B-tree的代码实现 - c / c++ 版本

//高大上

看到一篇相关的好文章，引用下：http://www.cnblogs.com/leoo2sk/archive/2011/07/10/mysql-index.html 。相当滴不错，备忘下。

在这篇文章中http://blog.csdn.net/weege/article/details/6526512介绍了B-tree/B+tree/B*tree,并且介绍了B-tree的查找，插入，删除操作。现在重新认识下B-TREE（温故而知新嘛~，确实如此。自己在写代码中会体会到，B-tree的操作出现的条件相对其他树比较复杂，调试也是一个理通思路的过程。)

B-tree又叫平衡多路查找树。一棵m阶的B-tree (m叉树)的特性如下：

（其中ceil(x)是一个取上限的函数）

1)  树中每个结点至多有m个孩子；

2)  除根结点和叶子结点外，其它每个结点至少有有ceil(m / 2)个孩子；

3)  若根结点不是叶子结点，则至少有2个孩子（特殊情况：没有孩子的根结点，即根结点为叶子结点，整棵树只有一个根节点）；

4)  所有叶子结点都出现在同一层，叶子结点不包含任何关键字信息(可以看做是外部结点或查询失败的结点，实际上这些结点不存在，指向这些结点的指针都为null)（PS:这种说法是按照严蔚敏那本教材给出的，具体操作不同而定，下面的实现中的叶子结点是树的终端结点，即没有孩子的结点）；

5)  每个非终端结点中包含有n个关键字信息： (n，P0，K1，P1，K2，P2，......，Kn，Pn)。其中：

             a)   Ki (i=1...n)为关键字，且关键字按顺序排序K(i-1)< Ki。

             b)   Pi为指向子树根的接点，且指针P(i-1)指向子树种所有结点的关键字均小于Ki，但都大于K(i-1)。

      c)   关键字的个数n必须满足： ceil(m / 2)-1 <= n <= m-1。

具体代码实现如下：(这里只是给出了简单的B-Tree结构，在内存中的数据操作。具体详情见代码吧~！）

头文件：（提供B-Tree基本的操作接口)

 /***************************************************************************
     @coder:weedge E-mail:[email protected]
     @date:2011/08/27
     @comment:
         参考：http://www.cppblog.com/converse/archive/2009/10/13/98521.html
         实现对order序(阶)的B-TREE结构基本操作的封装。
         查找：search，插入：insert，删除：remove。
         创建：create，销毁：destory，打印：print。
 **********************************************************/
 #ifndef BTREE_H
 #define BTREE_H

 #ifdef __cplusplus
 extern "C" {
 #endif

 ////* 定义m序(阶)B 树的最小度数BTree_D=ceil(m/2)*/
 /// 在这里定义每个节点中关键字的最大数目为:2 * BTree_D - 1，即序(阶)：2 * BTree_D.
 #define BTree_D        2
 #define ORDER        (BTree_D * 2) //定义为4阶B-tree,2-3-4树。(偶序)
 //#define ORDER        (BTree_D * 2-1)//最简单为3阶B-tree,2-3树。(奇序)

     typedef int KeyType;
     typedef struct BTNode{
         int keynum;                        /// 结点中关键字的个数，ceil(ORDER/2)-1<= keynum <= ORDER-1
         KeyType key[ORDER-1];                /// 关键字向量为key[0..keynum - 1]
         struct BTNode* child[ORDER];        /// 孩子指针向量为child[0..keynum]
         char isLeaf;                    /// 是否是叶子节点的标志
     }BTNode;

     typedef BTNode* BTree;  ///定义BTree

     ///给定数据集data,创建BTree。
     void BTree_create(BTree* tree, const KeyType* data, int length);

     ///销毁BTree，释放内存空间。
     void BTree_destroy(BTree* tree);

     ///在BTree中插入关键字key。
     void BTree_insert(BTree* tree, KeyType key);

     ///在BTree中移除关键字key。
     void BTree_remove(BTree* tree, KeyType key);

     ///深度遍历BTree打印各层结点信息。
     void BTree_print(const BTree tree, int layer);

     /// 在BTree中查找关键字 key，
     /// 成功时返回找到的节点的地址及 key 在其中的位置 *pos
     /// 失败时返回 NULL 及查找失败时扫描到的节点位置 *pos
     BTNode* BTree_search(const BTree tree, int key, int* pos);

 #ifdef __cplusplus
 }
 #endif

 #endif

源文件：（提供B-Tree基本的基本操作的实现）

 /***************************************************************************
     @coder:weedge E-mail:[email protected]
     @date:2011/08/27
     @comment:
         参考：http://www.cppblog.com/converse/archive/2009/10/13/98521.html
         实现对order序(阶)的B-TREE结构基本操作的封装。
         查找：search，插入：insert，删除：remove。
         创建：create，销毁：destory，打印：print。
 **********************************************************/
 #include <stdlib.h>
 #include <stdio.h>
 #include <assert.h>
 #include "btree.h"

 //#define max(a, b) (((a) > (b)) ? (a) : (b))
 #define cmp(a, b) ( ( ((a)-(b)) >= (0) ) ? (1) : (0) ) //比较a，b大小
 #define DEBUG_BTREE


 // 模拟向磁盘写入节点
 void disk_write(BTNode* node)
 {
     int i;
 //打印出结点中的全部元素，方便调试查看keynum之后的元素是否为0(即是否存在垃圾数据)；而不是keynum个元素。
     printf("向磁盘写入节点");
     for(i=0;i<ORDER-1;i++){
         printf("%c",node->key[i]);
     }
     printf("\n");
 }

