Binary Search Tree C语言实现

Binary Search Tree是数据结构中比较有用的一种二叉树结构，这种结构讲大量的数据进行平摊式分布，并且规定大的数在右边，小的数在左边，以这种方式存放的数据可以非常方便地做数据排序和检索。
关于BST的更多信息，可以查看这个链接（英文，讲的非常好，不得不赞）：http://algs4.cs.princeton.edu/32bst/
台湾国立清华大学韩永楷老师的MOOC(讲的超级棒，完爆国内，我的代码实现就是参考韩老师的课程内容)：http://www.icourse163.org/course/NTHU-451013#/info
下面给出使用C语言的实现方式，我使用了最简单的方式实现，代码中有很多注释，大家可以参考。代码可编译，可运行。

/*************************************************************************
    > File Name: bst.c
    > Author: Baniel Gao
    > Mail: createchance@163.com 
    > Created Time: Thu 01 Dec 2016 08:29:23 AM EST
 ************************************************************************/

#include <stdio.h>
#include <stdlib.h>

typedef struct node_t {
    int key;
    struct node_t* parent;
    struct node_t* left;
    struct node_t* right;
} node;

/*
 * Get min number of this tree pointed by root.
 * 
 * Return min node pointer, NULL if root is NULL.
 */
node* min(node* root)
{
    node* min_node = root;

    if (root == NULL) {
        return NULL;
    }

    while (min_node->left != NULL) {
        min_node = min_node->left;
    }

    return min_node;
}

/*
 * Get max number of this tree pointed by root.
 * 
 * Return max node pointer, NULL if root is NULL.
 */
node* max(node* root)
{
    node* max_node = root;

    if (root == NULL)
    {
        return NULL;
    }

    while (max_node->right != NULL)
    {
        max_node = max_node->right;
    }

    return max_node;
}

/*
 * Search the number k.
 *
 * Return node pointer which contains the key, NULL if do not match anything.
 */
node* search(node* root, int k)
{
    node* current = root;

    if (root == NULL) {
        return NULL;
    }

    while (1) {
        if (current->key == k) {
            break;
        } else if (current->key > k) {
            current = current->left;
        } else {
            current = current->right;
        }

        if (current == NULL) {
            break;
        }
    }

    return current;
}

/*
 * Find the predeccessor of k.
 *
 * Return node pointer of predeccessor if success, NULL if find nothing.
 */
node* predecessor(node* root, int k)
{
    if (root == NULL)
    {
        return NULL;
    }

    node* target = search(root, k);
    if (target != NULL) {
        if (target->left != NULL) {
            target = max(target->left);
        } else {
            while (1) {
                if (target->parent == NULL) {
                    target = target->parent;
                    break;
                } else if (target == target->parent->right) {
                    target = target->parent;
                    break;
                } else if (target == target->parent->left) {
                    target = target->parent;
                }
            }
        }
    }

    return target;
}

/*
 * Find successor of number k.
 * 
 * Return node pointer of successor if success, NULL if find nothing.
 */
node* successor(node* root, int k)
{
    if (root == NULL) {
        return NULL;
    }

    node* target = search(root, k);
    if (target != NULL) {
        if (target->right !=