红黑树的c++完整实现源码

红黑树的c++完整实现源码

作者：July、saturnman。
时间：二零一一年三月二十九日。
出处：http://blog.csdn.net/v_JULY_v。
声明：版权所有，侵权必究。
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前言：
    本人的原创作品红黑树系列文章，至此，已经写到第5篇了。虽然第三篇文章：红黑树的c源码实现与剖析，用c语言完整实现过红黑树，但个人感觉，代码还是不够清晰。特此，再奉献出一份c++的完整实现源码，以飨读者。

    此份c++实现源码，代码紧凑了许多，也清晰了不少，同时采取c++类实现的方式，代码也更容易维护以及重用。ok，有任何问题，欢迎指正。

版权声明
    本BLOG内的此红黑树系列，总计六篇文章，是整个国内有史以来有关红黑树的最具代表性，最具完整性，最具参考价值的资料。且，本人对此红黑树系列全部文章，享有版权，任何人，任何组织，任何出版社不得侵犯本人版权相关利益，违者追究法律责任。谢谢。

红黑树的c++完整实现源码

    本文包含红黑树c++实现的完整源码，所有的解释都含在注释中，所有的有关红黑树的原理及各种插入、删除操作的情况，都已在本人的红黑树系列的前4篇文章中，一一阐述。且在此红黑树系列第五篇文章中：红黑树从头至尾插入和删除结点的全程演示图，把所有的插入、删除情况都一一展示尽了。
    因此，有关红黑树的全部原理，请参考其它文章，重点可参考此文：红黑树算法的实现与剖析。因此，相关原理，本文不再赘述。

    ok，以下，即是红黑树c++实现的全部源码，先是RBTree.h，然后是RBTree.cpp。

 

