二叉搜索树

Posted 2021-01-13 rakint

#include <iostream>
using namespace std;
typedef struct TreeNode *SearchTree;
typedef struct TreeNode *Position;
struct TreeNode
{
 int Element;
 SearchTree Left;
 SearchTree Right;
};
//////////////函数声明//////////////////////////
void MakeEmpty(SearchTree T);  //清空一个树
SearchTree CreatTree(int x);    //创建一个根为x的空树
Position Find(int x, SearchTree T);     //查找函数
Position FindMin(SearchTree T);         //寻找二叉树的最小值
Position FindMax(SearchTree T);         //寻找二叉树的最大值
SearchTree Insert(int x, SearchTree T);   //插入元素
SearchTree Delete(int x, SearchTree T);    //删除元素
 //////////////函数定义//////////////////////////
void MakeEmpty(SearchTree T)
{
 if (T != NULL)
 {
  MakeEmpty(T->Left);
  MakeEmpty(T->Right);
  delete T;// free(T);//把最后的指向根结点的指针去掉。
 }

}
SearchTree CreatTree(int x)
{
 SearchTree T;
 T = static_cast<SearchTree>(malloc(sizeof(struct TreeNode)));
 T->Element = x;//这是指二叉树的结点值
 T->Left = NULL;
 T->Right = NULL;
 return T;//T指向一颗二叉树
}
Position Find(int x, SearchTree T)
{
 if (T == NULL)
 {
  return NULL;
 }
 if (x < T->Element)
 {
  return Find(x, T->Left);  //尾递归
 }
 else
 {
  if (x > T->Element)
  {
   return Find(x, T->Right);
  }
  else
  {
   return T;//这一步不可省略，处理相等的情况
  }
 }

}
Position FindMin(SearchTree T)
{
 if (T == NULL)
 {
  return NULL;
 }
 else
 {
  if (T->Left == NULL)
  {
   return T;
  }
  else
  {
   return FindMin(T->Left);//递归方式找最小值
  }
 }
}
Position FindMax(SearchTree T)
{
 if (T != NULL)
 {
  while (T->Right != NULL)
  {
   T = T->Right;//迭代方式找最大值
  }
 }
 return T;
}
SearchTree Insert(int x, SearchTree T)
{
 if (T == NULL)//处理递归的初始条件
 {
  T = static_cast<SearchTree>(malloc(sizeof(struct TreeNode)));
  if (T == NULL)
  {
   cout << "out of space" << endl;
  }
  else
  {
   T->Element = x;
   T->Left = NULL;
   T->Right = NULL;
  }
 }
 else
 {
  if (x < T->Element)
  {
   T->Left = Insert(x, T->Left);//递归实现
  }
  else
  {
   if (x > T->Element)
   {
    T->Right = Insert(x, T->Right);//递归实现
   }
  }
 }
 return T;
}
SearchTree Delete(int x, SearchTree T)
{
 Position TmpCell;
 if (T == NULL)
 {
  cout << "Element not found" << endl;
 }
 else
 {
  if (x < T->Element)
  {
   T->Left = Delete(x, T->Left);
  }
  else
  {
   if (x > T->Element)
   {
    T->Right = Delete(x, T->Right);
   }
   else   //此处找到了要删除的元素
   {
    if (T->Left && T->Right)    //如果这个节点有两个儿子
    {
     TmpCell = FindMin(T->Right);
     T->Element = TmpCell->Element;
     T->Right = Delete(T->Element, T->Right);
    }
    else    //一个儿子或者没有儿子
    {
     TmpCell = T;
     if (T->Left == NULL)
     {
      T = T->Right;

     }
     else
     {
      if (T->Right == NULL)
      {
       T = T->Left;
      }
     }
     free(TmpCell);
    }
   }
  }
 }
 return T;
}
int main()
{
 //////////////测试//////////////////////
 SearchTree Tree_1 = CreatTree(6);//根结点为6
 Tree_1 = Insert(2, Tree_1);
 Tree_1 = Insert(8, Tree_1);
 Tree_1 = Insert(1, Tree_1);
 Tree_1 = Insert(4, Tree_1);
 Tree_1 = Insert(3, Tree_1);
 ///////////////上面的二叉树为////////////////////////////
//  6           
// /
//   2   8
//  /
// 1   4
// /
//   3
 ///////////////////////////////////////////////////////
 cout << FindMax(Tree_1)->Element << endl;
 cout << FindMin(Tree_1)->Element << endl;
 cout << Find(2, Tree_1)->Right->Element << endl;//结点2的右下方元素
 MakeEmpty(Tree_1);
 return 0;
}