#ifndef BINARYTREE_H
#define BINARYTREE_Htypedef struct node *link;
/***节点中的数据类型重定义*/
typedef unsigned char TElemType;struct node { TElemType item; link lchild, rchild;
};link init(TElemType VLR[], TElemType LVR[], int n);void pre_order(link t, void (*visit)(link));
void in_order(link t, void (*visit)(link));
void post_order(link t, void (*visit)(link));
void pprint(link t);
int count(link t);
int depth(link t);
void destroy(link t);/**
*http://www.cnblogs.com/bizhu/archive/2012/08/19/2646328.html 算法图解
*
*二叉排序树(Binary Sort Tree)又称二叉查找树(Binary Search Tree),亦称二叉搜索树,
*它或者是一棵空树；或者是具有下列性质的二叉树:
*(1)若左子树不空，则左子树上所有结点的值均小于它的根结点的值;
*(2)若右子树不空，则右子树上所有结点的值均大于它的根结点的值;
*(3)左、右子树也分别为二叉排序树;
*(4)排序二叉树的中序遍历结果是从小到大排列的.
*
*二叉查找树相比于其他数据结构的优势在于查找、插入的时间复杂度较低,为O(log n)。
*二叉查找树是基础性数据结构，用于构建更为抽象的数据结构，如集合、multiset、关联数组等。
*
*搜索,插入,删除的复杂度等于树高，期望O(log n),最坏O(n)(数列有序,树退化成线性表)
*改进版的二叉查找树可以使树高为O(logn),如SBT,AVL,红黑树等.
*
*程序来源于Linux C编程一站式学习
*/
link bstSearch(link t, TElemType key);
link bstInsert(link t, TElemType key);
link bstDelete(link t, TElemType key);/***http://baike.baidu.com/view/593144.htm?fr=aladdin*平衡二叉树*/#endif

/* binarytree.c */
#include <stdio.h>
#include <stdlib.h>
#include "binarytree.h"/***生成节点*@param item is node value*@returns link point to new node*/
static link make_node(TElemType item)
{link p = malloc(sizeof *p);p->item = item;p->lchild = p->rchild = NULL;return p;
}/***释放节点*@param link to free*/
static void free_node(link p)
{free(p);
}/***根据前序与中序序列来初始化二叉树*@param VLR 前序序列*@param LVR 中序序列*@param n 序列中数值个数*@returns NULL when n <= 0*@returns link pointer to new binarytree*/
link init(TElemType VLR[], TElemType LVR[], int n)
{link t;int k;if (n <= 0)return NULL;for (k = 0; VLR[0] != LVR[k]; k++);t = make_node(VLR[0]);t->lchild = init(VLR+1, LVR, k);t->rchild = init(VLR+1+k, LVR+1+k, n-k-1);return t;
}#ifdef RECU
/***前序遍历(跟左右)*@param t to visit*@param visit point to a func*/
void pre_order(link t, void (*visit)(link))
{if (!t)return;visit(t);pre_order(t->lchild, visit);pre_order(t->rchild, visit);
}/***中序序遍历(左跟右)*@param t to visit*@param visit point to a func*/
void in_order(link t, void (*visit)(link))
{if (!t)return;in_order(t->lchild, visit);visit(t);in_order(t->rchild, visit);
}/***中序序遍历(左右跟)*@param t to visit*@param visit point to a func*/
void post_order(link t, void (*visit)(link))
{if (!t)return;post_order(t->lchild, visit);post_order(t->rchild, visit);visit(t);
}
#endif/***遍历二叉树,生成用于tree工具的字符串*@param root to visit*/
void pprint(link root)
{printf("(");if (root != NULL) {printf("%d", root->item);pprint(root->lchild);pprint(root->rchild);}printf(")");
}int count(link t)
{if (!t)return 0;return 1 + count(t->lchild) + count(t->rchild);
}int depth(link t)
{int dl, dr;if (!t)return 0;dl = depth(t->lchild);dr = depth(t->rchild);return 1 + (dl > dr ? dl : dr);
}void destroy(link t)
{post_order(t, free_node);
}/***在bst中查找值为key的节点**1、若b是空树，则搜索失败，否则;*2、若x等于b的根节点的数据域之值，则查找成功；否则;*3、若x小于b的根节点的数据域之值，则搜索左子树；否则;*4、查找右子树.**@param t to search*@param key the value of link to find*@returns the link of the key*/
link bstSearch(link t, TElemType key)
{if (t == NULL)return NULL;if (t->item > key) {return bstSearch(t->lchild, key);} else if (t->item < key){return bstSearch(t->rchild, key);} else {return t;}
}/***在bst中插入值为key的节点**1、若t是空树，则将key作为根节点的值插入，否则;*2、若t->item大于key，则把key插入到左子树中，否则;*3、把key插入到左子树中.**@param t 要插入的 bst*@param key 要插入的值*@returns 插入后的bst*/
link bstInsert(link t, TElemType key)
{if (t == NULL) {return make_node(key);}if (t->item > key) {t->lchild = bstInsert(t->lchild, key);} else {t->rchild = bstInsert(t->rchild, key);}return t;
}/***在bst中删除值为key的节点**1、若t为空树，则直接返回NULL,否则;*2、若t->item大于key，bst左子树为bst左子树删除key后的bst，否则;*3、若t->item小于key，bst右子树为bst右子树删除key后的bst，否则;*4、若t->item == key:*		1.若其左右子树为NULL,返回NULL,即对其父节点赋值为NULL*		2.若其左子树不为NULL,则在其左子树中找到最大节点p,将p->item赋值给当前节点,还需要在其左子树中删除p->item,3.若其右子树不为NULL,则在其左子树中找到最小节点p,将p->item赋值给当前节点,还需要在其右子树中删除p->item,**@param t 要插入的 bst*@param key 要插入的值*@returns 插入后的bst*/
link bstDelete(link t, TElemType key)
{if (t == NULL)return NULL;if (t->item > key) t->lchild = bstDelete(t->lchild, key);else if (t->item < key)t->rchild = bstDelete(t->rchild, key);else {link p;if (t->lchild == NULL && t->rchild == NULL) {free_node(t);t = NULL;} else if (t->lchild){for (p = t->lchild; p->rchild; p = p->rchild);t->item = p->item;t->lchild = bstDelete(t->lchild, t->item);} else {for (p = t->rchild; p->lchild; p = p->lchild);t->item = p->item;t->rchild = bstDelete(t->rchild, t->item);}}return t;
}