 // 模拟从磁盘读取节点
 void disk_read(BTNode** node)
 {
     int i;
 //打印出结点中的全部元素，方便调试查看keynum之后的元素是否为0(即是否存在垃圾数据)；而不是keynum个元素。
     printf("向磁盘读取节点");
     for(i=0;i<ORDER-1;i++){
         printf("%c",(*node)->key[i]);
     }
     printf("\n");
 }

 // 按层次打印 B 树
 void BTree_print(const BTree tree, int layer)
 {
     int i;
     BTNode* node = tree;

     if (node) {
         printf("第 %d 层， %d node : ", layer, node->keynum);

         //打印出结点中的全部元素，方便调试查看keynum之后的元素是否为0(即是否存在垃圾数据)；而不是keynum个元素。
         for (i = 0; i < ORDER-1; ++i) {
         //for (i = 0; i < node->keynum; ++i) {
             printf("%c ", node->key[i]);
         }

         printf("\n");

         ++layer;
         for (i = 0 ; i <= node->keynum; i++) {
             if (node->child[i]) {
                 BTree_print(node->child[i], layer);
             }
         }
     }
     else {
         printf("树为空。\n");
     }
 }

 // 结点node内对关键字进行二分查找。
 int binarySearch(BTNode* node, int low, int high, KeyType Fkey)
 {
     int mid;
     while (low<=high)
     {
         mid = low + (high-low)/2;
         if (Fkey<node->key[mid])
         {
             high = mid-1;
         }
         if (Fkey>node->key[mid])
         {
             low = mid+1;
         }
         if (Fkey==node->key[mid])
         {
             return mid;//返回下标。
         }
     }
     return -1;//未找到返回-1.
 }

 //=======================================================insert=====================================

 /***************************************************************************************
    将分裂的结点中的一半元素给新建的结点，并且将分裂结点中的中间关键字元素上移至父节点中。
    parent 是一个非满的父节点
    node 是 tree 孩子表中下标为 index 的孩子节点，且是满的，需分裂。
 *******************************************************************/
 void BTree_split_child(BTNode* parent, int index, BTNode* node)
 {
     int i;
     BTNode* newNode;
 #ifdef DEBUG_BTREE
     printf("BTree_split_child!\n");
 #endif
     assert(parent && node);


     // 创建新节点，存储 node 中后半部分的数据
     newNode = (BTNode*)calloc(sizeof(BTNode), 1);
     if (!newNode) {
         printf("Error! out of memory!\n");
         return;
     }

     newNode->isLeaf = node->isLeaf;
     newNode->keynum = BTree_D - 1;

     // 拷贝 node 后半部分关键字,然后将node后半部分置为0。
     for (i = 0; i < newNode->keynum; ++i){
         newNode->key[i] = node->key[BTree_D + i];
         node->key[BTree_D + i] = 0;
     }

     // 如果 node 不是叶子节点，拷贝 node 后半部分的指向孩子节点的指针，然后将node后半部分指向孩子节点的指针置为NULL。
     if (!node->isLeaf) {
         for (i = 0; i < BTree_D; i++) {
             newNode->child[i] = node->child[BTree_D + i];
             node->child[BTree_D + i] = NULL;
         }
     }

     // 将 node 分裂出 newNode 之后，里面的数据减半
     node->keynum = BTree_D - 1;

     // 调整父节点中的指向孩子的指针和关键字元素。分裂时父节点增加指向孩子的指针和关键元素。
     for (i = parent->keynum; i > index; --i) {
         parent->child[i + 1] = parent->child[i];
     }

     parent->child[index + 1] = newNode;

     for (i = parent->keynum - 1; i >= index; --i) {
         parent->key[i + 1] = parent->key[i];
     }

     parent->key[index] = node->key[BTree_D - 1];
     ++parent->keynum;

     node->key[BTree_D - 1] = 0;

     // 写入磁盘
      disk_write(parent);
      disk_write(newNode);
      disk_write(node);
 }

 void BTree_insert_nonfull(BTNode* node, KeyType key)
 {
     int i;
     assert(node);

     // 节点是叶子节点，直接插入
     if (node->isLeaf) {
         i = node->keynum - 1;
         while (i >= 0 && key < node->key[i]) {
             node->key[i + 1] = node->key[i];
             --i;
         }

         node->key[i + 1] = key;
         ++node->keynum;

         // 写入磁盘
         disk_write(node);
     }

     // 节点是内部节点
     else {
         /* 查找插入的位置*/
         i = node->keynum - 1;
         while (i >= 0 && key < node->key[i]) {
             --i;
         }

         ++i;

         // 从磁盘读取孩子节点
         disk_read(&node->child[i]);

         // 如果该孩子节点已满，分裂调整值
         if (node->child[i]->keynum == (ORDER-1)) {
             BTree_split_child(node, i, node->child[i]);
             // 如果待插入的关键字大于该分裂结点中上移到父节点的关键字，在该关键字的右孩子结点中进行插入操作。
             if (key > node->key[i]) {
                 ++i;
             }
         }
         BTree_insert_nonfull(node->child[i], key);
     }
 }

 void BTree_insert(BTree* tree, KeyType key)
 {
     BTNode* node;
     BTNode* root = *tree;

 #ifdef DEBUG_BTREE
     printf("BTree_insert:\n");
 #endif
     // 树为空
     if (NULL == root) {
         root = (BTNode*)calloc(sizeof(BTNode), 1);
         if (!root) {
             printf("Error! out of memory!\n");
             return;
         }
         root->isLeaf = 1;
         root->keynum = 1;
         root->key[0] = key;

         *tree = root;

         // 写入磁盘
         disk_write(root);

         return;
     }

     // 根节点已满，插入前需要进行分裂调整
     if (root->keynum == (ORDER-1)) {
         // 产生新节点当作根
         node = (BTNode*)calloc(sizeof(BTNode), 1);
         if (!node) {
             printf("Error! out of memory!\n");
             return;
         }

