#include <stdio.h>#include <stdlib.h>#define STACK_MAX_SIZE 30#define QUEUE_MAX_SIZE 30#ifndef elemTypetypedef char elemType;#endif/************************************************************************//* 以下是关于二叉树操作的11个简单算法 *//************************************************************************/ struct BTreeNode{elemType data;struct BTreeNode *left;struct BTreeNode *right;};/* 1.初始化二叉树 */void initBTree(struct BTreeNode* *bt){*bt = NULL;return;}/* 2.建立二叉树(根据a所指向的二叉树广义表字符串建立) */void createBTree(struct BTreeNode* *bt, char *a){struct BTreeNode *p;struct BTreeNode *s[STACK_MAX_SIZE];/* 定义s数组为存储根结点指针的栈使用 */ int top = -1; /* 定义top作为s栈的栈顶指针，初值为-1,表示空栈 */int k; /* 用k作为处理结点的左子树和右子树，k = 1处理左子树，k = 2处理右子树 * /int i = 0; /* 用i扫描数组a中存储的二叉树广义表字符串，初值为0 */*bt = NULL; /* 把树根指针置为空，即从空树开始建立二叉树 *//* 每循环一次处理一个字符，直到扫描到字符串结束符\0为止 */while(a[i] != '\0'){switch(a[i]){case ' ':break; /* 对空格不作任何处理 */case '(':if(top == STACK_MAX_SIZE - 1){printf("栈空间太小！\n");exit(1);}top++;s[top] = p;k = 1;break;case ')':if(top == -1){printf("二叉树广义表字符串错误!\n");exit(1);}top--;break;case ',':k = 2;break;default:p =(struct BTreeNode *) malloc(sizeof(struct BTreeNode)); p->data = a[i];p->left = p->right = NULL;if(*bt == NULL){*bt = p;}else{if( k == 1){s[top]->left = p;}else{s[top]->right = p;}}}i++; /* 为扫描下一个字符修改i值 */}return;}/* 3.检查二叉树是否为空，为空则返回1,否则返回0 */int emptyBTree(struct BTreeNode *bt){if(bt == NULL){return 1;}else{return 0;}}/* 4.求二叉树深度 */int BTreeDepth(struct BTreeNode *bt){if(bt == NULL){return 0; /* 对于空树，返回0结束递归 */}else{int dep1 = BTreeDepth(bt->left); /* 计算左子树的深度 */int dep2 = BTreeDepth(bt->right); /* 计算右子树的深度 */if(dep1 > dep2){return dep1 + 1;}else{return dep2 + 1;}}}/* 5.从二叉树中查找值为x的结点，若存在则返回元素存储位置，否则返回空值 */ elemType *findBTree(struct BTreeNode *bt, elemType x){if(bt == NULL){return NULL;}else{if(bt->data == x){return &(bt->data);}else{ /* 分别向左右子树递归查找 */elemType *p;if(p = findBTree(bt->left, x)){return p;}if(p = findBTree(bt->right, x)){return p;}return NULL;}}}/* 6.输出二叉树(前序遍历) */void printBTree(struct BTreeNode *bt){/* 树为空时结束递归，否则执行如下操作 */if(bt != NULL){printf("%c", bt->data); /* 输出根结点的值 */if(bt->left != NULL || bt->right != NULL){ printf("(");printBTree(bt->left);if(bt->right != NULL){printf(",");}printBTree(bt->right);printf(")");}}return;}/* 7.清除二叉树，使之变为一棵空树 */void clearBTree(struct BTreeNode* *bt) {if(*bt != NULL){clearBTree(&((*bt)->left));clearBTree(&((*bt)->right));free(*bt);*bt = NULL;}return;}/* 8.前序遍历 */void preOrder(struct BTreeNode *bt){if(bt != NULL){printf("%c ", bt->data); /* 访问根结点 */ preOrder(bt->left); /* 前序遍历左子树 */ preOrder(bt->right); /* 前序遍历右子树 */ }return;}/* 9.