RBTree.h//file RBTree.h //written by saturnman，20101008。 //updated by July，20110329。 /*----------------------------------------------- 版权声明： July和saturnman对此份红黑树的c++实现代码享有全部的版权， 谢绝转载，侵权必究。 ------------------------------------------------*/ #ifndef _RB_TREE_H_ #define _RB_TREE_H_ #include<iostream> #include<string> #include<sstream> #include<fstream> using namespace std; template<class KEY,class U> class RB_Tree { private: RB_Tree(const RB_Tree& input){} const RB_Tree& operator=(const RB_Tree& input){} private: enum COLOR{RED,BLACK}; class RB_Node { public: RB_Node() { //RB_COLOR = BLACK; right = NULL; left = NULL; parent = NULL; } COLOR RB_COLOR; RB_Node* right; RB_Node* left; RB_Node* parent; KEY key; U data; }; public: RB_Tree() { this->m_nullNode = new RB_Node(); this->m_root = m_nullNode; this->m_nullNode->right = this->m_root; this->m_nullNode->left = this->m_root; this->m_nullNode->parent = this->m_root; this->m_nullNode->RB_COLOR = BLACK; } bool Empty() { if(this->m_root == this->m_nullNode) { return true; } else { return false; } } //查找key RB_Node* find(KEY key) { RB_Node* index = m_root; while(index != m_nullNode) { if(key<index->key) { index = index->left; //比当前的小，往左 } else if(key>index->key) { index = index->right; //比当前的大，往右 } else { break; } } return index; } //--------------------------插入结点总操作---------------------------------- //全部的工作，都在下述伪代码中： /*RB-INSERT(T, z) 1 y ← nil[T] // y 始终指向 x 的父结点。 2 x ← root[T] // x 指向当前树的根结点， 3 while x ≠ nil[T] 4 do y ← x 5 if key[z] < key[x] //向左，向右.. 6 then x ← left[x] 7 else x ← right[x] //为了找到合适的插入点，x探路跟踪路径，直到x成为NIL 为止。 8 p[z] ← y //y置为 插入结点z 的父结点。 9 if y = nil[T] 10 then root[T] ← z 11 else if key[z] < key[y] 12 then left[y] ← z 13 else right[y] ← z //此 8-13行，置z 相关的指针。 14 left[z] ← nil[T] 15 right[z] ← nil[T] //设为空， 16 color[z] ← RED //将新插入的结点z作为红色 17 RB-INSERT-FIXUP(T, z) */ //因为将z着为红色，可能会违反某一红黑性质， //所以需要调用下面的RB-INSERT-FIXUP(T, z)来保持红黑性质。 bool Insert(KEY key,U data) { RB_Node* insert_point = m_nullNode; RB_Node* index = m_root; while(index!=m_nullNode) { insert_point = index; if(key<index->key) { index = index->left; } else if(key>index->key) { index = index->right; } else { return false; } } RB_Node* insert_node = new RB_Node(); insert_node->key = key; insert_node->data = data; insert_node->RB_COLOR = RED; insert_node->right = m_nullNode; insert_node->left = m_nullNode; if(insert_point==m_nullNode) //如果插入的是一颗空树 { m_root = insert_node; m_root->parent = m_nullNode; m_nullNode->left = m_root; m_nullNode->right = m_root; m_nullNode->parent = m_root; } else { if(key<insert_point->key) { insert_point->left = insert_node; } else { insert_point->right = insert_node; } insert_node->parent = insert_point; } InsertFixUp(insert_node); //调用InsertFixUp修复红黑树性质。 } //---------------------插入结点性质修复-------------------------------- //3种插入情况，都在下面的伪代码中(未涉及到所有全部的插入情况)。 /* RB-INSERT-FIXUP(T, z) 1 while color[p[z]] = RED 2 do if p[z] = left[p[p[z]]] 3 then y ← right[p[p[z]]] 4 if color[y] = RED 5 then color[p[z]] ← BLACK ? Case 1 6 color[y] ← BLACK ? Case 1 7 color[p[p[z]]] ← RED ? Case 1 8 z ← p[p[z]] ? Case 1 9 else if z = right[p[z]] 10 then z ← p[z] ? Case 2 11 LEFT-ROTATE(T, z) ? Case 2 12 color[p[z]] ← BLACK ? Case 3 13 color[p[p[z]]] ← RED ? Case 3 14 RIGHT-ROTATE(T, p[p[z]]) ? Case 3 15 else (same as then clause with "right" and "left" exchanged) 16 color[root[T]] ← BLACK */ //然后的工作，就非常简单了，即把上述伪代码改写为下述的c++代码： void InsertFixUp(RB_Node* node) { while(node->parent->RB_COLOR==RED) { if(node->parent==node->parent->parent->left) // { RB_Node* uncle = node->parent->parent->right; if(uncle->RB_COLOR == RED) //插入情况1，z的叔叔y是红色的。 { node->parent->RB_COLOR = BLACK; uncle->RB_COLOR = BLACK; node->parent->parent->RB_COLOR = RED; node = node->parent->parent; } else if(uncle->RB_COLOR == BLACK ) //插入情况2：z的叔叔y是黑色的，。 { if(node == node->parent->right) //且z是右孩子 { node = node->parent; RotateLeft(node); } else //插入情况3：z的叔叔y是黑色的，但z是左孩子。 { node->parent->RB_COLOR = BLACK; node->parent->parent->RB_COLOR = RED; RotateRight(node->parent->parent); } } } else //这部分是针对为插入情况1中，z的父亲现在作为祖父的右孩子了的情况，而写的。 //15 else (same as then clause with "right" and "left" exchanged) { RB_Node* uncle = node->parent->parent->left; if(uncle->RB_COLOR == RED) { node->parent->RB_COLOR = BLACK; uncle->RB_COLOR = BLACK; uncle->parent->RB_COLOR = RED; node = node->parent->parent; } else if(uncle->RB_COLOR == BLACK) { if(node == node->parent->left) { node = node->parent; RotateRight(node); //与上述代码相比，左旋改为右旋 } else { node->parent->RB_COLOR = BLACK; node->parent->parent->RB_COLOR = RED; RotateLeft(node->parent->parent); //右旋改为左旋，即可。 } } } } m_root->RB_COLOR = BLACK; } //左旋代码实现 bool RotateLeft(RB_Node* node) { if(node==m_nullNode || node->right==m_nullNode) { return false;//can't rotate } RB_Node* lower_right = node->right; lower_right->parent = node->parent; node->right=lower_right->left; if(lower_right->left!=m_nullNode) { lower_right->left->parent = node; } if(node->parent==m_nullNode) //rotate node is root { m_root = lower_right; m_nullNode->left = m_root; m_nullNode->right= m_root; //m_nullNode->parent = m_root; } else { if(node == node->parent->left) { node->parent->left = lower_right; } else { node->parent->right = lower_right; } } node->parent = lower_right; lower_right->left = node; } //右旋代码实现 bool RotateRight(RB_Node* node) { if(node==m_nullNode || node->left==m_nullNode) { return false;//can't rotate } RB_Node* lower_left = node->left; node->left = lower_left->right; lower_left->parent = node->parent; if(lower_left->right!=m_nullNode) { lower_left->right->parent = node; } if(node->parent == m_nullNode) //node is root { m_root = lower_left; m_nullNode->left = m_root; m_nullNode->right = m_root; //m_nullNode->parent = m_root; } else { if(node==node->parent->right) { node->parent->right = lower_left; } else { node->parent->left = lower_left; } } node->parent = lower_left; lower_left->right = node; } //--------------------------删除结点总操作---------------------------------- //伪代码，不再贴出，详情，请参考此红黑树系列第二篇文章： //经典算法研究系列：五、红黑树算法的实现与剖析： //http://blog.csdn.net/v_JULY_v/archive/2010/12/31/6109153.aspx。 