         *tree = node;
         node->isLeaf = 0;
         node->keynum = 0;
         node->child[0] = root;

         BTree_split_child(node, 0, root);

         BTree_insert_nonfull(node, key);
     }

     // 根节点未满，在当前节点中插入 key
     else {
         BTree_insert_nonfull(root, key);
     }
 }

 //=================================================remove========================================
 /***********************************************************************************
 // 对 tree 中的节点 node 进行合并孩子节点处理.
 // 注意：孩子节点的 keynum 必须均已达到下限，即均等于 BTree_D - 1
 // 将 tree 中索引为 index  的 key 下移至左孩子结点中，
 // 将 node 中索引为 index + 1 的孩子节点合并到索引为 index 的孩子节点中，右孩子合并到左孩子结点中。
 // 并调相关的 key 和指针。
 ***************************************************/
 void BTree_merge_child(BTree* tree, BTNode* node, int index)
 {
     int i;
     KeyType key;
     BTNode *leftChild, *rightChild;
 #ifdef DEBUG_BTREE
     printf("BTree_merge_child!\n");
 #endif
     assert(tree && node && index >= 0 && index < node->keynum);


     key = node->key[index];
     leftChild = node->child[index];
     rightChild = node->child[index + 1];

     assert(leftChild && leftChild->keynum == BTree_D - 1
         && rightChild && rightChild->keynum == BTree_D - 1);

     // 将 node中关键字下标为index 的 key 下移至左孩子结点中，该key所对应的右孩子结点指向node的右孩子结点中的第一个孩子。
     leftChild->key[leftChild->keynum] = key;
     leftChild->child[leftChild->keynum + 1] = rightChild->child[0];
     ++leftChild->keynum;

     // 右孩子的元素合并到左孩子结点中。
     for (i = 0; i < rightChild->keynum; ++i) {
         leftChild->key[leftChild->keynum] = rightChild->key[i];
         leftChild->child[leftChild->keynum + 1] = rightChild->child[i + 1];
         ++leftChild->keynum;
     }

     // 在 node 中下移的 key后面的元素前移
     for (i = index; i < node->keynum - 1; ++i) {
         node->key[i] = node->key[i + 1];
         node->child[i + 1] = node->child[i + 2];
     }
     node->key[node->keynum - 1] = 0;
     node->child[node->keynum] = NULL;
     --node->keynum;

     // 如果根节点没有 key 了，并将根节点调整为合并后的左孩子节点；然后删除释放空间。
     if (node->keynum == 0) {
         if (*tree == node) {
             *tree = leftChild;
         }

         free(node);
         node = NULL;
     }

     free(rightChild);
     rightChild = NULL;
 }

 void BTree_recursive_remove(BTree* tree, KeyType key)
 {
     // B-数的保持条件之一：
     // 非根节点的内部节点的关键字数目不能少于 BTree_D - 1

     int i, j, index;
     BTNode *root = *tree;
     BTNode *node = root;

     if (!root) {
         printf("Failed to remove %c, it is not in the tree!\n", key);
         return;
     }

     // 结点中找key。
     index = 0;
     while (index < node->keynum && key > node->key[index]) {
         ++index;
     }

 /*======================含有key的当前结点时的情况====================
 node:
 index of Key:            i-1  i  i+1
                         +---+---+---+---+
                           *  key   *
                     +---+---+---+---+---+
                            /     \
 index of Child:           i      i+1
                          /         \
                     +---+---+      +---+---+
                       *   *           *   *
                 +---+---+---+  +---+---+---+
                     leftChild     rightChild
 ============================================================*/
     /*一、结点中找到了关键字key的情况.*/
     if (index < node->keynum && node->key[index] == key) {
         BTNode *leftChild, *rightChild;
         KeyType leftKey, rightKey;
         /* 1，所在节点是叶子节点，直接删除*/
         if (node->isLeaf) {
             for (i = index; i < node->keynum-1; ++i) {
                 node->key[i] = node->key[i + 1];
                 //node->child[i + 1] = node->child[i + 2];叶子节点的孩子结点为空，无需移动处理。
             }
             node->key[node->keynum-1] = 0;
             //node->child[node->keynum] = NULL;
             --node->keynum;

             if (node->keynum == 0) {
                 assert(node == *tree);
                 free(node);
                 *tree = NULL;
             }

             return;
         }
         /*2.选择脱贫致富的孩子结点。*/
         // 2a，选择相对富有的左孩子结点。
         // 如果位于 key 前的左孩子结点的 key 数目 >= BTree_D，
         // 在其中找 key 的左孩子结点的最后一个元素上移至父节点key的位置。
         // 然后在左孩子节点中递归删除元素leftKey。
         else if (node->child[index]->keynum >= BTree_D) {
             leftChild = node->child[index];
             leftKey = leftChild->key[leftChild->keynum - 1];
             node->key[index] = leftKey;

             BTree_recursive_remove(&leftChild, leftKey);
         }
         // 2b，选择相对富有的右孩子结点。
         // 如果位于 key 后的右孩子结点的 key 数目 >= BTree_D，
         // 在其中找 key 的右孩子结点的第一个元素上移至父节点key的位置
         // 然后在右孩子节点中递归删除元素rightKey。
         else if (node->child[index + 1]->keynum >= BTree_D) {
             rightChild = node->child[index + 1];
             rightKey = rightChild->key[0];
             node->key[index] = rightKey;

