数据结构之二叉树的一些基本操作

二叉树是树的特殊一种，具有如下特点：1、每个结点最多有两颗子树，结点的度最大为2。2、左子树和右子树是有顺序的，次序不能颠倒。3、即使某结点只有一个子树，也要区分左右子树。
头文件 BTree.h

#ifndef __BTREE_H__#define __BTREE_H__#define BLEFT  0                 // 表示插入二叉树的左边#define BRIGHT 1                 // 表示插入二叉树的右边#define TRUE   1#define FALSE  0typedef char BTreeData;// 二叉树的结点typedef struct _btreeNode{    BTreeData data;    struct _btreeNode* lchild;   // 指向左孩子结点的指针    struct _btreeNode* rchild;   // 指向右孩子结点的指针}BTreeNode;// 二叉树typedef struct _btree{    BTreeNode *root;             // 指向二叉树的根节点    int  count;                  // 记录二叉树结点的个数}BTree;typedef void(*Print_BTree)(BTreeNode*);// 创建一棵二叉树BTree* Create_BTree();// pos 走的路径 值类似 110（左右右）  011 （右右左）// count 代表走的步数// flag  代表被替换的结点应该插入在新节点的位置，如果是BLEFT 表示插在左边，BRIGHT表示插在右边int Btree_Insert (BTree* tree, BTreeData data, int pos, int count, int flag);// 打印二叉树void Display (BTree* tree, Print_BTree pfunc);// 删除pos处的结点int Delete   (BTree* tree, int pos, int count);// 求树的高度int BTree_Height  (BTree* tree);// 求树的度int BTree_Degree  (BTree* tree);// 清除树int BTree_Clear   (BTree* tree);// 销毁树int BTree_Destroy (BTree** tree);// 打印void printA (BTreeNode* node);// 前序遍历void pre_order  (BTreeNode* node);// 中序遍历void mid_order  (BTreeNode* node);// 后序遍历void last_order (BTreeNode* node);#endif // __BTREE_H__