中序遍历 */void inOrder(struct BTreeNode *bt){if(bt != NULL){inOrder(bt->left); /* 中序遍历左子树 */ printf("%c ", bt->data); /* 访问根结点 */inOrder(bt->right); /* 中序遍历右子树 */}return;}/* 10.后序遍历 */void postOrder(struct BTreeNode *bt){if(bt != NULL){postOrder(bt->left); /* 后序遍历左子树 */postOrder(bt->right); /* 后序遍历右子树 */printf("%c ", bt->data); /* 访问根结点 */}return;}/* 11.按层遍历 */void levelOrder(struct BTreeNode *bt){struct BTreeNode *p;struct BTreeNode *q[QUEUE_MAX_SIZE];int front = 0, rear = 0;/* 将树根指针进队 */if(bt != NULL){rear = (rear + 1) % QUEUE_MAX_SIZE;q[rear] = bt;}while(front != rear){ /* 队列非空 */front = (front + 1) % QUEUE_MAX_SIZE; /* 使队首指针指向队首元素 */ p = q[front];printf("%c ", p->data);/* 若结点存在左孩子，则左孩子结点指针进队 */if(p->left != NULL){rear = (rear + 1) % QUEUE_MAX_SIZE;q[rear] = p->left;}/* 若结点存在右孩子，则右孩子结点指针进队 */if(p->right != NULL){rear = (rear + 1) % QUEUE_MAX_SIZE;q[rear] = p->right;}}return;}/************************************************************************//*int main(int argc, char *argv[]){struct BTreeNode *bt; /* 指向二叉树根结点的指针 */char *b; /* 用于存入二叉树广义表的字符串 */elemType x, *px;initBTree(&bt);printf("输入二叉树广义表的字符串：\n");/* scanf("%s", b); */b = "a(b(c), d(e(f, g), h(, i)))";createBTree(&bt, b);if(bt != NULL)printf(" %c ", bt->data);printf("以广义表的形式输出：\n");printBTree(bt); /* 以广义表的形式输出二叉树 */printf("\n");printf("前序："); /* 前序遍历 */preOrder(bt);printf("\n");printf("中序："); /* 中序遍历 */inOrder(bt);printf("\n");printf("后序："); /* 后序遍历 */postOrder(bt);printf("\n");printf("按层："); /* 按层遍历 */levelOrder(bt);printf("\n");/* 从二叉树中查找一个元素结点 */printf("输入一个待查找的字符：\n");scanf(" %c", &x); /* 格式串中的空格跳过空白字符 */px = findBTree(bt, x);if(px){printf("查找成功：%c\n", *px);}else{printf("查找失败！\n");}printf("二叉树的深度为：");printf("%d\n", BTreeDepth(bt));clearBTree(&bt);return 0;}*/#include <stdio.h>#define QUEUE_MAX_SIZE 20#define STACK_MAX_SIZE 10typedef int elemType;#include "BT.c"/************************************************************************/ /* 以下是关于二叉搜索树操作的4个简单算法*//************************************************************************//* 1.查找*//* 递归算法*/elemType *findBSTree1(struct BTreeNode *bst, elemType x){/* 树为空则返回NULL */if (bst == NULL){return NULL;}else{if (x == bst->data){return &(bst->data);}else{if (x < bst->data){ /* 向左子树查找并直接返回*/return findBSTree1(bst->left, x);}else{ /* 向右子树查找并直接返回*/return findBSTree1(bst->right, x);}}}}/* 非递归算法*/elemType *findBSTree2(struct BTreeNode *bst, elemType x){while (bst != NULL){if (x == bst->data){return &(bst->data);}else if (x < bst->data){bst = bst->left;}else{bst = bst->right;}}return NULL;}/* 2.