B-树（c++实现）

 从10月14日b-树第1个版本，经过1天多的反复测试和修改，终于出了今天10月16日的最终版本，哈哈，b-树顺利拿下

template<class K, class E, int M>class BMTree{public:BMTree() {root = 0; height = 0;}~BMTree() { }bool Search(const K& k, E& e) const;BMTree<K,E,M>& Insert(const E& e);BMTree<K,E,M>& Delete(const K& k, E& e);intGetHeight() const { return height; }void LevelOrder(void(*Visit)(BMTree_Node<K,E,M> *u));void LevelOutput() {LevelOrder(Output); cout << endl;}public:static const int D = (M + 1)/2 ;//D为子节点的最少个数,元素最少个数是D-1static const int COUNT_OF_FIRST = D - 1;//分裂节点时,第1个节点的元素个数static const int COUNT_OF_SECOND = M - D;//分裂节点时,第2个节点的元素个数private:BMTree_Node<K,E,M> *root;int height;BMTree_Node<K,E,M>* Search_Node(const K& k, int& index, bool& match) const;void Insert_Not_Full(BMTree_Node<K,E,M> *p, int index, const E& e);int Insert_Not_Full(BMTree_Node<K,E,M> *p, const E& e);void Split(BMTree_Node<K,E,M> *op, BMTree_Node<K,E,M> *np, E& es);void Delete_Leaf(BMTree_Node<K,E,M>* p, int index, const K& k, E& e);void Merge(BMTree_Node<K,E,M>* p);static void Output(BMTree_Node<K,E,M> *p);};template<class K, class E, int M>bool BMTree<K,E,M>::Search(const K& k, E& e) const{BMTree_Node<K,E,M> *p = root;while(p){int i = 0;for(;i < p->count && p->data[i] < k; i++);if( (i < p->count) && (p->data[i] == k) ){e = p->data[i];return true;}//下潜p = p->child[i];}return false;}template<class K, class E, int M>void BMTree<K,E,M>::Split(BMTree_Node<K,E,M> *op, BMTree_Node<K,E,M> *np, E& es){int i = 0;for(; i < COUNT_OF_SECOND; i++){np->data[COUNT_OF_SECOND-i-1] = op->data[M-i-1];np->child[COUNT_OF_SECOND-i] = op->child[M-i];op->child[M-i] = 0;if(np->child[COUNT_OF_SECOND-i]){np->child[COUNT_OF_SECOND-i]->parent = np;np->child[COUNT_OF_SECOND-i]->index = COUNT_OF_SECOND-i;}}np->child[0] = op->child[M-i];op->child[M-i] = 0;if(np->child[0]){np->child[0]->parent = np;np->child[0]->index = 0;}es = op->data[D-1];op->count = COUNT_OF_FIRST;np->count = COUNT_OF_SECOND;}template<class K, class E, int M>int BMTree<K,E,M>::Insert_Not_Full(BMTree_Node<K,E,M> *p, const E& e){//assert(p);int i = 0;for(; i < p->count && p->data[i] < e; i++);for(int j = p->count-1; j >= i; j--){p->data[j+1] = p->data[j];p->child[j+2] = p->child[j+1];if(p->child[j+2])p->child[j+2]->index = j+2;}p->data[i] = e;p->count++;return i;}template<class K, class E, int M>BMTree<K,E,M>& BMTree<K,E,M>::Insert(const E& e){if(!root){BMTree_Node<K,E,M> *p = new BMTree_Node<K,E,M>;p->data[0] = e;p->count++;root = p;height = 1;return *this;}int index;bool match;BMTree_Node<K,E,M> *p = Search_Node(e, index, match);if(match){throw BadInput();}else{Insert_Not_Full(p,index,e);while( p->count == M ){BMTree_Node<K,E,M> *np = new BMTree_Node<K,E,M>;//分裂E _es;Split(p, np, _es);if( p != root ){BMTree_Node<K,E,M> *pp = p->parent;index = Insert_Not_Full(pp, _es);p->index = index;np->index = index+1;pp->child[index] = p;pp->child[index+1] = np;np->parent = pp;p = pp;}else{BMTree_Node<K,E,M> *nh = new BMTree_Node<K,E,M>;nh->child[0] = p;p->parent = nh;p->index = 0;nh->child[1] = np;np->parent = nh;np->index = 1;nh->data[0] = _es;nh->count++;root = nh;height++;}}}return *this;}template<class K, class E, int M>void BMTree<K,E,M>::Insert_Not_Full(BMTree_Node<K,E,M> *p, int index, const E& e){//assert(p);//assert(index >=0 && index < p->count); for(int j = p->count-1; j >= index; j--){p->data[j+1] = p->data[j];p->child[j+2] = p->child[j+1];if(p->child[j+2])p->child[j+2]->index = j+2;}p->data[index] = e;p->count++;}template<class K, class E, int M>BMTree_Node<K,E,M>* BMTree<K,E,M>::Search_Node(const K& k, int& index, bool& match) const{BMTree_Node<K,E,M> *p = root;match = false;index = -1;while(p){for(index = 0; index < p->count && p->data[index] < k; index++);if( (index < p->count) && (p->data[index] == k) ){match = true;return p;}if( p->child[index] == 0 )return p;//下潜p = p->child[index];}return p;}template<class K, class E, int M>void BMTree<K,E,M>::Delete_Leaf(BMTree_Node<K,E,M>* p, int index, const K& k, E& e){//assert(p);//保证p是叶节点if( p->count > D - 1 || p == root ){for(int i = index; i < p->count-1; i++ ){p->data[i] = p->data[i+1];}p->count--;if( p == root && p->count == 0 ){delete p;root = 0;height = 0;}}else{//assert(p->parent!=0);//检查左兄弟if( p->index > 0 && p->parent->child[p->index-1]->count > D - 1 ){BMTree_Node<K,E,M>* left = p->parent->child[p->index-1];//删除index元素,空出0位置for(int i = index; i > 0; i-- ){p->data[i] = p->data[i-1];}p->data[0] = p->parent->data[p->index-1];p->parent->data[p->index-1] = left->data[left->count-1];left->count--;}//检查右兄弟else if( p->index < p->parent->count && p->parent->child[p->index+1]->count > D - 1){BMTree_Node<K,E,M>* right = p->parent->child[p->index+1];//删除index元素,空出p->count-1位置for(int i = index; i < p->count-1; i++ ){p->data[i] = p->data[i+1];}p->data[p->count-1] = p->parent->data[p->index];p->parent->data[p->index] = right->data[0];//右兄弟删除0元素for(int i = 0; i < right->count-1; i++ ){right->data[i] = right->data[i+1];}right->count--;}else{if( p->index > 0 ){BMTree_Node<K,E,M>* left = p->parent->child[p->index-1];left->data[left->count++] = p->parent->data[p->index-1];for(int i = 0; i < index; i++ ){left->data[left->count++] = p->data[i];}for(int i = index + 1; i < p->count; i++ ){left->data[left->count++] = p->data[i];}for( int i = p->index; i < p->parent->count; ++i ){p->parent->data[i-1] = p->parent->data[i];p->parent->child[i] = p->parent->child[i+1];if( p->parent->child[i] )p->parent->child[i]->index = i;}p->parent->count--;delete p;if( left->parent->count < D-1)Merge(left->parent);}else if( p->index < p->parent->count ){BMTree_Node<K,E,M>* right = p->parent->child[p->index+1];//删除index元素for(int i = index; i < p->count-1; i++ ){p->data[i] = p->data[i+1];}p->count--;p->data[p->count++] = p->parent->data[p->index];for(int i = 0; i < right->count; i++ ){p->data[p->count++] = right->data[i];}for( int i = p->index; i < p->parent->count-1; ++i ){p->parent->data[i] = p->parent->data[i+1];p->parent->child[i+1] = p->parent->child[i+2];if( p->parent->child[i+1] )p->parent->child[i+1]->index = i+1;}p->parent->count--;delete right;if( p->parent->count < D-1)Merge(p->parent);}}}}template<class K, class E, int M>void BMTree<K,E,M>::Merge(BMTree_Node<K,E,M>* p){//assert(p->parent);//检查左兄弟if( p->index > 0 && p->parent->child[p->index-1]->count > D - 1 ){BMTree_Node<K,E,M>* left = p->parent->child[p->index-1];//空出0位置for(int i = p->count; i > 0; i-- ){p->data[i] = p->data[i-1];p->child[i+1] = p->child[i];if( p->child[i+1] )p->child[i+1]->index = i+1;}p->child[1] = p->child[0];p->child[0] = left->child[left->count];left->child[left->count] = 0;if( p->child[0] ){p->child[0]->parent = p;p->child[0]->index = 0;}p->data[0] = p->parent->data[p->index-1];p->count++;p->parent->data[p->index-1] = left->data[left->count-1];left->count--;}//检查右兄弟else if( p->index < p->parent->count && p->parent->child[p->index+1]->count > D - 1){BMTree_Node<K,E,M>* right = p->parent->child[p->index+1];p->data[p->count] = p->parent->data[p->index];p->child[p->count+1] = right->child[0];if( p->child[p->count+1] ){p->child[p->count+1]->parent = p;p->child[p->count+1]->index = p->count+1;}p->count++;p->parent->data[p->index] = right->data[0];//右兄弟删除0元素for(int i = 0; i < right->count-1; i++ ){right->data[i] = right->data[i+1];right->child[i] = right->child[i+1];if( right->child[i] )right->child[i]->index = i;}right->child[right->count-1] = right->child[right->count];right->child[right->count] = 0;if( right->child[right->count-1] )right->child[right->count-1]->index = right->count-1;right->count--;}else{do{if( p->index > 0 ){BMTree_Node<K,E,M>* left = p->parent->child[p->index-1];left->data[left->count++] = p->parent->data[p->index-1];left->child[left->count] = p->child[0];if( left->child[left->count] ){left->child[left->count]->parent = left;left->child[left->count]->index = left->count;}for(int i = 0; i < p->count; i++ ){left->data[left->count++] = p->data[i];left->child[left->count] = p->child[i+1];if( left->child[left->count] ){left->child[left->count]->parent = left;left->child[left->count]->index = left->count;}}for( int i = p->index; i < p->parent->count; ++i ){p->parent->data[i-1] = p->parent->data[i];p->parent->child[i] = p->parent->child[i+1];if( p->parent->child[i] ){p->parent->child[i]->index = i;}}p->parent->count--;delete p;if( left->parent == root && left->parent->count == 0 ){left->parent = 0;delete root;root = left;height--;break;}else{p = left->parent;}}else if( p->index < p->parent->count ){BMTree_Node<K,E,M>* right = p->parent->child[p->index+1];p->data[p->count++] = p->parent->data[p->index];p->child[p->count] = right->child[0];if( p->child[p->count] ){p->child[p->count]->parent = p;p->child[p->count]->index = p->count;}for(int i = 0; i < right->count; i++ ){p->data[p->count++] = right->data[i];p->child[p->count] = right->child[i+1];if( p->child[p->count] ){p->child[p->count]->parent = p;p->child[p->count]->index = p->count;}}for( int i = p->index; i < p->parent->count-1; ++i ){p->parent->data[i] = p->parent->data[i+1];p->parent->child[i+1] = p->parent->child[i+2];if( p->parent->child[i+1] ){p->parent->child[i+1]->index = i+1;}}p->parent->count--;delete right;if( p->parent == root && p->parent->count == 0 ){p->parent = 0;delete root;root = p;height--;break;}else{p = p->parent;}}}while(p->count < D-1);}}template<class K, class E, int M>BMTree<K,E,M>& BMTree<K,E,M>::Delete(const K& k, E& e){bool match = false;int index = -1;BMTree_Node<K,E,M> * p = Search_Node(k,index,match);if( !match )throw BadInput();//是否叶节点if(!p->child[0]){//是叶节点，直接删除Delete_Leaf(p, index, k, e);return *this;}else{BMTree_Node<K,E,M> * tmp = p->child[index];BMTree_Node<K,E,M> * tmpp = p;while(tmp){//assert(tmp->count > 0)tmpp = tmp;tmp = tmp->child[tmp->count];}p->data[index] = tmpp->data[tmpp->count-1];Delete_Leaf(tmpp, tmpp->count-1, tmpp->data[tmpp->count-1], e );}return *this;}template<class K, class E, int M>void BMTree<K,E,M>::Output(BMTree_Node<K,E,M> *p){for( int i = 0; i < p->count; i++){cout << p->data[i] << ' ';}}template<class K, class E, int M>void BMTree<K,E,M>::LevelOrder(void(*Visit)(BMTree_Node<K,E,M> *u)){LinkedQueue<BMTree_Node<K,E,M>* > Q;BMTree_Node<K,E,M>* p = root;while (p) {Visit(p);if( p->child[0] ){for( int i = 0; i <= p->count; i++){Q.Add(p->child[i]);}}try {Q.Delete(p);}catch(OutOfBounds) {return;}}}

 

//M叉B-树的节点template<class K, class E, int M>struct BMTree_Node{static const int D = (M + 1)/2 ;//D为子节点的最少个数,元素最少个数是D-1static const int COUNT_OF_FIRST = D - 1;//分裂节点时,第1个节点的元素个数static const int COUNT_OF_SECOND = M - D;//分裂节点时,第2个节点的元素个数int count;//此节点已存放的元素个数int index;//是父节点第几个子节点E data[M];//M-1个元素,多一个是因为节点分裂操作BMTree_Node<K,E,M> *child[M+1];//M个子节点,多一个是因为节点分裂操作BMTree_Node<K,E,M> *parent;//父节点BMTree_Node(){count = 0;index = 0;memset( data, 0, sizeof(data));memset( child, 0, sizeof(child));parent = 0;}};