/** * BTree.h * * 采用网上流传已久的插入删除算法——回溯方式 * 与《算法导论》中的不一样，但是效率更高 * * 790042744@qq.com * 2012/3/5 * **/#ifndef BTREE_H#define BTREE_H#include <iostream>#include <vector>using std::vector;using std::cout;using std::endl;/** * Knuth's definition, a B-tree of order m: * Every node has at most m children. * Every node (except root) has at least ceil(m/2) children. * The root has at least two children if it is not a leaf node. * All leaves appear in the same level, and carry information. * A non-leaf node with k children contains k-1 keys. * * 不应该把BTreeNode暴露给用户 **/template< typename FileName, typename DiskAddr, int m >class BTree;template< typename FileName, typename DiskAddr, int m >class BTreeNode{public:static const int MaxKeyCnt = m-1;static const int MinKeyCnt = ((m+1)>>1)-1;private:FileName filename[m]; //多一个槽位，我是先插入再分裂DiskAddr fileaddr[m];//子树个数：ceil(m/2)~mBTreeNode *child[m+1];BTreeNode *parent;int keycnt;bool isleaf;public:BTreeNode(): keycnt(0), isleaf(false), parent(NULL){//子女指针初始化为0memset( child, 0, sizeof(child) );};~BTreeNode() {};bool IsFull() { return ( keycnt == MaxKeyCnt ); }FileName const GetKey(int index) {if ( index < 0 || index >= 2*t-1 )throw index;return filename[index];}FileName const& GetKey(int index) const {if ( index < 0 || index >= 2*t-1 )throw index;return filename[index];}DiskAddr const GetValue(int index){if ( index < 0 || index >= 2*t-1 )throw index;return fileaddr[index];}DiskAddr const& GetValue(int index) const{if ( index < 0 || index >= 2*t-1 )throw index;return fileaddr[index];}friend class BTree<FileName, DiskAddr, m>;};//===================================================================================================template< typename FileName, typename DiskAddr, int m >class BTree{public:typedef BTreeNode<FileName, DiskAddr, m> Node;typedef Node& RNode;typedef Node* PNode;typedef Node const * PCNode;private:PNode root;public:BTree(): root(NULL) {}~BTree();PCNode Search( FileName name, int& index );bool Insert( FileName name, DiskAddr addr );bool Delete( FileName name );//test, output the whole treevoid PrintTree();void PrintTree(PNode pnode);private:PNode Allocate( bool isleaf=false );void Clear( PNode pnode );PNode SubTreeSearch( PNode pnode, FileName name, int& index );bool NodeSearch( PNode pnode, FileName name, int& index );int NodeInsert( PNode pnode, FileName name, DiskAddr addr );void SplitNode( PNode pnode );PNode FindMinNode( PNode pnode );PNode FindMaxNode( PNode pnode );void Update( PNode pnode );void FromLeftSibling( PNode child, PNode parent, int chind );void FromRightSibling( PNode child, PNode parent, int chind );void MergeChild( PNode pnode, int index );};//=======================================================================================//public:template< typename FileName, typename DiskAddr, int m >inline BTree<FileName, DiskAddr, m>::~BTree(){if ( NULL != root )Clear(root);}/** * 如果存在，返回指向常节点的指针，index表示节点中第几个关键字 * 否则，返回NULL，index置为-1 **/template< typename FileName, typename DiskAddr, int m >typename BTree<FileName, DiskAddr, m>::PCNode BTree<FileName, DiskAddr, m>::Search(FileName name, int& index){if ( NULL == root ){index = -1;return NULL;}PNode p = SubTreeSearch( root, name, index );if ( -1 == index )p = NULL;return p;}/** * 插入关键字伪代码：1、找到应该插入位置的节点，一定是叶子节点，直接插入；2、如果该叶子节点关键字个数大于m-1；分裂该叶子节点；分裂节点伪代码：1、分裂该节点，产生一个新节点；2、将中间关键字插入父节点中；3、如果父节点关键字个数大于m-1，递归分裂父节点，否则直接返回； * 如果name已经存在，返回false **/template< typename FileName, typename DiskAddr, int m >bool BTree<FileName, DiskAddr, m>::Insert( FileName name, DiskAddr addr ){if ( NULL == root ){root = Allocate(true);root->filename[0] = name;root->fileaddr[0] = addr;root->keycnt = 1;}else {int index;PNode pnode = SubTreeSearch( root, name, index ); //返回的一定是叶子节点if ( -1 != index )//关键字存在return false;NodeInsert( pnode, name, addr );if ( pnode->keycnt > Node::MaxKeyCnt )SplitNode( pnode );}return true;}/** * 删除关键字伪代码; 1、查找包含这个关键字key的节点node:2、如果这个节点是内节点：a 找到左子树中含有最大关键字的节点leafnode，及其最大的关键字keyx； b 在叶子节点leafnode上删除关键字keyx，并用keyx代替原来将要删除的关键字keyc 维护leafnode 如果这个节点是叶子节点： a 直接删除这个关键字，移动后面的其他关键字b 维护这个节点维护节点伪代码：a 如果关键字满足要求，直接返回；b 如果左右兄弟节点有足够多的关键字，向其借一个，返回；c 如果左右兄弟节点都没有足够的关键字，合并一个兄弟节点，回溯维护父节点。 * * 如果name已经存在，返回false **/template< typename FileName, typename DiskAddr, int m >bool BTree<FileName, DiskAddr, m>::Delete( FileName name ){if ( NULL == root )return false;int index;PNode pnode, leafnode;pnode = SubTreeSearch( root, name, index );if ( -1 == index )return false;if ( false == pnode->isleaf ){leafnode = FindMinNode( pnode->child[index+1] );pnode->filename[index] = leafnode->filename[0];pnode->fileaddr[index] = leafnode->fileaddr[0];index = 0;}else {leafnode = pnode;}for ( int i = index; i < leafnode->keycnt-1; ++ i ){leafnode->filename[i] = leafnode->filename[i+1];leafnode->fileaddr[i] = leafnode->fileaddr[i+1];}-- leafnode->keycnt;if ( leafnode->keycnt < Node::MinKeyCnt )Update( leafnode );return true;}//just for testtemplate< typename FileName, typename DiskAddr, int m >void BTree<FileName, DiskAddr, m>::PrintTree(){if ( NULL == root )return;vector<PNode> one, two, *tmp, *tmp2, *xx;vector<PNode>::iterator it;PNode pnode;int level = 0, j;one.push_back( root );tmp = &one;tmp2 = &two;while ( !tmp->empty() ){cout << "level: " << level << " ";for ( it = tmp->begin(); it != tmp->end(); ++ it )PrintTree( *it );cout << endl;it = tmp->begin();if ( false == (*it)->isleaf ){for ( it = tmp->begin(); it != tmp->end(); ++ it ){pnode = *it;for ( j = 0; j < pnode->keycnt+1; ++ j )tmp2->push_back( pnode->child[j] );}}tmp->clear();++ level;xx = tmp;tmp = tmp2;tmp2 = xx;}}template< typename FileName, typename DiskAddr, int m >void BTree<FileName, DiskAddr, m>::PrintTree(PNode pnode){if ( NULL == pnode )return;cout << "[ ";for ( int i = 0; i < pnode->keycnt; ++ i )cout << pnode->filename[i] << "(" <<pnode->fileaddr[i] << ") ";cout << "] ";}//=======================================================================================//private:template< typename FileName, typename DiskAddr, int m >typename BTree<FileName, DiskAddr, m>::PNode BTree<FileName, DiskAddr, m>::Allocate( bool isleaf ){PNode pnode = new Node();pnode->isleaf = isleaf;return pnode;}template< typename FileName, typename DiskAddr, int m >void BTree<FileName, DiskAddr, m>::Clear(PNode pnode){for ( int i = 0; i < pnode->keycnt; ++ i ){if ( NULL != pnode->child[i] )Clear( pnode->child[i] );}}/** * 在以pnode为根节点的子树中查找指定的key值 * 返回指向节点的指针，index表示节点中第几个关键字 * 若不存在，index置为-1,但是返回相应的节点（为了Insert操作） **/template< typename FileName, typename DiskAddr, int m >typename BTree<FileName, DiskAddr, m>::PNode BTree<FileName, DiskAddr, m>::SubTreeSearch( PNode pnode, FileName name, int& index ){if ( NULL == pnode ){index = -1;return NULL;}int keyind;PNode presult = pnode;if ( true == NodeSearch( pnode, name, keyind ) ){index = keyind;}else {//那么keyind就是子节点的索引if ( true == pnode->isleaf )index = -1;elsepresult = SubTreeSearch( pnode->child[keyind], name, index );}return presult;}/** * 在节点内二分搜索 * 如果相等，返回true, index为关键字的索引号；否则，返回false，index为子女指针序号 **/template< typename FileName, typename DiskAddr, int m >bool BTree<FileName, DiskAddr, m>::NodeSearch( PNode pnode, FileName name, int& index ){int i, j, mid;i = 0;j = pnode->keycnt-1;while ( i <= j ){mid = (i+j)>>1;//FileName类型最低要求：operator <if ( pnode->filename[mid] < name )i = mid+1;else if ( name < pnode->filename[mid] )j = mid-1;else {index = mid;return true;}}index = i;return false;}/** * 直接在节点中插入关键字，不一定是叶子节点 * 返回插入的位置 **/template< typename FileName, typename DiskAddr, int m >int BTree<FileName, DiskAddr, m>::NodeInsert( PNode pnode, FileName name, DiskAddr addr ){int i, position;NodeSearch( pnode, name, position );for ( i = pnode->keycnt; i > position; -- i ){pnode->filename[i] = pnode->filename[i-1];pnode->fileaddr[i] = pnode->fileaddr[i-1];pnode->child[i+1] = pnode->child[i];}pnode->child[ position+1 ] = pnode->child[ position ]; //如果pnode是新建的空root，不会有影响 pnode->filename[position] = name;pnode->fileaddr[position] = addr;pnode->child[position] = NULL;++ pnode->keycnt;return position;}/** * 分裂pnode节点，主要当pnode为root * **/template< typename FileName, typename DiskAddr, int m >void BTree<FileName, DiskAddr, m>::SplitNode( PNode pnode ){PNode parent, pnew;int index, lcnt, rcnt, i;pnew = Allocate( pnode->isleaf );lcnt = (Node::MaxKeyCnt)>>1;rcnt = Node::MaxKeyCnt-lcnt;//直接使用memcpy更快，但是如果FileName、DiskAddr有深复制？for ( i = 0; i < rcnt; ++ i ){pnew->filename[i] = pnode->filename[lcnt+i+1];pnew->fileaddr[i] = pnode->fileaddr[lcnt+i+1];}if ( false == pnode->isleaf ){memcpy( (void*)pnew->child, (void*)(pnode->child+lcnt+1), sizeof(void*)*(rcnt+1) );for ( i = 0; i < rcnt+1; ++ i )pnew->child[i]->parent = pnew;}pnew->keycnt = rcnt;pnode->keycnt = lcnt;//关键字上移if ( NULL == pnode->parent ) //pnode为root{root = pnode->parent = Allocate();}parent = pnode->parent;index = NodeInsert( parent, pnode->filename[lcnt], pnode->fileaddr[lcnt] );parent = pnode->parent;parent->child[index] = pnode;parent->child[index+1] = pnew;pnew->parent = parent;if ( parent->keycnt > Node::MaxKeyCnt )SplitNode( parent );}/** * 寻找以pnode为根节点的子树中含最小关键字的节点 * **/template< typename FileName, typename DiskAddr, int m >inline typename BTree<FileName, DiskAddr, m>::PNode BTree<FileName, DiskAddr, m>::FindMinNode( PNode pnode ){PNode presult;presult = pnode;while ( false == presult->isleaf )presult = presult->child[0];return presult;}/** * 寻找以pnode为根节点的子树中含最大关键字的节点 * **/template< typename FileName, typename DiskAddr, int m >inline typename BTree<FileName, DiskAddr, m>::PNode BTree<FileName, DiskAddr, m>::FindMaxNode( PNode pnode ){PNode presult;presult = pnode;while ( false == presult->isleaf )presult = presult->child[ presult->keycnt ];return presult;}/** * 更新pnode，使得满足B-tree的定义 * **/template< typename FileName, typename DiskAddr, int m >void BTree<FileName, DiskAddr, m>::Update( PNode pnode ){if ( pnode->keycnt >= Node::MinKeyCnt || ( pnode == root && pnode->keycnt > 0 ) )return;if ( pnode == root && 0 == pnode->keycnt ){root = root->child[0];if ( NULL != root ){delete root->parent;root->parent = NULL;}return;}PNode parent;int index;parent = pnode->parent;//如果pnode->keycnt == 0, m = 3；很特殊的一种情况。