-根-右）（中序相当于排序）
void inorder(pnode root)
{
  if (root == NULL)
    return;
  pnode temp = root;
  if (temp != NULL)
  {
    inorder(temp->left);//访问左子节点
    visit(temp);//访问根结点
    inorder(temp->right);//访问右子结点
  }
}

//二叉排序树的查找
pnode search_tree(pnode root, int data)
{
  pnode temp = root;
  while (temp != NULL)
  {
    if (temp->data == data)
      return temp;
    else if (data < temp->data )
      temp = temp->left;
    else
      temp = temp->right;
  }
  return NULL;
}

pnode max_left_tree(pnode root)
{
  pnode temp = root->left;
  while (temp != NULL && temp->right != NULL)
  {
    temp = temp->right;
  }
  return temp;
}
pnode min_right_tree(pnode root)
{
  pnode temp = root->right;
  while (temp != NULL && temp->left != NULL)
  {
    temp = temp->left;
  }
  return temp;
}
void cut_link_from_tree(pnode node)
{
  if (node->left == NULL && node->right == NULL)
  {
    if (node->parent->left == node)
      node->parent->left = NULL;
    else if(node->parent->right == node)
      node->parent->right = NULL;
  }
  else
  {
    if (node->left != NULL)
      node->parent->right = node->left;
    else if (node->right != NULL)
      node->parent->left = node->right;
  }
}
//二叉排序树的删除
pnode del_tree(pnode root, int data)
{
  pnode res = search_tree(root, data);
  pnode replace = NULL;
  if (res == NULL)
  {
    printf("not has this data \n ");
    return root;
  }
  if (res->left != NULL)
  {
    replace = max_left_tree(res);
  }
  else if(res->right != NULL)
  {
    replace = min_right_tree(res);
  }
  else
  {
    if (res == root)
      return NULL;
    else
    {
      cut_link_from_tree(res);
      free(res);
      return root;
    }
  }
  cut_link_from_tree(replace);
  res->data = replace->data;
  free(replace);
}

int main()
{
  //构建二叉排序树
  pnode root = NULL;
  int num = 10;
  for (int i = 0; i < num; i++)
  {
    pnode temp = construct_node(rand()%100);
    printf("%d  ", temp->data);
    root = add_node(root, temp);
  }

  //中序遍历输出（左-根-右）
  printf("\n");
  inorder(root);
  printf("\n");
  
  //二叉排序树的查找
  printf("pls input search data:");
  int data;
  scanf_s("%d", &data);
  pnode res = search_tree(root, data);
  if (res == NULL)
    printf("not found.\n");
  else
    printf("found,data local:%p,data:%d\n", res, res->data);

  //二叉排序树的删除
  while (1)
  {
    printf("pls input del data:");
    int data;
    scanf_s("%d", &data);
    del_tree(root, data);
    inorder(root);
    printf("\n");
  }
  return 0;
}

二叉排序树的查找与删除_结点_02