源文件 BTree.c

#include "BTree.h"#include <stdlib.h>#include <stdio.h>BTree *Create_BTree(){    BTree* btree = (BTree*) malloc(sizeof(BTree)/sizeof(char));    if (NULL == btree)    {        return NULL;    }    btree->count = 0;    btree->root  = NULL;    return btree;}int Btree_Insert (BTree* tree, BTreeData data, int pos, int count, int flag){    if (NULL == tree || (flag != BLEFT && flag != BRIGHT))    {        return FALSE;    }    BTreeNode* node = (BTreeNode*) malloc(sizeof(BTreeNode)/sizeof(char));    if (NULL == node)    {        return FALSE;    }    node->data   = data;    node->lchild = NULL;    node->rchild = NULL;    // 找插入的位置    BTreeNode *parent  = NULL;    BTreeNode *current = tree->root;     // current 一开始指向根节点，根节点的父节点是空    int way;                             // 保存当前走的位置    while (count > 0 && current != NULL)    {        way = pos &  1;                  // 取出当前走的方向        pos = pos >> 1;                  // 移去走过的路线        // 因为当前位置就是走完以后的位置的父节点        parent = current;        if (way == BLEFT)   // 往左走        {            current = current->lchild;        }        else        {            current = current->rchild;        }        count --;    }    // 把被替换掉的结点插入到新节点下面    if (flag == BLEFT)    {        node->lchild = current;    }    else    {        node->rchild = current;    }    // 把新节点插入到二叉树中,way保存了应该插入在父节点的左边还是右边    if (NULL != parent)    {        if (way == BLEFT)        {            parent->lchild = node;        }        else        {            parent->rchild = node;        }    }    else    {        tree->root = node;  // 替换根节点    }    tree->count++;    return TRUE;}void r_display (BTreeNode* node, Print_BTree pfunc, int gap){    int i;    if (node == NULL)    {        for (i = 0; i < gap; i++)        {            printf ("-");        }        printf ("\n");        return;    }    for (i = 0; i < gap; i++)    {        printf ("-");    }    // 打印结点    // printf ("%c\n", node->data);    pfunc (node);    if (NULL != node->lchild || NULL != node->rchild)    {        // 打印左孩子        r_display (node->lchild, pfunc, gap+4);        // 打印右孩子        r_display (node->rchild, pfunc, gap+4);    }}void Display (BTree* tree, Print_BTree pfunc){    if (tree == NULL)    {        return;    }    r_display (tree->root, pfunc, 0);}void r_delete (BTree* tree, BTreeNode* node){    if (NULL == node || NULL == tree)    {        return;    }    // 先删除左孩子    r_delete (tree, node->lchild);    // 删除右孩子    r_delete (tree, node->rchild);    free (node);    tree->count--;}int Delete (BTree* tree, int pos, int count){    if (NULL == tree)        return FALSE;    // 找结点    BTreeNode* parent  = NULL;    BTreeNode* current = tree->root;    int way;    while (count > 0 && NULL != current)    {        way = pos &  1;        pos = pos >> 1;        parent = current;        if (way == BLEFT)        {            current = current->lchild;        }        else        {            current = current->rchild;        }               count--;    }    if (NULL != parent)    {        if (way == BLEFT)        {            parent->lchild = NULL;        }        else        {            parent->rchild = NULL;        }    }    else    {        tree->root = NULL;    }    // 释放结点    r_delete (tree, current);    return TRUE;}int r_height (BTreeNode* node){    if (NULL == node)    {        return 0;    }    int lh = r_height (node->lchild);    int rh = r_height (node->rchild);    return (lh > rh ? lh+1 : rh+1);}int BTree_Height (BTree* tree){    if (NULL == tree)    {        return FALSE;    }    int ret = r_height (tree->root);    return ret;}int r_degree (BTreeNode* node){    if (NULL == node)    {        return 0;    }    int degree = 0;    if (NULL != node->lchild)    {        degree++;    }    if (NULL != node->rchild)    {        degree++;    }    if (1 == degree)    {        int ld = r_degree (node->lchild);        if (2 == ld)        {            return 2;        }        int rd = r_degree (node->rchild);        if (2 == rd)        {            return 2;        }    }    return degree;}int BTree_Degree (BTree* tree){    if (NULL == tree)    {        return FALSE;    }    int ret = r_degree (tree->root);    return ret;}int BTree_Clear (BTree* tree){    if (NULL == tree)    {        return FALSE;    }    Delete (tree, 0, 0);  // 删除根节点    tree->root = NULL;    return TRUE;}int BTree_Destroy (BTree** tree){    if (NULL == tree)    {        return FALSE;    }    BTree_Clear (*tree);    free (*tree);    *tree = NULL;    return TRUE;}void pre_order  (BTreeNode* node){    if (NULL == node)    {        return;    }    printf    ("%4c", node->data);    pre_order (node->lchild);    pre_order (node->rchild);}void mid_order  (BTreeNode* node){    if (NULL == node)    {        return;    }    mid_order (node->lchild);    printf    ("%4c", node->data);    mid_order (node->rchild);}void last_order (BTreeNode* node){    if (NULL == node)    {        return;    }    last_order (node->lchild);      last_order (node->rchild);    printf     ("%4c", node->data);}void printA (BTreeNode* node){    printf ("%c\n", node->data);}

主函数 main.c

#include "BTree.h"#include <stdio.h>int main(){    BTree* btree = Create_BTree();    if (NULL == btree)    {        printf ("创建失败\n");    }    else    {        printf ("创建成功\n");    }    Btree_Insert (btree, 'A', 0, 0, 0);    Btree_Insert (btree, 'B', 0, 1, 0);    Btree_Insert (btree, 'C', 1, 1, 0);    Btree_Insert (btree, 'D', 0, 2, 0);    Btree_Insert (btree, 'E', 2, 2, 0);    Btree_Insert (btree, 'F', 0, 3, 0);    Btree_Insert (btree, 'G', 4, 3, 0);    Btree_Insert (btree, 'H', 3, 2, 0);    Display (btree, printA);    printf ("前序遍历：\n");    pre_order (btree->root);    printf ("\n");    printf ("中序遍历：\n");    mid_order (btree->root);    printf ("\n");    printf ("后序遍历：\n");    last_order (btree->root);    printf ("\n");#if 0    Delete (btree, 0, 1);    printf ("删除后--------------\n");    Display (btree, printA);    printf ("高度： %d\n", BTree_Height (btree));    printf ("度 ：  %d\n", BTree_Degree (btree));    printf ("清空后--------------\n");    BTree_Clear (btree);    Display (btree, printA);    BTree_Destroy (&btree);    //btree = NULL;#endif      return 0;}