/* main.c */
#include <stdio.h>
#include <time.h>
#include "binarytree.h"#define RANGE  	50
#define N 		15void print_item(link p)
{printf("%d\t", p->item);
}void testBst()
{int i;link root = NULL;srand(time(NULL));for (i=0; i<N; i++)root = bstInsert(root, rand()%RANGE);printf("\\tree");pprint(root);printf("\n");TElemType key = rand() % RANGE;if (bstSearch(root, key)) {bstDelete(root, key);printf("\n%d\n", key);printf("\\tree");pprint(root);printf("\n");}
}void testInitByList()
{TElemType pre_seq[] = { 4, 2, 1, 3, 6, 5, 7 };TElemType in_seq[] = { 1, 2, 3, 4, 5, 6, 7 };link root = init(pre_seq, in_seq, 7);printf("\\tree");pprint(root);printf("\n");pre_order(root, print_item);putchar('\n');in_order(root, print_item);putchar('\n');post_order(root, print_item);putchar('\n');printf("count=%d depth=%d\n", count(root), depth(root));destroy(root);printf("+++++++++++++++++++++++++++++++++++++++++++++++++++\n\n");
}int main()
{//testInitByList();testBst();return 0;
}

对应的Makefie

#if you want to use recursive func,please make recu=y
ifeq (y, $(recu))CFLAGS += -DRECU
endififeq (y, $(debug))CFLAGS += -g
endifall:gcc $(CFLAGS) main.c binarytree.c binarytree.h -o treeclean:$(RM) tree

编译测试

make recu=y debug=y

\tree(15(6(0()())(7()(14(11(8()())())())))(41(36(18(16()())(23(22()())(29()())))())(41()())))22
\tree(15(6(0()())(7()(14(11(8()())())())))(41(36(18(16()())(23()(29()())))())(41()())))

echo "\tree(15(6(0()())(7()(14(11(8()())())())))(41(36(18(16()())(23(22()())(29()())))())(41()())))" | tree -b2