bool Delete(KEY key) { RB_Node* delete_point = find(key); if(delete_point == m_nullNode) { return false; } if(delete_point->left!=m_nullNode && delete_point->right!=m_nullNode) { RB_Node* successor = InOrderSuccessor(delete_point); delete_point->data = successor->data; delete_point->key = successor->key; delete_point = successor; } RB_Node* delete_point_child; if(delete_point->right!=m_nullNode) { delete_point_child = delete_point->right; } else if(delete_point->left!=m_nullNode) { delete_point_child = delete_point->left; } else { delete_point_child = m_nullNode; } delete_point_child->parent = delete_point->parent; if(delete_point->parent==m_nullNode)//delete root node { m_root = delete_point_child; m_nullNode->parent = m_root; m_nullNode->left = m_root; m_nullNode->right = m_root; } else if(delete_point == delete_point->parent->right) { delete_point->parent->right = delete_point_child; } else { delete_point->parent->left = delete_point_child; } if(delete_point->RB_COLOR==BLACK && !(delete_point_child==m_nullNode && delete_point_child->parent==m_nullNode)) { DeleteFixUp(delete_point_child); } delete delete_point; return true; } //---------------------删除结点性质修复----------------------------------- //所有的工作，都在下述23行伪代码中： /* RB-DELETE-FIXUP(T, x) 1 while x ≠ root[T] and color[x] = BLACK 2 do if x = left[p[x]] 3 then w ← right[p[x]] 4 if color[w] = RED 5 then color[w] ← BLACK ? Case 1 6 color[p[x]] ← RED ? Case 1 7 LEFT-ROTATE(T, p[x]) ? Case 1 8 w ← right[p[x]] ? Case 1 9 if color[left[w]] = BLACK and color[right[w]] = BLACK 10 then color[w] ← RED ? Case 2 11 x p[x] ? Case 2 12 else if color[right[w]] = BLACK 13 then color[left[w]] ← BLACK ? Case 3 14 color[w] ← RED ? Case 3 15 RIGHT-ROTATE(T, w) ? Case 3 16 w ← right[p[x]] ? Case 3 17 color[w] ← color[p[x]] ? Case 4 18 color[p[x]] ← BLACK ? Case 4 19 color[right[w]] ← BLACK ? Case 4 20 LEFT-ROTATE(T, p[x]) ? Case 4 21 x ← root[T] ? Case 4 22 else (same as then clause with "right" and "left" exchanged) 23 color[x] ← BLACK */ //接下来的工作，很简单，即把上述伪代码改写成c++代码即可。 void DeleteFixUp(RB_Node* node) { while(node!=m_root && node->RB_COLOR==BLACK) { if(node == node->parent->left) { RB_Node* brother = node->parent->right; if(brother->RB_COLOR==RED) //情况1：x的兄弟w是红色的。 { brother->RB_COLOR = BLACK; node->parent->RB_COLOR = RED; RotateLeft(node->parent); } else //情况2：x的兄弟w是黑色的， { if(brother->left->RB_COLOR == BLACK && brother->right->RB_COLOR == BLACK) //且w的俩个孩子都是黑色的。 { brother->RB_COLOR = RED; node = node->parent; } else if(brother->right->RB_COLOR == BLACK) //情况3：x的兄弟w是黑色的，w的右孩子是黑色（w的左孩子是红色）。 { brother->RB_COLOR = RED; brother->left->RB_COLOR = BLACK; RotateRight(brother); } else if(brother->right->RB_COLOR == RED) //情况4：x的兄弟w是黑色的，且w的右孩子时红色的。 { brother->RB_COLOR = node->parent->RB_COLOR; node->parent->RB_COLOR = BLACK; brother->right->RB_COLOR = BLACK; RotateLeft(node->parent); node = m_root; } } } else //下述情况针对上面的情况1中，node作为右孩子而阐述的。 //22 else (same as then clause with "right" and "left" exchanged) //同样，原理一致，只是遇到左旋改为右旋，遇到右旋改为左旋，即可。其它代码不变。 { RB_Node* brother = node->parent->left; if(brother->RB_COLOR == RED) { brother->RB_COLOR = BLACK; node->parent->RB_COLOR = RED; RotateRight(node->parent); } else { if(brother->left->RB_COLOR==BLACK && brother->right->RB_COLOR == BLACK) { brother->RB_COLOR = RED; node = node->parent; } else if(brother->left->RB_COLOR==BLACK) { brother->RB_COLOR = RED; brother->right->RB_COLOR = BLACK; RotateLeft(brother); } else if(brother->left->RB_COLOR==RED) { brother->RB_COLOR = node->parent->RB_COLOR; node->parent->RB_COLOR = BLACK; brother->left->RB_COLOR = BLACK; RotateRight(node->parent); node = m_root; } } } } m_nullNode->parent = m_root; //最后将node置为根结点， node->RB_COLOR = BLACK; //并改为黑色。 } // inline RB_Node* InOrderPredecessor(RB_Node* node) { if(node==m_nullNode) //null node has no predecessor { return m_nullNode; } RB_Node* result = node->left; //get node's left child while(result!=m_nullNode) //try to find node's left subtree's right most node { if(result->right!=m_nullNode) { result = result->right; } else { break; } } //after while loop result==null or result's right child is null if(result==m_nullNode) { RB_Node* index = node->parent; result = node; while(index!=m_nullNode && result == index->left) { result = index; index = index->parent; } result = index; // first right parent or null } return result; } // inline RB_Node* InOrderSuccessor(RB_Node* node) { if(node==m_nullNode) //null node has no successor { return m_nullNode; } RB_Node* result = node->right; //get node's right node while(result!=m_nullNode) //try to find node's right subtree's left most node { if(result->left!=m_nullNode) { result = result->left; } else { break; } } //after while loop result==null or result's left child is null if(result == m_nullNode) { RB_Node* index = node->parent; result = node; while(index!=m_nullNode && result == index->right) { result = index; index = index->parent; } result = index; //first parent's left or null } return result; } //debug void InOrderTraverse() { InOrderTraverse(m_root); } void CreateGraph(string filename) { //delete } void InOrderCreate(ofstream& file,RB_Node* node) { //delete } void InOrderTraverse(RB_Node* node) { if(node==m_nullNode) { return; } else { InOrderTraverse(node->left); cout<<node->key<<endl; InOrderTraverse(node->right); } } ~RB_Tree() { clear(m_root); delete m_nullNode; } private: // utility function for destructor to destruct object; void clear(RB_Node* node) { if(node==m_nullNode) { return ; } else { clear(node->left); clear(node->right); delete node; } } private: RB_Node *m_nullNode; RB_Node *m_root; }; #endif /*_RB_TREE_H_*/

