数据结构—二叉搜索树

原理：参考趣学数据结构

代码：

队列代码：

#pragma once
#define N 100
#define elemType bstTree*
#include<stdlib.h>
typedef struct bstTree {int data;struct bstTree* lchild, *rchild;
}bstTree;
typedef struct dQueue {elemType data;struct dQueue* next;
}dQueue;
typedef struct queue {dQueue *front, *rear;
}queue;
bool initQueue(queue &Queue) {//初始化队列//Queue.front = new dQueue;Queue.front = Queue.rear = (dQueue*)malloc(sizeof(dQueue));if (!Queue.front) {return false;}Queue.front->next = NULL;//头结点return true;
}
elemType getQueueTopElem(queue &Queue) {//获取队列队头的元素elemType u=NULL ;if (Queue.front != Queue.rear) {dQueue* p = Queue.front->next;u = p->data;}return u;
}
bool enQueue(queue &Queue, elemType e) {//入队dQueue* p = Queue.rear;dQueue* s = (dQueue*)malloc(sizeof(dQueue));s->data = e;s->next = NULL;p->next = s;Queue.rear = s;return true;
}
bool deQueue(queue &Queue, elemType &e) {//出队if (Queue.front == Queue.rear) {return false;//空队}dQueue* p = Queue.front->next;e = p->data;Queue.front->next = p->next;if (p == Queue.rear) {//队尾只有一个元素的时候Queue.rear = Queue.front;}delete p;return true;
}
bool emptyQueue(queue Queue) {//队列为空的判断if (Queue.front == Queue.rear) {return true;}return false;
}

删除结点和四种（前序、中序、后序、层次）树的结点遍历：

#include<stdio.h>
#include<stdlib.h>
#include"queue.h"
void createBSTTree(bstTree* & T,int data) {//创建二叉排序树bstTree *p = NULL;if (!T) {p = (bstTree*)malloc(sizeof(bstTree));p->data = data;p->lchild = p->rchild = NULL;T = p;return;}if (data < T->data) {//左子树插入createBSTTree(T->lchild,data);}else {//右子树插入createBSTTree(T->rchild,data);}
}
void prePrint(bstTree*  BSTTree) {//前序遍历二叉排序树if (BSTTree) {printf("%d ", BSTTree->data);prePrint(BSTTree->lchild);prePrint(BSTTree->rchild);}
}
void midPrint(bstTree*  BSTTree) {//中序遍历二叉排序树if (BSTTree) {midPrint(BSTTree->lchild);printf("%d ", BSTTree->data);midPrint(BSTTree->rchild);}
}
void lastPrint(bstTree*  BSTTree) {//后序遍历二叉排序树if (BSTTree) {lastPrint(BSTTree->lchild);lastPrint(BSTTree->rchild);printf("%d ", BSTTree->data);}
}
void layerPrint(bstTree*  BSTTree) {//层次遍历二叉排序树printf("\n层次遍历二叉排序树:");queue Queue;initQueue(Queue);if (!BSTTree) {return;}enQueue(Queue, BSTTree);//入队while(!emptyQueue(Queue)) {//队列不为空时bstTree* e1 = getQueueTopElem(Queue),*e;deQueue(Queue, e);printf("%d ", e1->data);if (e1->lchild) {enQueue(Queue, e1->lchild);}if (e1->rchild) {enQueue(Queue, e1->rchild);}}printf("\n");
}
void deleteElemBSTTree(bstTree* &T, int e) {//删除元素ebstTree *f=NULL, *p=T, *q,*s;//f指向p当前指向结点的父节点if (!T) {return;}//查找元素ewhile (p) {if (p->data == e) {break;}f = p;if (p->data < e) {p = p->lchild;//左查找}else {p = p->rchild;//右查找}}if (!p) {//查找失败printf("\n没有要删除的元素%d\n", e);return;}if ((p->lchild)&&(p->rchild)) {//如果左右子树都不为空q = p->lchild;s = q;while (q->rchild) {s = q;q = q->rchild;}p->data = q->data;if (s != q) {s->rchild = q->lchild;}else {p->lchild=q->lchild;p = q;}delete q;}else {//其他情况，左孩子或右孩子为空，或者左右孩子都为空q = p;if (!p->lchild) {//左孩子为空p = p->rchild;}else if (!p->rchild) {//右孩子为空p = p->lchild;}if (!f) {//根节点的左孩子为空或者右孩子为空，或者左右孩子都为空T=p;}else if (f->lchild == q) {f->lchild = p;//f父节点的作用来了，起连接跳跃要删除结点的功能}else {f->rchild = p;}delete q;//一定要记得删除}
}
int main() {bstTree* T=NULL;//一定要初始化为空树int count,data;printf("开始构造二叉排序树:\n输入二叉排序树结点的数目:");scanf_s("%d", &count);while (count--) {//构造二叉排序树printf("输入二叉排序树的第%d个结点:",count+1);scanf_s("%d", &data);createBSTTree(T,data);}printf("前序遍历二叉排序树\n");prePrint(T);//前序遍历二叉排序树printf("\n");printf("中序遍历二叉排序树\n");midPrint(T);//中序遍历二叉排序树printf("\n");printf("后序遍历二叉排序树\n");lastPrint(T);//后序遍历二叉排序树printf("\n");layerPrint(T);//层次遍历二叉排序树printf("\n");int delElem;int counts = 2;while (counts--) {printf("删除元素:");scanf_s("%d", &delElem);deleteElemBSTTree(T, delElem);}printf("删除元素后的遍历如下:\n");printf("前序遍历二叉排序树\n");prePrint(T);//前序遍历二叉排序树printf("\n");printf("中序遍历二叉排序树\n");midPrint(T);//中序遍历二叉排序树printf("\n");printf("后序遍历二叉排序树\n");lastPrint(T);//后序遍历二叉排序树printf("\n");layerPrint(T);//层次遍历二叉排序树printf("\n");system("pause");return 0;
}

测试截图：

删除元素的时间复杂度O(logn),空间复杂度为O(1)

如果存在什么问题，欢迎批评指正！谢谢！