             BTree_recursive_remove(&rightChild, rightKey);
         }
         /*左右孩子结点都刚脱贫。删除前需要孩子结点的合并操作*/
         // 2c，左右孩子结点只包含 BTree_D - 1 个节点，
         // 合并是将 key 下移至左孩子节点，并将右孩子节点合并到左孩子节点中，
         // 删除右孩子节点，在父节点node中移除 key 和指向右孩子节点的指针，
         // 然后在合并了的左孩子节点中递归删除元素key。
         else if (node->child[index]->keynum == BTree_D - 1
             && node->child[index + 1]->keynum == BTree_D - 1){
             leftChild = node->child[index];

             BTree_merge_child(tree, node, index);

             // 在合并了的左孩子节点中递归删除 key
             BTree_recursive_remove(&leftChild, key);
         }
     }

 /*======================未含有key的当前结点时的情况====================
 node:
 index of Key:            i-1  i  i+1
                         +---+---+---+---+
                           *  keyi *
                     +---+---+---+---+---+
                        /    |    \
 index of Child:      i-1    i     i+1
                      /      |       \
             +---+---+   +---+---+      +---+---+
              *   *        *   *          *   *
         +---+---+---+   +---+---+---+  +---+---+---+
         leftSibling       Child        rightSibling
 ============================================================*/
     /*二、结点中未找到了关键字key的情况.*/
     else {
         BTNode *leftSibling, *rightSibling, *child;
         // 3. key 不在内节点 node 中，则应当在某个包含 key 的子节点中。
         //  key < node->key[index], 所以 key 应当在孩子节点 node->child[index] 中
         child = node->child[index];
         if (!child) {
             printf("Failed to remove %c, it is not in the tree!\n", key);
             return;
         }
         /*所需查找的该孩子结点刚脱贫的情况*/
         if (child->keynum == BTree_D - 1) {
             leftSibling = NULL;
             rightSibling = NULL;

             if (index - 1 >= 0) {
                 leftSibling = node->child[index - 1];
             }

             if (index + 1 <= node->keynum) {
                 rightSibling = node->child[index + 1];
             }
             /*选择致富的相邻兄弟结点。*/
             // 3a，如果所在孩子节点相邻的兄弟节点中有节点至少包含 BTree_D 个关键字
             // 将 node 的一个关键字key[index]下移到 child 中，将相对富有的相邻兄弟节点中一个关键字上移到
             // node 中，然后在 child 孩子节点中递归删除 key。
             if ((leftSibling && leftSibling->keynum >= BTree_D)
                 || (rightSibling && rightSibling->keynum >= BTree_D)) {
                 int richR = 0;
                 if(rightSibling) richR = 1;
                 if(leftSibling && rightSibling) {
                     richR = cmp(rightSibling->keynum,leftSibling->keynum);
                 }
                 if (rightSibling && rightSibling->keynum >= BTree_D && richR) {
                     //相邻右兄弟相对富有，则该孩子先向父节点借一个元素，右兄弟中的第一个元素上移至父节点所借位置，并进行相应调整。
                     child->key[child->keynum] = node->key[index];
                     child->child[child->keynum + 1] = rightSibling->child[0];
                     ++child->keynum;

                     node->key[index] = rightSibling->key[0];

                     for (j = 0; j < rightSibling->keynum - 1; ++j) {//元素前移
                         rightSibling->key[j] = rightSibling->key[j + 1];
                         rightSibling->child[j] = rightSibling->child[j + 1];
                     }
                     rightSibling->key[rightSibling->keynum-1] = 0;
                     rightSibling->child[rightSibling->keynum-1] = rightSibling->child[rightSibling->keynum];
                     rightSibling->child[rightSibling->keynum] = NULL;
                     --rightSibling->keynum;
                 }
                 else {//相邻左兄弟相对富有，则该孩子向父节点借一个元素，左兄弟中的最后元素上移至父节点所借位置，并进行相应调整。
                     for (j = child->keynum; j > 0; --j) {//元素后移
                         child->key[j] = child->key[j - 1];
                         child->child[j + 1] = child->child[j];
                     }
                     child->child[1] = child->child[0];
                     child->child[0] = leftSibling->child[leftSibling->keynum];
                     child->key[0] = node->key[index - 1];
                     ++child->keynum;

                     node->key[index - 1] = leftSibling->key[leftSibling->keynum - 1];

                     leftSibling->key[leftSibling->keynum - 1] = 0;
                     leftSibling->child[leftSibling->keynum] = NULL;

                     --leftSibling->keynum;
                 }
             }
             /*相邻兄弟结点都刚脱贫。删除前需要兄弟结点的合并操作,*/
             // 3b, 如果所在孩子节点相邻的兄弟节点都只包含 BTree_D - 1 个关键字，
             // 将 child 与其一相邻节点合并，并将 node 中的一个关键字下降到合并节点中，
             // 再在 node 中删除那个关键字和相关指针，若 node 的 key 为空，删之，并调整根为合并结点。
             // 最后，在相关孩子节点child中递归删除 key。
             else if ((!leftSibling || (leftSibling && leftSibling->keynum == BTree_D - 1))
                 && (!rightSibling || (rightSibling && rightSibling->keynum == BTree_D - 1))) {
                 if (leftSibling && leftSibling->keynum == BTree_D - 1) {

                     BTree_merge_child(tree, node, index - 1);//node中的右孩子元素合并到左孩子中。

                     child = leftSibling;
                 }

                 else if (rightSibling && rightSibling->keynum == BTree_D - 1) {

                     BTree_merge_child(tree, node, index);//node中的右孩子元素合并到左孩子中。
                 }
             }
         }

         BTree_recursive_remove(&child, key);//调整后，在key所在孩子结点中继续递归删除key。
     }
 }

 void BTree_remove(BTree* tree, KeyType key)
 {
 #ifdef DEBUG_BTREE
     printf("BTree_remove:\n");
 #endif
     if (*tree==NULL)
     {
         printf("BTree is NULL!\n");
         return;
     }