插入*//* 递归算法*/void insertBSTree1(struct BTreeNode* *bst, elemType x){/* 新建一个根结点*/if (*bst == NULL){struct BTreeNode *p = (struct BTreeNode *)malloc(sizeof(struct BTreeNode)); p->data = x;p->left = p->right = NULL;*bst = p;return;}else if (x < (*bst)->data){ /* 向左子树完成插入运算*/insertBSTree1(&((*bst)->left), x);}else{ /* 向右子树完成插入运算*/insertBSTree1(&((*bst)->right), x);}}/* 非递归算法*/void insertBSTree2(struct BTreeNode* *bst, elemType x){struct BTreeNode *p;struct BTreeNode *t = *bst, *parent = NULL;/* 为待插入的元素查找插入位置*/while (t != NULL){parent = t;if (x < t->data){t = t->left;}else{t = t->right;}}/* 建立值为x，左右指针域为空的新结点*/p = (struct BTreeNode *)malloc(sizeof(struct BTreeNode));p->data = x;p->left = p->right = NULL;/* 将新结点链接到指针为空的位置*/if (parent == NULL){*bst = p; /* 作为根结点插入*/}else if (x < parent->data){ /* 链接到左指针域*/parent->left = p;}else{parent->right = p;}return;}/* 3.建立*/void createBSTree(struct BTreeNode* *bst, elemType a[], int n){int i;*bst = NULL;for (i = 0; i < n; i++){insertBSTree1(bst, a[i]);}return;}/* 4.删除值为x的结点，成功返回1,失败返回0 */int deleteBSTree(struct BTreeNode* *bst, elemType x){struct BTreeNode *temp = *bst;if (*bst == NULL){return 0;}if (x < (*bst)->data){return deleteBSTree(&((*bst)->left), x); /* 向左子树递归*/}if (x > (*bst)->data){return deleteBSTree(&((*bst)->right), x); /* 向右子树递归*/}/* 待删除的元素等于树根结点值且左子树为空，将右子树作为整个树并返回1 */ if ((*bst)->left == NULL){*bst = (*bst)->right;free(temp);return 1;}/* 待删除的元素等于树根结点值且右子树为空，将左子树作为整个树并返回1 */ if ((*bst)->right == NULL){*bst = (*bst)->left;free(temp);return 1;}else{/* 中序前驱结点为空时，把左孩子结点值赋给树根结点，然后从左子树中删除根结点*/ if ((*bst)->left->right == NULL){(*bst)->data = (*bst)->left->data;return deleteBSTree(&((*bst)->left), (*bst)->data);}else{ /* 定位到中序前驱结点，把该结点值赋给树根结点，然后从以中序前驱结点为根的树上删除根结点*/struct BTreeNode *p1 = *bst, *p2 = p1->left;while (p2->right != NULL){p1 = p2;p2 = p2->right;}(*bst)->data = p2->data;return deleteBSTree(&(p1->right), p2->data);}}}/************************************************************************/int main(int argc, char *argv[]){int x, *px;elemType a[10] = {30, 50, 20, 40, 25, 70, 54, 23, 80, 92};struct BTreeNode *bst = NULL;createBSTree(&bst, a, 10);printf("建立的二叉搜索树的广义表形式为：");printBTree(bst);printf(" ");printf("中序遍历：");inOrder(bst);printf(" ");printf("输入待查找元素的值：");scanf(" %d", &x);if (px = findBSTree1(bst, x)){printf("查找成功！得到的x为：%d ", *px);}else{printf("查找失败！");}printf("输入待插入的元素值：");scanf(" %d", &x);insertBSTree1(&bst, x);printf("输入待删除元素值：");scanf(" %d", &x);if (deleteBSTree(&bst, x)){printf("1 ");}else{printf("0 ");}printf("进行相应操作后的中序遍历为："); inOrder(bst);printf(" ");printf("操作后的二叉搜索树的广义表的形式为："); printBTree(bst);printf(" ");clearBTree(&bst);return 0;}。