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叉搜索树(Binary Search Tree)的一般形式如下图所示，每个节点中的元素大于它的左子树中的所有元素，小于它的右子树中的所有元素。对该图中的二叉树进行中序遍历得到一个从小到大排列的有序序列。
本文给出了上述二叉树的一个C语言实现，包括二叉树的节点添加，删除，查找等等。源码分为三个文件，
使用VC 6.0编译，其中bstree.h是二叉搜索树的数据结构和函数声明，bstree.c是二叉搜索树的函数实现，main.c是
二叉树的测试文件。这里实现的二叉搜索树的增、删、查三个操作的平均时间复杂度都为log2N,其中N为元素个数。
但是如果建树时的元素本身有序，那么上述操作的时间复杂度将会退化为O(N)。
/*
* File : bstree.h
* Purpose: implementation of a Binary Search Tree
* Author: puresky
* Comiler: VC 6.0
* Language: C
*/
#ifndef _BINARY_SEARCH_TREE_H
#define _BINARY_SEARCH_TREE_H
// Binary Search Tree Node Struct
typedef struct BSTNodeStruct BSTNode;
struct BSTNodeStruct
{
int _key;
void *_data;
struct BSTNodeStruct *_left;
struct BSTNodeStruct *_right;
};
//Binary Search Tree Struct
typedef struct BSTreeStruct BSTree;
struct BSTreeStruct
{
BSTNode *_root;
int _count;
};
BSTree *bstree_new();
void bstree_free(BSTree *bst);
void bstree_insert(BSTree *bst, int key, void *data);
void bstree_remove(BSTree *bst, int key);
BSTNode *bstree_find(BSTree *bst, int key);
int bstree_size(BSTree *bst);
int bstree_height(BSTree *bst);
void bstree_print(BSTree *bst);
#endif
/*
* File : bstree.c
* Purpose: implementation of a Binary Search Tree
* Author: puresky
* Comiler: VC 6.0
* Language: C
*/
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include "bstree.h"
static BSTNode *bstnode_new(int key, void *data)
{
BSTNode *bstn = (BSTNode *)malloc(sizeof(BSTNode));
bstn->_key = key;
bstn->_data = data;
bstn->_left = bstn->_right = NULL;
fprintf(stdout, "create BSTNode:%d\n", key);
return bstn;
}
static void bstnode_free(BSTNode *bstn)
{
if(bstn)
{
fprintf(stdout, "free BSTNode :%d\n", bstn->_key);
free(bstn);
}
}
static void bstnode_free_recursively(BSTNode *bstn)
{
if(bstn)
{
if(bstn->_left)
bstnode_free_recursively(bstn->_left);
if(bstn->_right)
bstnode_free_recursively(bstn->_right);
bstnode_free(bstn);
}
}
static int bstnode_insert(BSTNode **pbstn, int key, void *data)
{
BSTNode *bstn = *pbstn;
if(bstn == NULL)
{
*pbstn = bstnode_new(key, data);
return 1;
}
else if(bstn->_key > key)
{
return bstnode_insert(&bstn->_left, key, data);
}
else if(bstn->_key < key)
{
return bstnode_insert(&bstn->_right, key, data);
}
else //bstn->_key == key
{
return 0;
}
}
static BSTNode *bstnode_find(BSTNode *bstn, int key)
{
if(bstn == NULL)
return NULL;
else if(bstn->_key == key)
return bstn;
else if(bstn->_left && bstn->_key > key)
return bstnode_find(bstn->_left, key);
else if(bstn->_right && bstn->_key < key)
return bstnode_find(bstn->_right, key);
else
return NULL;
}
//To delete the max Node in the Tree
static int bstnode_remove_left_max(BSTNode **pbstn, BSTNode *toRemove)
{
BSTNode *bstn = *pbstn;
if(bstn->_right != NULL)
{
bstnode_remove_left_max(&bstn->_right, toRemove);
}
else
{
toRemove->_key = bstn->_key;
toRemove->_data = bstn->_data;
*pbstn = bstn->_left;
bstnode_free(bstn);
}
}
static int bstnode_remove(BSTNode **pbstn, int key)
{
BSTNode *bstn = *pbstn;
if(bstn == NULL)
return 0;
if(bstn->_key > key)
{
return bstnode_remove(&bstn->_left, key);
}
else if(bstn->_key < key)
{
return bstnode_remove(&bstn->_right, key);
}
else //bstn->_key == key
{
if(bstn->_left == NULL)
{
*pbstn = bstn->_right;
bstnode_free(bstn);
}
else if(bstn->_right == NULL)
{
*pbstn = bstn->_left;
bstnode_free(bstn);
}
else //bstn->right != NULL && bstn->left != NULL
{
//Both the left and the right are not NULL.