     BTree_recursive_remove(tree, key);
 }

 //=====================================search====================================

 BTNode* BTree_recursive_search(const BTree tree, KeyType key, int* pos)
 {
     int i = 0;

     while (i < tree->keynum && key > tree->key[i]) {
         ++i;
     }

     // Find the key.
     if (i < tree->keynum && tree->key[i] == key) {
         *pos = i;
         return tree;
     }

     // tree 为叶子节点，找不到 key，查找失败返回
     if (tree->isLeaf) {
         return NULL;
     }

     // 节点内查找失败，但 tree->key[i - 1]< key < tree->key[i]，
     // 下一个查找的结点应为 child[i]

     // 从磁盘读取第 i 个孩子的数据
     disk_read(&tree->child[i]);

     // 递归地继续查找于树 tree->child[i]
     return BTree_recursive_search(tree->child[i], key, pos);
 }

 BTNode* BTree_search(const BTree tree, KeyType key, int* pos)
 {
 #ifdef DEBUG_BTREE
     printf("BTree_search:\n");
 #endif
     if (!tree) {
         printf("BTree is NULL!\n");
         return NULL;
     }
     *pos = -1;
     return BTree_recursive_search(tree,key,pos);
 }

 //===============================create===============================
 void BTree_create(BTree* tree, const KeyType* data, int length)
 {
     int i, pos = -1;
     assert(tree);

 #ifdef DEBUG_BTREE
     printf("\n 开始创建 B-树，关键字为:\n");
     for (i = 0; i < length; i++) {
         printf(" %c ", data[i]);
     }
     printf("\n");
 #endif

     for (i = 0; i < length; i++) {
 #ifdef DEBUG_BTREE
         printf("\n插入关键字 %c:\n", data[i]);
 #endif

         BTree_search(*tree,data[i],&pos);//树的递归搜索。
         if (pos!=-1)
         {
             printf("this key %c is in the B-tree,not to insert.\n",data[i]);
         }else{
             BTree_insert(tree, data[i]);//插入元素到BTree中。
         }

 #ifdef DEBUG_BTREE
         BTree_print(*tree,1);//树的深度遍历,从第一层开始。
 #endif
     }

     printf("\n");
 }
 //===============================destroy===============================
 void BTree_destroy(BTree* tree)
 {
     int i;
     BTNode* node = *tree;

     if (node) {
         for (i = 0; i <= node->keynum; i++) {
             BTree_destroy(&node->child[i]);
         }

         free(node);
     }

     *tree = NULL;
 }

测试文件：（测试B-Tree基本的操作接口)

 /***************************************************************************
     @coder:weedge E-mail:[email protected]
     @date:2011/08/28
     @comment:
         测试order序(阶)的B-TREE结构基本操作。
         查找：search，插入：insert，删除：remove。
         创建：create，销毁：destory，打印：print。
 **********************************************************/

 #include <stdio.h>
 #include "btree.h"

 void test_BTree_search(BTree tree, KeyType key)
 {
     int pos = -1;
     BTNode*    node = BTree_search(tree, key, &pos);
     if (node) {
         printf("在%s节点（包含 %d 个关键字）中找到关键字 %c，其索引为 %d\n",
             node->isLeaf ? "叶子" : "非叶子",
             node->keynum, key, pos);
     }
     else {
         printf("在树中找不到关键字 %c\n", key);
     }
 }

 void test_BTree_remove(BTree* tree, KeyType key)
 {
     printf("\n移除关键字 %c \n", key);
     BTree_remove(tree, key);
     BTree_print(*tree);
     printf("\n");
 }

 void test_btree()
 {

     KeyType array[] = {
         'G','G', 'M', 'P', 'X', 'A', 'C', 'D', 'E', 'J', 'K',
         'N', 'O', 'R', 'S', 'T', 'U', 'V', 'Y', 'Z', 'F', 'X'
     };
     const int length = sizeof(array)/sizeof(KeyType);
     BTree tree = NULL;
     BTNode* node = NULL;
     int pos = -1;
     KeyType key1 = 'R';        // in the tree.
     KeyType key2 = 'B';        // not in the tree.

     // 创建
     BTree_create(&tree, array, length);

     printf("\n=== 创建 B- 树 ===\n");
     BTree_print(tree);
     printf("\n");

     // 查找
     test_BTree_search(tree, key1);
     printf("\n");
     test_BTree_search(tree, key2);

     // 移除不在B树中的元素
     test_BTree_remove(&tree, key2);
     printf("\n");

     // 插入关键字
     printf("\n插入关键字 %c \n", key2);
     BTree_insert(&tree, key2);
     BTree_print(tree);
     printf("\n");

     test_BTree_search(tree, key2);

     // 移除关键字
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'M';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'E';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'G';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'A';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'D';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'K';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'P';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'J';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'C';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'X';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'O';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'V';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'R';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'U';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'T';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     key2 = 'N';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);
     key2 = 'S';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);
     key2 = 'Y';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);
     key2 = 'F';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);
     key2 = 'Z';
     test_BTree_remove(&tree, key2);
     test_BTree_search(tree, key2);

     // 销毁
     BTree_destroy(&tree);
 }

 int main()
 {
     test_btree();

     return 0;
 }

另外参考《Data.structures.and.Program.Design.in.Cpp》-Section 11.3:EXTERNALSEARCHING:B-TREES的讲解实现，这边书个人认为比较经典，如果对数据结构和算法比较感兴趣的话，可以作为参考读物，不错的，根据数据结构上的操作与程序上的实现相结合，讲的很细。这本书好像没有中文版的，即使有，也推荐看原版吧，毕竟写代码都是用英文字符，实现也比较贴切易懂。去网上找这本书的资料还挺多的。而且国内有些大学也参考这本书讲解数据结构和算法。比如：http://sist.sysu.edu.cn/~isslxm/DSA/CS09/。

