数据结构---二叉平衡排序树的删除

数据结构—二叉平衡排序树的删除

原理：参考趣学数据结构

代码：

#include<stdio.h>
#include<stdlib.h>
typedef struct avlTree {int data;struct avlTree *lchild, *rchild;int height;
}avlTree;int height(avlTree* AVLTree);//声明avl树的深度
void updateHeight(avlTree* &AVLTree);//声明更新avl树每个结点的高度avlTree* LL(avlTree* &AVLTree) {//单向右旋avlTree* temp = AVLTree->lchild;AVLTree->lchild = temp->rchild;temp->rchild = AVLTree;updateHeight(temp);//更新avl树的高度updateHeight(AVLTree);return temp;
}
avlTree* RR(avlTree* &AVLTree) {//单向左旋avlTree* temp = AVLTree->rchild;AVLTree->rchild=temp->lchild;temp->lchild = AVLTree;updateHeight(temp);//更新avl树的高度updateHeight(AVLTree);//调整顺序的两个节点都要更新高度return temp;
}
avlTree* LR(avlTree* &AVLTree) {//先右后左双向旋转AVLTree->lchild=RR(AVLTree->lchild);return LL(AVLTree);
}
avlTree* RL(avlTree* &AVLTree) {//先左后右双向旋转AVLTree->rchild = LL(AVLTree->rchild);return RR(AVLTree);
}
int height(avlTree* AVLTree) {//计算树的高度int m, n;if (!AVLTree) {return 0;}else {m = height(AVLTree->lchild);//左子树深度n = height(AVLTree->rchild);//右子树深度if (m > n) {return m + 1;}else {return n + 1;}}
}
void updateHeight(avlTree* &AVLTree) {//更新每个结点的高度值if (AVLTree) {AVLTree->height = height(AVLTree);updateHeight(AVLTree->lchild);updateHeight(AVLTree->rchild);}
}
avlTree* insertAVLTree(avlTree* &AVLTree,int e) {//插入一个结点if (!AVLTree) {//如果为空树，生成一个新的结点AVLTree = (avlTree*)malloc(sizeof(avlTree));AVLTree->data = e;AVLTree->lchild = AVLTree->rchild = NULL;//不能写成二个都是左指针AVLTree->height = 1;return AVLTree;}else {//查找元素要插入的位置if (AVLTree->data == e) {printf("已经存在元素%d,不需要插入\n", e);return AVLTree;//结束}if (e < AVLTree->data) {AVLTree->lchild = insertAVLTree(AVLTree->lchild, e);//插入左边if (height(AVLTree->lchild) - height(AVLTree->rchild) == 2) {if (e > AVLTree->lchild->data) {AVLTree =LR(AVLTree);//一定要有返回值覆盖}else {AVLTree =LL(AVLTree);}}}else {AVLTree->rchild = insertAVLTree(AVLTree->rchild, e);//插入右边if (height(AVLTree->rchild) - height(AVLTree->lchild) == 2) {if (AVLTree->rchild->data > e) {AVLTree =RL(AVLTree);}else {AVLTree =RR(AVLTree);}}}}updateHeight(AVLTree);//更新AVL每个结点的高度return AVLTree;
}
avlTree * adjustAVLTree(avlTree * &AVLTree) {//调整删除结点后的树if (!AVLTree) {return NULL;}if (height(AVLTree->lchild) - height(AVLTree->rchild) == 2) {if (height(AVLTree->lchild->lchild) >= height(AVLTree->lchild->rchild)) {AVLTree = LL(AVLTree);//单向右旋}else {AVLTree = LR(AVLTree);//先左后右双向旋转}}else if (height(AVLTree->rchild) - height(AVLTree->lchild) == 2) {if (height(AVLTree->rchild->rchild) >= height(AVLTree->rchild->lchild)) {AVLTree = RR(AVLTree);//单向左旋}else {AVLTree = RL(AVLTree);//先右后左双向旋转}}updateHeight(AVLTree);//更新avl树中每个结点的高度return AVLTree;
}
avlTree * deleteElemAVL(avlTree * &AVLTree,int data) {//删除avl的元素if (AVLTree == NULL) {return AVLTree;}if (AVLTree->data == data) {//查找到了该元素if (!AVLTree->rchild) {//如果右子树为空avlTree* temp = AVLTree;AVLTree = AVLTree->lchild;delete temp;}else {//右子树不为空avlTree* p = AVLTree->rchild;while (p->rchild) {p = p->lchild;}AVLTree->data = p->data;//右孩子的右孩子，一直下去AVLTree->rchild = deleteElemAVL(AVLTree->rchild, AVLTree->data);updateHeight(AVLTree);//更新avl树中每个结点的高度}return AVLTree;//这个结束后返回}else if (data < AVLTree->data) {//左子树查找AVLTree->lchild = deleteElemAVL(AVLTree->lchild, data);}else {//右子树查找AVLTree->rchild = deleteElemAVL(AVLTree->rchild, data);}if (AVLTree->lchild) {//先调左右子树，最后调整根节点AVLTree->lchild = adjustAVLTree(AVLTree->lchild);}if (AVLTree->rchild) {AVLTree->lchild = adjustAVLTree(AVLTree->rchild);}if (AVLTree) {AVLTree = adjustAVLTree(AVLTree);}return AVLTree;
}
void prePrint(avlTree*  T) {//前序遍历AVLif (T) {printf("%d ", T->data);prePrint(T->lchild);prePrint(T->rchild);}
}
int main() {avlTree* T = NULL;//一定要初始化为空树int count, data;printf("开始构造avl:\n输入avl结点的数目:");scanf_s("%d", &count);int counts = 0;while (count--) {//构造avlcounts += 1;printf("输入avl的第%d个结点:", counts);scanf_s("%d", &data);insertAVLTree(T, data);}printf("前序遍历avl\n");prePrint(T);//前序遍历avlprintf("\n");printf("删除avl的结点:");scanf_s("%d", &count);deleteElemAVL(T, count);printf("删除avl的结点后的前序遍历\n");prePrint(T);//前序遍历avlprintf("\n");system("pause");return 0;
}