btree各操作实现 code

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根据上篇从B树中删除关键字书写的代码，可以从中了解原理

btree.h

/* * 实现BTree的创建、插入、删除、查找、销毁操作 * */ #ifndef __BTREE_H__  #define __BTREE_H__    #ifdef __cplusplus  extern "C" {  #endif     typedef int KeyType;  typedef struct BTNode BTNode;typedef struct BTree BTree;  // 创建BTree，n为内结点最少的孩子数，n必须大于等于2 BTree *BTreeCreate(int n);     // BTree的插入操作    int BTreeInsert(BTree *tree, KeyType key);  // BTree的删除操作  int BTreeRemove(BTree *tree, KeyType key);  // 深度遍历BTree  void BTreeTraverse(const BTree *tree);    // BTree的查找操作，返回key所在节点指针，pos保存key所在节点内的位置BTNode *BTreeSearch(const BTree *tree, int key, int *pos); // 销毁BTreevoid BTreeDestroy(BTree *tree);         #ifdef __cplusplus  }  #endif    #endif

btree.c

#include <stdio.h>#include <stdlib.h>#include <string.h>  #include "btree.h"  // BTree的结点struct BTNode {  int nkey;                             /// 结点中关键字数  KeyType *key;                /// 关键字向量  struct BTNode **child;                /// 孩子指针向量  char leaf;                            /// 是否为叶子节点  };struct BTree {BTNode *root;                         /// 根结点int mindegree;                        /// 内结点的最小孩子数};// 分配结点空间, degree为内结点的最小孩子数BTNode *NewNode(int degree){BTNode *node = (BTNode*)calloc(1, sizeof(BTNode));      if (!node)         return NULL;node->key = (KeyType *)calloc((degree << 1) - 1, sizeof(KeyType));if (!(node->key)) {free(node);return NULL;}node->child = (BTNode **)calloc((degree << 1), sizeof(BTNode *));if (!(node->child)) {free(node->key);free(node);return NULL;}node->leaf = 1;return node;}void FreeNode(BTNode *node){if (!node)return;if (node->key)free(node->key);if (node->child)free(node->child);free(node);}  // 向磁盘写入结点  void DiskWrite(BTNode *node)  { printf("Write to btree:\n");    for(int i = 0; i < node->nkey; i++){          printf("%d ",node->key[i]);      }      printf("\n");  }    // 从磁盘读取结点  void DiskRead(BTNode *node)  {    printf("Read from btree:\n");      for(int i = 0;i < node->nkey; i++){          printf("%d ", node->key[i]);      }      printf("\n");  }  BTree *BTreeCreate(int n)  {   BTree *tree;if (n < 2)return NULL;tree = (BTree *)calloc(1, sizeof(BTree));if (!tree)return NULL;tree->mindegree = n;tree->root = NewNode(n);if (!(tree->root)) {free(tree);return NULL;}//--DiskWrite(tree->root);return tree;}  void BTreeTraverse_(const BTNode *node, int layer){if (!node)return;printf("Layrer: %d\n", layer);for (int i = 0; i < node->nkey; i++)printf("%d ", node->key[i]);printf("\n");for (int i = 0; i <= node->nkey; i++)BTreeTraverse_(node->child[i], layer + 1);} void BTreeTraverse(const BTree *tree)  {  BTNode *node;if (!tree)return;node = tree->root;BTreeTraverse_(node, 0);}    // 二分查找，找到第一个大于或等于key的关键字所在位置  int BinarySearch(const BTNode *node, int low, int high, KeyType key)  {      int mid;if (low > high)return -1;    while (low <= high) {          mid = (low + high) / 2;        if (key > node->key[mid])low = mid + 1;               elsehigh = mid - 1;                }    return low;  }  // 对满结点node进行分裂，parent为node的父结点且为非满结点，// index为node在parent中的ID  void BTreeSplitChild(BTNode *parent, int index, BTNode *node, int degree)  {  int pos;    // 新结点用于保存node分裂出的key和指针    BTNode* newnode = NewNode(degree);     if (!newnode)         return;      newnode->leaf = node->leaf;      newnode->nkey = degree - 1;  /// 新结点key的最少数量// node中pos及其后的key值复制到新结点中pos = node->nkey - newnode->nkey;     for (int i = 0; i < newnode->nkey; ++i){          newnode->key[i] = node->key[pos + i];          node->key[pos + i] = 0;      }    // node若为非叶子结点，则把pos及其后的孩子指针复制到新结点中    if (!node->leaf) {          for (int i = 0; i <= newnode->nkey; i++) {              newnode->child[i] = node->child[pos + i];              node->child[pos + i] = NULL;          }      }        for (int i = parent->nkey; i > index; --i) {          parent->child[i + 1] = parent->child[i];      }        parent->child[index + 1] = newnode;        for (int i = parent->nkey - 1; i >= index; --i) {          