M路平衡B树

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#pragma once// M路平衡B树template<class K, size_t M = 3>struct BTreeNode{// KV结构//pair<K,V> _kvs[M];// 关键字、孩纸// 关键字和孩纸都多给一个，先插入节点再进行分裂// 简化了分裂逻辑，但是效率会低一些K _keys[M];BTreeNode<K, M>* _subs[M+1];size_t _size;// 关键字个数BTreeNode<K, M>* _parent;// 父亲BTreeNode():_parent(NULL),_size(0){for (size_t i = 0; i < M+1; ++i){_subs[i] = NULL;}}};template<class K, size_t M = 3>class BTree{typedef BTreeNode<K, M> Node;public:BTree():_root(NULL){}// pair<Node*, int> Node*为节点指针，int为关键字位置，-1则表示不存在pair<Node*, int> Find(const K& key){Node* parent = NULL;Node* cur = _root;while(cur){size_t i = 0;while(i < cur->_size){if (cur->_keys[i] == key)return pair<Node*, int>(cur, i);else if (cur->_keys[i] < key)++i;elsebreak;}parent = cur;cur= cur->_subs[i];}// 没有找到key则返回叶子节点，下标值为-1，这样方便Insert/Remove时复用return pair<Node*, int>(parent, -1);}bool Insert(const K& key){if (_root == NULL){_root = new Node();_root->_keys[0] = key;_root->_size = 1;return true;}pair<Node*, int> ret = Find(key);if (ret.second != -1){return false;}// 在cur节点中插入k和sub，最开始sub为空// 分裂后把中间节点和分裂出来的节点同样的逻辑往父节点插入// 如果插入后cur节点<M，则满足条件，否则一直网上分裂，直到根节点//K  k = key;Node* cur = ret.first;Node* sub = NULL;while (1){_InsertKey(cur, k, sub);if (cur->_size < M)return true;int boundary = M/2;k = cur->_keys[boundary];// 分裂出新节点Node* tmp = new Node();// 拷贝keyint index = 0;for (int i = boundary+1; i < cur->_size; ++i){tmp->_keys[index++] = cur->_keys[i];tmp->_size++;cur->_keys[i] = K();}// 拷贝子节点，注意子节点要多一个index = 0;for (int i = boundary+1; i <= cur->_size; ++i){tmp->_subs[index] = cur->_subs[i];if (tmp->_subs[index])tmp->_subs[index]->_parent = tmp;cur->_subs[i] = NULL;++index;}cur->_size /= 2;// 如果已经到根节点，则if (cur->_parent == NULL){_root = new Node;_root->_keys[0] = k;_root->_size = 1;_root->_subs[0] = cur;_root->_subs[1] = tmp;tmp->_parent = cur->_parent = _root;return true;}// 把k、sub当成新增节点向上层插入cur = cur->_parent;sub = tmp;}return true;}void _InsertKey(Node* cur, const K& key, Node* sub){int i = cur->_size-1;while(i >= 0){if (cur->_keys[i] > key){cur->_keys[i+1] = cur->_keys[i];// 子节点挪动后面的那一位cur->_subs[i+2] = cur->_subs[i+1];--i;}else{break;}}cur->_keys[i+1] = key;cur->_subs[i+2] = sub;cur->_size++;if (sub)sub->_parent = cur;}void InOrder(){_InOrder(_root);}void _InOrder(Node* cur){if (cur == NULL){return;}for (size_t i = 0; i < cur->_size; ++i){_InOrder(cur->_subs[i]);cout<<cur->_keys[i]<<" ";}_InOrder(cur->_subs[cur->_size]);}protected:Node* _root;};void TestBTree(){int a[] = {53, 75, 139, 49, 145, 36, 101};BTree<int, 5> t1;for (int i = 0; i < sizeof(a)/sizeof(int); ++i){t1.Insert(a[i]);}t1.InOrder();}
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