头文件：（采用C++模板（template）来实现B-Tree基本的操作接口)

 /***************************************************************************
     @editer:weedge E-mail:[email protected]
     @date:2011/08/27
     @comment:
         Data.structures.and.Program.Design.in.Cpp
         Section 11.3:EXTERNALSEARCHING:B-TREES
         采用泛型编程（模板template），Record为关键字类型，order为序(阶)，
         实现对order序(阶)的B-TREE结构基本操作的封装。
         查找：search，插入：insert，删除：remove。
 **********************************************************/

 #ifndef B_Tree_H_
 #define B_Tree_H_

 enum Error_code{overflow=-2,duplicate_error=-1,not_present=0,success=1};

 template <class Record, int order>
 struct B_node {
 ///  data members:
    int count;
    Record data[order - 1];
    B_node<Record, order> *branch[order];///在大多数应用中，这些指针被不同的磁盘中块(block)的地址代替。
 ///  constructor:
    B_node();
 };

 template <class Record, int order>
 class B_tree {
 public:
     ////*  Add public methods. */

     Error_code search_tree(Record &target);

     Error_code insert(const Record &new_entry);

     Error_code remove(const Record &target);

 protected:
     ////*  data members */

     ////*  Add protected auxiliary functions here in order to inherit for subclass. */
     ///=============================search=========================================

     Error_code recursive_search_tree(B_node<Record, order> *current, Record &target);

     Error_code search_node(B_node<Record, order> *current, const Record &target, int &position);

     ///=============================insert=========================================

     Error_code push_down(B_node<Record, order> *current,const Record &new_entry,
         Record &median,B_node<Record, order> *&right_branch);

     void push_in(B_node<Record, order> *current, const Record &entry,
         B_node<Record, order> *right_branch, int position);

     void split_node(B_node<Record, order> *current,   const Record &extra_entry, B_node<Record, order> *extra_branch,
         int position, B_node<Record, order> *&right_half, Record &median);

     ///==============================remove========================================

     Error_code recursive_remove(B_node<Record, order> *current, const Record &target);

     void remove_data(B_node<Record, order> *current, int position);

     void copy_in_predecessor(B_node<Record, order> *current, int position);

     void restore(B_node<Record, order> *current,int position);

     void move_left(B_node<Record, order> *current, int position);

     void move_right(B_node<Record, order> *current,int position);

     void combine(B_node<Record, order> *current, int position);

 private:
     ////*  data members */
     B_node<Record, order> *root;

     ////*  Add private auxiliary functions here. */
 };

 #endif //end B_Tree_H_

原文件：（实现B-Tree基本的基本操作)

 /***************************************************************************
     @editor:weedge E-mail:[email protected]
     @date:2011/08/27
     @comment:
         Data.structures.and.Program.Design.in.Cpp
         Section 11.3:EXTERNALSEARCHING:B-TREES
         采用泛型编程（模板template），
         实现对B-TREE结构基本操作的封装。
         查找：search，插入：insert，删除：remove。
 **********************************************************/
 #include "B_Tree.h"

 template <class Record, int order>
 Error_code B_tree<Record, order>::search_tree(Record &target)
 /*
 Post: If there is an entry in the B-tree whose key matches that in target,
       the parameter target is replaced by the corresponding Record from
       the B-tree and a code of success is returned.  Otherwise
       a code of not_present is returned.
 Uses: recursive_search_tree
 */
 {
    return recursive_search_tree(root, target);
 }


 template <class Record, int order>
 Error_code B_tree<Record, order>::recursive_search_tree(
            B_node<Record, order> *current, Record &target)
 /*
 Pre:  current is either NULL or points to a subtree of the B_tree.
 Post: If the Key of target is not in the subtree, a code of not_present
       is returned. Otherwise, a code of success is returned and
       target is set to the corresponding Record of the subtree.
 Uses: recursive_search_tree recursively and search_node
 */
 {
    Error_code result = not_present;
    int position;
    if (current != NULL) {
       result = search_node(current, target, position);
       if (result == not_present)
          result = recursive_search_tree(current->branch[position], target);
       else
          target = current->data[position];
    }
    return result;
 }


 template <class Record, int order>
 Error_code B_tree<Record, order>::search_node(
    B_node<Record, order> *current, const Record &target, int &position)
 /*
 Pre:  current points to a node of a B_tree.
 Post: If the Key of target is found in *current, then a code of
       success is returned, the parameter position is set to the index
       of target, and the corresponding Record is copied to
       target.  Otherwise, a code of not_present is returned, and
       position is set to the branch index on which to continue the search.
 Uses: Methods of class Record.
 */
 {
    position = 0;
    while (position < current->count && target > current->data[position])
       position++;         //  Perform a sequential search through the keys.
    if (position < current->count && target == current->data[position])
       return success;
    else
       return not_present;
 }


 template <class Record, int order>
 Error_code B_tree<Record, order>::insert(const Record &new_entry)
 /*
 Post: If the Key of new_entry is already in the B_tree,
       a code of duplicate_error is returned.
       Otherwise, a code of success is returned and the Record new_entry
       is inserted into the B-tree in such a way that the properties of a B-tree
       are preserved.
 Uses: Methods of struct B_node and the auxiliary function push_down.
 */
 {
    Record median;
    B_node<Record, order> *right_branch, *new_root;
    Error_code result = push_down(root, new_entry, median, right_branch);

    if (result == overflow) {  //  The whole tree grows in height.
                               //  Make a brand new root for the whole B-tree.
       new_root = new B_node<Record, order>;
       new_root->count = 1;
       new_root->data[0] = median;
       new_root->branch[0] = root;
       new_root->branch[1] = right_branch;
       root = new_root;
       result = success;
    }
    return result;
 }