parent->key[i + 1] = parent->key[i];      }        parent->key[index] = node->key[pos - 1];node->key[pos - 1] = 0;    ++parent->nkey;node->nkey = pos - 1;      // 写入磁盘       //--DiskWrite(parent);       //--DiskWrite(newnode);       //--DiskWrite(node);  }  // 向未满的结点node中插入keyint BTreeInsertNonfull(BTNode* node, KeyType key, int degree)  {  int pos;pos = BinarySearch(node, 0, node->nkey - 1, key);if (pos >= 0 && pos < node->nkey && node->key[pos] == key)return -1;pos = pos >= 0 ? pos : 0;// node为叶子结点则直接插入if (node->leaf) {  for (int i = node->nkey - 1; i >= pos; i--)  node->key[i + 1] = node->key[i]; node->key[pos] = key;  ++node->nkey; //--DiskWrite(node); return 0;}  // 从磁盘读取孩子节点  //--DiskRead(node->child[pos]);  // 对满孩子结点进行分裂操作  if (node->child[pos]->nkey == ((degree << 1) - 1)) {  BTreeSplitChild(node, pos, node->child[pos], degree);    if (key > node->key[pos])++pos;    }return BTreeInsertNonfull(node->child[pos], key, degree);   }    int BTreeInsert(BTree *tree, KeyType key)  { BTNode *node;      BTNode *root;int degree;if (!tree)return -1;root = tree->root;    if (!root)return -1;degree = tree->mindegree;    // 根结点未满      if (root->nkey < (degree << 1) - 1)return BTreeInsertNonfull(root, key, degree);      node = NewNode(degree);      if (!node)         return -1;      tree->root = node;      node->leaf = 0;      node->nkey = 0;      node->child[0] = root;        BTreeSplitChild(node, 0, root, degree);      return BTreeInsertNonfull(node, key, degree);  }   // 合并结点rchild到lchild，同时将parent中id为index的key下移到lchild中// lchild和rchild的key数均为degree - 1void BTreeMergeChild(BTNode *parent, int index, BTNode *lchild, BTNode *rchild, int degree)  {     lchild->nkey = (degree << 1) - 1;lchild->key[degree - 1] = parent->key[index];for (int i = 0; i < degree - 1; i++)lchild->key[i + degree] = rchild->key[i];if (!(lchild->leaf)) {for (int i = 0; i < degree; i++)lchild->child[i + degree] = rchild->child[i];}for (int i = index + 1; i < parent->nkey; i++) {parent->key[i - 1] = parent->key[i];parent->child[i] = parent->child[i + 1];}parent->nkey--;FreeNode(rchild);//--DiskWrite(parent);//--DiskWrite(lchild);} // 查找前驱BTNode *BTreeSearchPredecessor(BTNode *node){while (!(node->leaf))node = node->child[node->nkey];return node;}// 查找后继BTNode *BTreeSearchSuccessor(BTNode *node){while(!(node->leaf))node = node->child[0];return node;}// lchild中最后一个key上移到parent，parent中的id为index的key下移到rchildvoid BTreeShiftToRightChild(BTNode *parent, int index, BTNode *lchild, BTNode *rchild){for (int i = rchild->nkey; i > 0; i--) rchild->key[i] = rchild->key[i - 1];rchild->key[0] = parent->key[index];parent->key[index] = lchild->key[lchild->nkey - 1];if (!(lchild->leaf)) {for (int i = rchild->nkey + 1; i > 0; i--) rchild->child[i] = rchild->child[i - 1];rchild->child[0] = lchild->child[lchild->nkey];}lchild->nkey--;rchild->nkey++;//--DiskWrite(parent);//--DiskWrite(lchild);//--DiskWrite(rchild);}// rchild中第一个key上移到parent，parent中的id为index的key下移到lchildvoid BTreeShiftToLeftChild(BTNode *parent, int index, BTNode *lchild, BTNode *rchild){lchild->key[lchild->nkey] = parent->key[index];parent->key[index] = rchild->key[0];for (int i = 0; i < rchild->nkey - 1; i++) rchild->key[i] = rchild->key[i + 1];if (!(rchild->leaf)){lchild->child[lchild->nkey + 1] = rchild->child[0];for (int i = 0; i < rchild->nkey; i++)rchild->child[i] = rchild->child[i + 1];}lchild->nkey++;rchild->nkey--;//--DiskWrite(parent);//--DiskWrite(lchild);//--DiskWrite(rchild);}int BTreeDeleteNotNone(BTNode *node, KeyType key, int degree){int pos, kps;BTNode *nps, *lchild = NULL, *mchild = NULL, *rchild = NULL;pos = BinarySearch(node, 0, node->nkey - 1, key);pos = pos >= 0 ? pos : 0;if (node->leaf) {// key不存在if (pos >= node->nkey || key < node->key[pos])return -1;// 1、node为叶结点且在其中找到keyfor (int i = pos; i < node->nkey - 1; i++)node->key[i] = node->key[i + 1];node->nkey--;//--DiskWrite(node);return 0;}mchild = node->child[pos];//--DiskRead(mchild);if (pos < node->nkey) {rchild = node->child[pos + 1];//--DiskRead(rchild);}// 2、node为非叶结点且在其中找到keyif (pos < node->nkey && key == node->key[pos]) {// 2aif (mchild->nkey >= degree) {nps = BTreeSearchPredecessor(mchild);kps = nps->key[nps->nkey - 1];node->key[pos] = kps;return BTreeDeleteNotNone(mchild, kps, degree);}// 2belse if (rchild->nkey >= degree) {nps = BTreeSearchSuccessor(rchild);kps = nps->key[0];node->key[pos] = kps;return BTreeDeleteNotNone(mchild, kps, degree);}// 2celse {BTreeMergeChild(node, pos, mchild, rchild, degree);return BTreeDeleteNotNone(mchild, key, degree);}}else {if (pos > 0) {lchild = node->child[pos - 1];//--DiskRead(lchild);}// 3、node为非叶结点且未找到key，且key所在的子树的根结点key数为degree - 1if (mchild->nkey == degree - 1) {// 3aif (lchild && lchild->nkey >= degree) {BTreeShiftToRightChild(node, pos - 1, lchild, mchild);}// 3aelse if (rchild && rchild->nkey >= degree) {BTreeShiftToLeftChild(node, pos, mchild, rchild);}// 3belse if (pos > 0){BTreeMergeChild(node, pos - 1, lchild, mchild, degree);mchild = lchild;}// 3belse {BTreeMergeChild(node, pos, mchild, rchild, degree);}}return BTreeDeleteNotNone(mchild, key, degree);}}int BTreeRemove(BTree *tree, KeyType key)  {  BTNode *root;int degree;if (!tree)return -1;root = tree->root;    if (tree == NULL)          return -1;  degree = tree->mindegree;if (root->nkey == 1 && !(root->leaf)) {BTNode *lchild, *rchild;lchild = root->child[0];rchild = root->child[1];//--DiskRead(root->child[0]);//--DiskRead(root->child[1]);if (lchild->nkey == degree - 1 && rchild->nkey == degree - 1) {BTreeMergeChild(root, 0, lchild, rchild, degree);FreeNode(root);tree->root = lchild;return BTreeDeleteNotNone(lchild, key, degree);}}return BTreeDeleteNotNone(root, key, degree);}     BTNode* BTreeRecursiveSearch(const BTNode *node, KeyType key, int *pos)  {      int index;    index = BinarySearch(node, 0, node->nkey - 1, key);if (index < 0)return NULL;      // 找到key    if (index < node->nkey && node->key[index] == key) {          *pos = index;          return (BTNode *)node;      }        // 已经是叶子结点，未找到      if (node->leaf)        return NULL;        //--DiskRead(node->child[index]);      return BTreeRecursiveSearch(node->child[index], key, pos);  }    BTNode* BTreeSearch(const BTree *tree, KeyType key, int *pos)  {  BTNode *node;    if (!tree)        return NULL;  node = tree->root;if (!node)return NULL;//--DiskRead(node);    *pos = -1;      return BTreeRecursiveSearch(node, key, pos);  }    void BTreeDestroy_(BTNode *node){if (!node)return;for (int i = 0; i <= node->nkey; i++) {  BTreeDestroy_(node->child[i]);  }FreeNode(node);}void BTreeDestroy(BTree *tree)  {if (!tree)return;BTreeDestroy_(tree->root);  } int main(){int pos;BTNode *node;BTree *tree = BTreeCreate(2);for (int i = 0; i < 10; i++)BTreeInsert(tree, i);printf("-------------------BTreeTraverse-------------------\n");BTreeTraverse(tree);printf("---------------------------------------------------\n\n\n");for (int i = 19; i >= 10; i--)BTreeInsert(tree, i);printf("-------------------BTreeTraverse-------------------\n");BTreeTraverse(tree);printf("---------------------------------------------------\n\n\n");for (int i = 10; i <= 15; i++)BTreeInsert(tree, i);printf("-------------------BTreeTraverse-------------------\n");BTreeTraverse(tree);printf("---------------------------------------------------\n\n\n");printf("-------------------BTreeSearch---------------------\n");node = BTreeSearch(tree, 15, &pos);printf("%d\n", node ? node->key[pos] : -1);printf("---------------------------------------------------\n\n\n");for (int i = 6; i <= 15; i++) {BTreeRemove(tree, i);printf("-------------------BTreeRemove--BTreeTraverse-------------------\n");BTreeTraverse(tree);printf("\n\n\n");}printf("-------------------BTreeSearch---------------------\n");node = BTreeSearch(tree, 15, &pos);printf("%d\n", node ? node->key[pos] : -1);printf("---------------------------------------------------\n\n\n");BTreeDestroy(tree);return 0;}

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