二叉查找树（Binary Search Tree）

Date：2019-06-25 14:40:32

基本操作

• 注意：数据量较大时，插入建树的时间复杂度会很高，慎用！

 //查找
 void Search(node *root, int x)
 {
     if(root == NULL)
     {
         printf("search failed\n");
         return;
     }
     if(x == root->data)
         printf("%d\n", root->data);
     else if(x < root->data)
         Search(root->lchild, x);
     else if(x > root->data)
         Search(root->data)
         Search(root->rchild, x);
 }

 //插入
 void Insert(node *root, int x)
 {
     if(root == NULL)
     {
         root = newNode(x);  //新建结点
         return;
     }
     if(x == root->data)
         return;
     else if(x > root->data)
         Insert(root->rchild, x);
     else if(x < root->data)
         Insert(root->lchild, x);
 }

 //建立
 node* Create(int data[], int n)
 {
     node *root = NULL;
     for(int i=; i<n; i++)
         Insert(root, data[i]);

     return root;
 }

 //删除

 //寻找前驱
 node* FindMax(node *root)
 {
     while(root->rchild != NULL)
         root = root->rchild;
     return root;
 }

 //寻找后继
 node* FindMin(node *root)
 {
     while(root->lchild != NULL)
         root = root->lchild;
     return root;
 }

 //删除结点root
 void Delete(node *&root, int x)
 {
     if(root == NULL)
         return;
     if(root->data == x)
     {
         if(root->lchild==NULL & root->rchild==NULL) //叶子结点直接删除即可
             root = NULL;
         else if(root->lchild != NULL)
         {
             node *pre = FindMax(root->lchild);      //寻找左子树的最大值（最右结点）
             root->data = pre->data;                 //与被删除结点替换
             Delete(root->lchild, pre->data);        //删除替换后的结点
         }
         else if(root->rchild != NULL)
         {
             node *pre = FindMin(root->rchild);      //寻找右子树的最小值（最左结点）
             root->data = pre->data;
             Delete(root->rchild, pre->data);
         }
     }
     else if(x < root->data)
         Delete(root->lchild, x);
     else if(x > root->data)
         Delete(root->rchild, x);
 }

删除优化

• 删除操作中，找到替换结点后，该结点就是接下来需要删除的结点，直接删除即可
• 目前PAT考试中还没有考察过删除结点相关的算法

 #include<stdio.h>
 const int M = ;
 const int data[M] = {,,,,,,,,,};

 struct node
 {
     int data;
     node *lchild, *rchild;
 };

 node* FindMax(node *root)
 {
     while(root->rchild->rchild)
         root = root->rchild;
     return root;
 }

 node *FindMin(node *root)
 {
     while(root->lchild->lchild)
         root = root->lchild;
     return root;
 }

 void BST(node *&root, int x)
 {
     if(!root)
     {
         root = new node;
         root->data = x;
         root->lchild = NULL;
         root->rchild = NULL;
         return;
     }
     if(x == root->data)
     {
         if(!root->lchild && !root->rchild)
             root = NULL;
         else if(root->lchild)
         {
             node *pre;
             if(root->lchild->rchild == NULL)
             {
                 pre = root->lchild;
                 root->lchild = pre->lchild;
             }
             else
             {
                 node *fa = FindMax(root->lchild);
                 pre = fa->rchild;
                 fa->rchild = pre->lchild;
             }
             root->data = pre->data;
             delete(pre);
         }
         else if(root->rchild)
         {
             node *pre;
             if(root->rchild->lchild == NULL)
             {
                 pre = root->rchild;
                 root->rchild = pre->rchild;
             }
             else
             {
                 node *fa = FindMin(root->rchild);
                 pre = fa->rchild;
                 fa->rchild = pre->lchild;
             }
             root->data = pre->data;
             delete(pre);
         }
     }
     else if(x < root->data)
         BST(root->lchild, x);
     else if(x > root->data)
         BST(root->rchild, x);
 }

 void Traverse(node *root)
 {
     if(root == NULL)
         return;
     Traverse(root->lchild);
     printf("%d ", root->data);
     Traverse(root->rchild);
 }

 node* Create()
 {
     node *root = NULL;
     for(int i=; i<M; i++)
         BST(root, data[i]);

     return root;
 }

 int main()
 {
 #ifdef ONLINE_JUDGE
 #else
     freopen("Test.txt", "r", stdin);
 #endif // ONLINE_JUDGE

     node *root = Create();
     Traverse(root);
     printf("\n");
     BST(root, );
     Traverse(root);

     return ;
 }