 template <class Record, int order>
 Error_code B_tree<Record, order>::push_down(
                  B_node<Record, order> *current,
                  const Record &new_entry,
                  Record &median,
                  B_node<Record, order> *&right_branch)
 /*
 Pre:  current is either NULL or points to a node of a B_tree.
 Post: If an entry with a Key matching that of new_entry is in the subtree
       to which current points, a code of duplicate_error is returned.
       Otherwise, new_entry is inserted into the subtree: If this causes the
       height of the subtree to grow, a code of overflow is returned, and the
       Record median is extracted to be reinserted higher in the B-tree,
       together with the subtree right_branch on its right.
       If the height does not grow, a code of success is returned.
 Uses: Functions push_down (called recursively), search_node,
       split_node, and push_in.
 */
 {
    Error_code result;
    int position;
    if (current == NULL) { //  Since we cannot insert in an empty tree, the recursion terminates.
       median = new_entry;
       right_branch = NULL;
       result = overflow;
    }
    else {   //   Search the current node.
       if (search_node(current, new_entry, position) == success)
          result = duplicate_error;
       else {
          Record extra_entry;
          B_node<Record, order> *extra_branch;
          result = push_down(current->branch[position], new_entry,
                             extra_entry, extra_branch);
          if (result == overflow) {  //  Record extra_entry now must be added to current
             if (current->count < order - 1) {
                result = success;
                push_in(current, extra_entry, extra_branch, position);
             }

             else split_node(current, extra_entry, extra_branch, position,
                             right_branch, median);
             //  Record median and its right_branch will go up to a higher node.
          }
       }
    }
    return result;
 }


 template <class Record, int order>
 void B_tree<Record, order>::push_in(B_node<Record, order> *current,
    const Record &entry, B_node<Record, order> *right_branch, int position)
 /*
 Pre:  current points to a node of a B_tree.  The node *current is not full
       and entry belongs in *current at index position.
 Post: entry has been inserted along with its right-hand branch
       right_branch into *current at index position.
 */
 {
    for (int i = current->count; i > position; i--) {  //  Shift all later data to the right.
       current->data[i] = current->data[i - 1];
       current->branch[i + 1] = current->branch[i];
    }
    current->data[position] = entry;
    current->branch[position + 1] = right_branch;
    current->count++;
 }


 template <class Record, int order>
 void B_tree<Record, order>::split_node(
    B_node<Record, order> *current,    //  node to be split
    const Record &extra_entry,          //  new entry to insert
    B_node<Record, order> *extra_branch,//  subtree on right of extra_entry
    int position,                  //  index in node where extra_entry goes
    B_node<Record, order> *&right_half, //  new node for right half of entries
    Record &median)                     //  median entry (in neither half)
 /*
 Pre:  current points to a node of a B_tree.
       The node *current is full, but if there were room, the record
       extra_entry with its right-hand pointer extra_branch would belong
       in *current at position position, 0 <= position < order.
 Post: The node *current with extra_entry and pointer extra_branch at
       position position are divided into nodes *current and *right_half
       separated by a Record median.
 Uses: Methods of struct B_node, function push_in.
 */
 {
    right_half = new B_node<Record, order>;
    int mid = order/2;  //  The entries from mid on will go to right_half.
    if (position <= mid) {   //  First case:  extra_entry belongs in left half.
       for (int i = mid; i < order - 1; i++) {  //  Move entries to right_half.
          right_half->data[i - mid] = current->data[i];
          right_half->branch[i + 1 - mid] = current->branch[i + 1];
       }
       current->count = mid;
       right_half->count = order - 1 - mid;
       push_in(current, extra_entry, extra_branch, position);
    }
    else {  //  Second case:  extra_entry belongs in right half.
       mid++;      //  Temporarily leave the median in left half.
       for (int i = mid; i < order - 1; i++) {  //  Move entries to right_half.
          right_half->data[i - mid] = current->data[i];
          right_half->branch[i + 1 - mid] = current->branch[i + 1];
       }
       current->count = mid;
       right_half->count = order - 1 - mid;
       push_in(right_half, extra_entry, extra_branch, position - mid);
    }
       median = current->data[current->count - 1]; //  Remove median from left half.
       right_half->branch[0] = current->branch[current->count];
       current->count--;
 }


 template <class Record, int order>
 Error_code B_tree<Record, order>::remove(const Record &target)
 /*
 Post: If a Record with Key matching that of target belongs to the
       B_tree, a code of success is returned and the corresponding node
       is removed from the B-tree.  Otherwise, a code of not_present
       is returned.
 Uses: Function recursive_remove
 */
 {
    Error_code result;
    result = recursive_remove(root, target);
    if (root != NULL && root->count == 0) {  //  root is now empty.
       B_node<Record, order> *old_root = root;
       root = root->branch[0];
       delete old_root;
    }
    return result;
 }


 template <class Record, int order>
 Error_code B_tree<Record, order>::recursive_remove(
    B_node<Record, order> *current, const Record &target)
 /*
 Pre:  current is either NULL or
       points to the root node of a subtree of a B_tree.
 Post: If a Record with Key matching that of target belongs to the subtree,
       a code of success is returned and the corresponding node is removed
       from the subtree so that the properties of a B-tree are maintained.
       Otherwise, a code of not_present is returned.
 Uses: Functions search_node, copy_in_predecessor,
       recursive_remove (recursively), remove_data, and restore.
 */
 {
    Error_code result;
    int position;
    if (current == NULL) result = not_present;
    else {
       if (search_node(current, target, position) == success) {  //  The target is in the current node.
          result = success;
          if (current->branch[position] != NULL) {     //  not at a leaf node
             copy_in_predecessor(current, position);