//We can choose either of them to apply a deletion.
//Here we choose the left child!
//Actually, we find the max node in the left subtree.
//And store the data in of max node in the node to be removed really.
//Then delete the max node!
bstnode_remove_left_max(&bstn->_left, bstn);
}
}
}
static int bstnode_height(BSTNode *bstn)
{
int ret, left, right;
if(!bstn)
ret = 0;
else
{
left = bstnode_height(bstn->_left);
right = bstnode_height(bstn->_right);
ret = (left > right ? left : right) + 1;
}
return ret;
}
static void bstnode_print(BSTNode *bstn, int depth)
{
int i;
for(i = 0; i < depth; ++i) printf(" ");
if(bstn)
{
printf("[%d]\n", bstn->_key);
bstnode_print(bstn->_left, depth + 1);
bstnode_print(bstn->_right, depth + 1);
}
else
{
printf("NULL\n");
}
}
BSTree *bstree_new()
{
BSTree *bst = (BSTree *)malloc(sizeof(BSTree));
bst->_count = 0;
bst->_root = NULL;
return bst;
}
void bstree_free(BSTree *bst)
{
if(bst)
{
bstnode_free_recursively(bst->_root);
free(bst);
}
}
void bstree_insert(BSTree *bst, int key, void *data)
{
if(bstnode_insert(&bst->_root, key, data))
bst->_count++;
}
void bstree_remove(BSTree *bst, int key)
{
if(bstnode_remove(&bst->_root, key))
bst->_count--;
}
BSTNode *bstree_find(BSTree *bst, int key)
{
return bstnode_find(bst->_root, key);
}
int bstree_size(BSTree *bst)
{
return bst->_count;
}
int bstree_height(BSTree *bst)
{
return bstnode_height(bst->_root);
}
void bstree_print(BSTree *bst)
{
printf("size:%d, height:%d\n",
bst->_count,
bstree_height(bst));
bstnode_print(bst->_root, 0);
}
/*
* File : main.c
* Purpose: implementation of a Binary Search Tree
* Author: puresky
* Comiler: VC 6.0
* Language: C
*/
#include <stdio.h>
#include <stdlib.h>
#include "bstree.h"
#define MAX_NUM 10
void test()
{
int i;
int a[] ={7, 9, 12, 5, 4, 2, 10, 8, 7, 6, 3, 100, 20, 1};
BSTree *bst = bstree_new();
for(i = 0; i < sizeof(a) / sizeof(int); ++i)
bstree_insert(bst, a[i], NULL);
bstree_print(bst);
printf("==================================\n");
printf("%d\n", bstree_find(bst, 10)->_key);
printf("%d\n", bstree_find(bst, 3)->_key);
printf("==================================\n");
bstree_remove(bst, 4);
bstree_remove(bst, 1);
bstree_remove(bst, 10);
bstree_remove(bst, 3);
bstree_remove(bst, 7);
bstree_print(bst);
bstree_free(bst);
}
int main(int argc, char **argv)
{
test();
system("pause");
}
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