 

 RBTree.cpp//file RBTree.cpp //written by saturnman，20101008。 //updated by July，20110329。 //此处，省去了所有要包含的头文件 //主函数测试用例 int main() { RB_Tree<int,int> tree; vector<int> v; for(int i=0;i<20;++i) { v.push_back(i); } random_shuffle(v.begin(),v.end()); copy(v.begin(),v.end(),ostream_iterator<int>(cout," ")); cout<<endl; stringstream sstr; for(i=0;i<v.size();++i) { tree.Insert(v[i],i); cout<<"insert:"<<v[i]<<endl; //添加结点 } for(i=0;i<v.size();++i) { cout<<"Delete:"<<v[i]<<endl; tree.Delete(v[i]); //删除结点 tree.InOrderTraverse(); } cout<<endl; tree.InOrderTraverse(); return 0; }

 

运行效果图（先是一一插入各结点，然后再删除所有的结点）：

 

参考文献，本人的原创作品红黑树系列的前五篇文章：

4、一步一图一代码，R-B Tree

1、教你透彻了解红黑树

5、红黑树插入和删除结点的全程演示

3、红黑树的c源码实现与剖析

2、红黑树算法的实现与剖析

6、致谢：http://saturnman.blog.163.com/。

完。

 

版权所有。谢绝转载，杜绝一切的侵犯版权的任何举动。
违者，必定追究法律责任。谢谢，各位。