             recursive_remove(current->branch[position],
                              current->data[position]);
          }
          else remove_data(current, position);     //  Remove from a leaf node.
       }
       else result = recursive_remove(current->branch[position], target);
       if (current->branch[position] != NULL)
          if (current->branch[position]->count < (order - 1) / 2)
             restore(current, position);
    }
    return result;
 }


 template <class Record, int order>
 void B_tree<Record, order>::remove_data(B_node<Record, order> *current,
                                         int position)
 /*
 Pre:  current points to a leaf node in a B-tree with an entry at position.
 Post: This entry is removed from *current.
 */
 {
    for (int i = position; i < current->count - 1; i++)
       current->data[i] = current->data[i + 1];
    current->count--;
 }


 template <class Record, int order>
 void B_tree<Record, order>::copy_in_predecessor(
                     B_node<Record, order> *current, int position)
 /*
 Pre:  current points to a non-leaf node in a B-tree with an entry at position.
 Post: This entry is replaced by its immediate predecessor under order of keys.
 */
 {
    B_node<Record, order> *leaf = current->branch[position];  //   First go left from the current entry.
    while (leaf->branch[leaf->count] != NULL)
       leaf = leaf->branch[leaf->count]; //   Move as far rightward as possible.
    current->data[position] = leaf->data[leaf->count - 1];
 }


 template <class Record, int order>
 void B_tree<Record, order>::restore(B_node<Record, order> *current,
                                     int position)
 /*
 Pre:  current points to a non-leaf node in a B-tree; the node to which
       current->branch[position] points has one too few entries.
 Post: An entry is taken from elsewhere to restore the minimum number of
       entries in the node to which current->branch[position] points.
 Uses: move_left, move_right, combine.
 */
 {
    if (position == current->count)   //  case:  rightmost branch
       if (current->branch[position - 1]->count > (order - 1) / 2)
          move_right(current, position - 1);
       else
          combine(current, position);
    else if (position == 0)       //  case: leftmost branch
       if (current->branch[1]->count > (order - 1) / 2)
          move_left(current, 1);
       else
          combine(current, 1);
    else                          //  remaining cases: intermediate branches
       if (current->branch[position - 1]->count > (order - 1) / 2)
          move_right(current, position - 1);
       else if (current->branch[position + 1]->count > (order - 1) / 2)
          move_left(current, position + 1);
       else
          combine(current, position);
 }


 template <class Record, int order>
 void B_tree<Record, order>::move_left(B_node<Record, order> *current,
                                       int position)
 /*
 Pre:  current points to a node in a B-tree with more than the minimum
       number of entries in branch position and one too few entries in branch
       position - 1.
 Post: The leftmost entry from branch position has moved into
       current, which has sent an entry into the branch position - 1.
 */
 {
    B_node<Record, order> *left_branch = current->branch[position - 1],
                          *right_branch = current->branch[position];
    left_branch->data[left_branch->count] = current->data[position - 1];  //  Take entry from the parent.
    left_branch->branch[++left_branch->count] = right_branch->branch[0];
    current->data[position - 1] = right_branch->data[0];  //   Add the right-hand entry to the parent.
    right_branch->count--;
    for (int i = 0; i < right_branch->count; i++) {   //  Move right-hand entries to fill the hole.
       right_branch->data[i] = right_branch->data[i + 1];
       right_branch->branch[i] = right_branch->branch[i + 1];
    }
    right_branch->branch[right_branch->count] =
       right_branch->branch[right_branch->count + 1];
 }


 template <class Record, int order>
 void B_tree<Record, order>::move_right(B_node<Record, order> *current,
                                        int position)
 /*
 Pre:  current points to a node in a B-tree with more than the minimum
       number of entries in branch position and one too few entries
       in branch position + 1.
 Post: The rightmost entry from branch position has moved into
       current, which has sent an entry into the branch position + 1.
 */
 {
    B_node<Record, order> *right_branch = current->branch[position + 1],
                          *left_branch = current->branch[position];
    right_branch->branch[right_branch->count + 1] =
       right_branch->branch[right_branch->count];
    for (int i = right_branch->count ; i > 0; i--) {  //  Make room for new entry.
       right_branch->data[i] = right_branch->data[i - 1];
       right_branch->branch[i] = right_branch->branch[i - 1];
    }
    right_branch->count++;
    right_branch->data[0] = current->data[position]; //  Take entry from parent.
    right_branch->branch[0] = left_branch->branch[left_branch->count--];
    current->data[position] = left_branch->data[left_branch->count];
 }


 template <class Record, int order>
 void B_tree<Record, order>::combine(B_node<Record, order> *current,
                                     int position)
 /*
 Pre:  current points to a node in a B-tree with entries in the branches
       position and position - 1, with too few to move entries.
 Post: The nodes at branches position - 1 and position have been combined
       into one node, which also includes the entry formerly in current at
       index  position - 1.
 */
 {
    int i;
    B_node<Record, order> *left_branch = current->branch[position - 1],
                          *right_branch = current->branch[position];
    left_branch->data[left_branch->count] = current->data[position - 1];
    left_branch->branch[++left_branch->count] = right_branch->branch[0];
    for (i = 0; i < right_branch->count; i++) {
       left_branch->data[left_branch->count] = right_branch->data[i];
       left_branch->branch[++left_branch->count] =
                                         right_branch->branch[i + 1];
    }
    current->count--;
    for (i = position - 1; i < current->count; i++) {
       current->data[i] = current->data[i + 1];
       current->branch[i + 1] = current->branch[i + 2];
    }
    delete right_branch;
 }

测试文件：（待写)

//原文地址