二叉排序树的基本操作

花了一个星期的时间把算法导论中的二叉排序树看完了，下面是我自己按照伪代码实现的代码。

其中有几处和书中的伪代码不一样(是书中的错了)。

1.后继和前驱的函数successor 和presuccessor. 书中有while循环，但是实际上完全用不到。

2.searchBSTree中，要把T = NULL的情况和T->key = key 的情况分开，而书中合在一起放到if中了

3.delete函数，说实话，书中的delete函数太复杂了(虽然很短)，再看了中文翻译版的之后大致掌握了思想，然后自己实现的。

先从思想开始：从要删除结点node的孩子个数角度出发。

①node是叶子结点，无孩子，这种情况最简单，将node的parent指向NULL，node的指针都指向NULL，然后直接删除node

②node只有一个孩子，这种情况也不复杂。讲node的parent指向node的孩子，也是改变一些指针，然后删除node

③node有两个孩子，这种情况最复杂(但是当你回头看的时候也并不是太复杂)。首先要找到node的后继y，用后继y的key值替换node的key值(node->key = y->key)，然后删除y(分两种情况)，如下：

在这里介绍一个我发现的小窍门，那就是：如果node有两个孩子，那么它的后继y最多有一个孩子。所以删除y的时候就按照 ①②的方法删除就搞定了！

#include<iostream>using namespace std;typedef struct Node{int key;Node *lchild, *rchild;Node *parent;}*BSTree;void preOrderWalk(BSTree T){if(T){printf("%d\n",T->key);preOrderWalk(T->lchild);preOrderWalk(T->rchild);}}void inOrderWalk(BSTree T){if(T){inOrderWalk(T->lchild);printf("%d\n",T->key);inOrderWalk(T->rchild);}}void postOrderWalk(BSTree T){if(T){postOrderWalk(T->lchild);postOrderWalk(T->rchild);printf("%d\n",T->key);}}Node* MinNode(BSTree T){BSTree p = T;while(p->lchild != NULL)p = p->lchild;return p;}Node* MaxNode(BSTree T){BSTree p = T;while(p->rchild != NULL)p = p->rchild;return p;}Node* successor(BSTree T,Node* x){if( x->rchild != NULL)return MinNode( x->rchild);  else return NULL;//---------------------------下面这几条语句没看出作用，有上面的不够么？够了，下面的是错误的/*BSTree y = NULL;while( y != NULL && x == y->rchild){x = y;}return y;*/}Node* presuccessor(BSTree T, Node* x){if(x->lchild != NULL)return MaxNode(x->lchild);elsereturn NULL;/*BSTree y = x->parent;while(y != NULL && x == y->lchild){x = y;y = y->parent;}return y;*/}Node* searchBStree(BSTree T,Node* node){if(T== NULL)return NULL;if(T->key < node->key)return searchBSTree(T->rchild,node);else if(T->key >node->key)return searchBSTree(T->rchild,node);elsereturn T;}Node* searchBSTree(BSTree T,int key){if(T != NULL){if(T->key == key)return T;else if(T->key < key)return searchBSTree(T->rchild,key);elsereturn searchBSTree(T->lchild,key);}elsereturn NULL;}BSTree InsertBSTree(BSTree T, Node* z){Node* y = NULL;Node* x = T;while(x != NULL){y = x;if( z->key < x->key)x = x->lchild;else if(z->key == x->key)return T;elsex = x->rchild;}if(y == NULL)T = z;else if(z->key < y->key)//循环中已经加了等于情况的检测，所以到这里直接插入{y->lchild = z;z->parent = y;}else{y->rchild = z;z->parent = y;}return T;}BSTree InsertBSTree(BSTree T, int key)//插入在加了parent之后也没错{Node* y = NULL;Node* x = T;Node* newNode = (BSTree )malloc(sizeof(Node));newNode->key = key;newNode->lchild = NULL;newNode->rchild = NULL;newNode->parent = NULL;while(x != NULL){y = x;if( key< x->key)x = x->lchild;else if (key == x->key)return T;elsex = x->rchild;}if(y == NULL){T = newNode;newNode->parent = NULL;}else if(key < y->key){y->lchild = newNode;newNode->parent = y;}else{y->rchild = newNode;newNode->parent = y;}return T;}void deleteNode(BSTree T, int key)//暂时没问题了，如果有问题就是searchBSTree函数的问题{Node* node = searchBSTree(T,key);if(node == NULL){printf("this key is not in the tree");exit(0);}else{//-----------------------------------------------------------------node是叶子节点，无孩子if(node->lchild == NULL && node->rchild == NULL){if(node->parent->lchild == node)node->parent->lchild = NULL;elsenode->parent->rchild = NULL;delete node;}else{//-----------------------------------------------------------------node只有一个孩子if((node->lchild && node->rchild ) == NULL){if(node->lchild != NULL){node->parent->lchild = node->lchild;node->lchild = NULL;node->parent = NULL;delete node;}else{node->parent->rchild = node->rchild;node->rchild = NULL;node->parent = NULL;delete node;}}//-----------------------------------------------------------------node有两个孩子else{//-----------------------------------------------------------------既然是node的successor，那么y肯定不会有两个孩子//-----------------------------------------------------------------为什么不用node的presuccessor呢？试一试，好像可以Node* y = presuccessor(T,node);node->key = y->key;if((y->lchild!=NULL)){if(y->parent->lchild == y)y->parent->lchild = y->lchild;elsey->parent->rchild = y->lchild;y->lchild = NULL;y->parent = NULL;delete y;}else if(y->rchild!=NULL){if(y->parent->rchild == y)y->parent->rchild = y->rchild;elsey->parent->lchild = y->rchild;y->rchild = NULL;y->parent = NULL;delete y;}else{if(y->parent->lchild == y)y->parent->lchild = NULL;elsey->parent->rchild = NULL;y->parent = NULL;delete y;}}}}}BSTree createBSTree()//建立也没有错{BSTree T = NULL;int key;while(scanf("%d",&key) != EOF)//EOF标志是ctrl+ZT = InsertBSTree(T,key);return T;}int main(){BSTree T = NULL;T = createBSTree();BSTree succ = (BSTree)malloc(sizeof(Node));preOrderWalk(T);BSTree node = T->lchild;deleteNode(T,5);preOrderWalk(T);return 0;}