if ( pnode->keycnt > 0 )NodeSearch( parent, pnode->filename[0], index );else{for ( index = 0; index < parent->keycnt+1; ++ index )if ( parent->child[index] == pnode )break;}if ( index > 0 && parent->child[index-1]->keycnt > Node::MinKeyCnt ){FromLeftSibling( pnode, parent, index );}else if ( index < parent->keycnt && parent->child[index+1]->keycnt > Node::MinKeyCnt ){FromRightSibling( pnode, parent, index );}else{//合并if ( index == parent->keycnt ) //pnode是parent的最后一个子女节点-- index;MergeChild( parent, index );if ( parent->keycnt < Node::MinKeyCnt )Update( parent );}}/* * leftsibling节点最右边的关键字 --> parent节点的第chind-1个关键字 --> child节点最左边位置 */template< typename FileName, typename DiskAddr, int t >void BTree<FileName, DiskAddr, t>::FromLeftSibling( PNode child, PNode parent, int chind ){int i;PNode left;//child向后移动一个位置for ( i = child->keycnt; i > 0; -- i ){child->filename[i] = child->filename[i-1];child->fileaddr[i] = child->fileaddr[i-1];child->child[i+1] = child->child[i];}child->child[1] = child->child[0];left = parent->child[chind-1];child->child[0] = left->child[ left->keycnt ];if ( false == child->isleaf ){child->child[0]->parent = child;}//parent关键字移到child中child->filename[0] = parent->filename[chind-1];child->fileaddr[0] = parent->fileaddr[chind-1];++ child->keycnt;//left关键字移到parent中-- left->keycnt;parent->filename[chind-1] = left->filename[ left->keycnt ];parent->fileaddr[chind-1] = left->fileaddr[ left->keycnt ];}/* * rightsibling节点最左边的关键字 --> parent节点的第chind个关键字 --> child节点最右边位置 */template< typename FileName, typename DiskAddr, int t >void BTree<FileName, DiskAddr, t>::FromRightSibling( PNode child, PNode parent, int chind ){int i;PNode right;right = parent->child[chind+1];//child->filename[ child->keycnt ] = parent->filename[ chind ];child->fileaddr[ child->keycnt ] = parent->fileaddr[ chind ];child->child[ child->keycnt+1 ] = right->child[0];if ( false == child->isleaf ){child->child[ child->keycnt+1 ]->parent = child;}++ child->keycnt;//right第一个关键字移到parentparent->filename[ chind ] = right->filename[0];parent->fileaddr[ chind ] = right->fileaddr[0];//right向前移动一个位置-- right->keycnt;for ( i = 0; i < right->keycnt; ++ i ){right->filename[i] = right->filename[i+1];right->fileaddr[i] = right->fileaddr[i+1];right->child[i] = right->child[i+1];}right->child[i] = right->child[i+1];}/* * 将pnode->child[i]、pnode->child[i+1]和pnode->filename[i]合并 */template< typename FileName, typename DiskAddr, int t >void BTree<FileName, DiskAddr, t>::MergeChild( PNode pnode, int keyind ){if ( NULL == pnode )return;PNode left, right;int i;left = pnode->child[keyind];right = pnode->child[keyind+1];//merging left and right node!for ( i = 0; i < right->keycnt; ++ i ){//留一个位置给关键字下移left->filename[left->keycnt+i+1] = right->filename[i];left->fileaddr[left->keycnt+i+1] = right->fileaddr[i];}if ( false == left->isleaf ){memcpy( left->child+left->keycnt+1, right->child, sizeof(PNode)*(right->keycnt+1) );if ( false == left->isleaf ){for ( i = 0; i < right->keycnt+1; ++ i )left->child[ left->keycnt + 1 + i ]->parent = left;}}//关键字下移left->filename[ left->keycnt ] = pnode->filename[ keyind ];left->fileaddr[ left->keycnt ] = pnode->fileaddr[ keyind ];left->keycnt += right->keycnt + 1;delete right;right = NULL;for ( i = keyind; i < pnode->keycnt-1; ++ i ){pnode->filename[i] = pnode->filename[i+1];pnode->fileaddr[i] = pnode->fileaddr[i+1];pnode->child[i+1] = pnode->child[i+2];}-- pnode->keycnt;}//=======================================================================================#endif
