红黑书（三）红黑树的删除操作
来源：互联网 发布：阿里云 ddns 编辑：程序博客网 时间：2024/06/06 02:56
c++完整代码(带插入、删除、查找等)：
#include <iostream>using namespace std;#include <stack>//颜色枚举;enum _color{ _None, _Red, _Black};//结点结构;struct tNode{ int iKey; int iColor; tNode* pParent; tNode* pLeft; tNode* pRight; tNode(): iKey(NULL), iColor(_None), pParent(nullptr), pLeft(nullptr), pRight(nullptr) { }};class RBTree{public: RBTree(): m_pRoot(nullptr), m_iCount(0) { m_pSentryNULL = new tNode(); m_pSentryNULL->iColor = _Black; //哨兵的颜色为黑色; m_pRoot = m_pSentryNULL; } ~RBTree() { delete m_pSentryNULL; m_pSentryNULL = nullptr; }private: //根结点; tNode* m_pRoot; //哨兵; tNode* m_pSentryNULL; //元素数量; int m_iCount;private: //左旋; void left_Rotate(tNode* pNode) { if(pNode == nullptr||pNode == m_pSentryNULL||pNode->pRight == m_pSentryNULL) { return; } pNode->pRight->pParent = pNode->pParent; if (pNode->pParent == m_pSentryNULL) { m_pRoot = pNode->pRight; } else { if (pNode == pNode->pParent->pLeft) { pNode->pParent->pLeft = pNode->pRight; } else { pNode->pParent->pRight = pNode->pRight; } } pNode->pParent = pNode->pRight; if (pNode->pParent->pLeft == m_pSentryNULL) { pNode->pRight = m_pSentryNULL; } else { pNode->pRight->pLeft->pParent = pNode; pNode->pRight = pNode->pParent->pLeft; } pNode->pParent->pLeft = pNode; } //右旋; void right_Rotate(tNode* pNode) { if(pNode == nullptr||pNode == m_pSentryNULL||pNode->pLeft == m_pSentryNULL) { return; } pNode->pLeft->pParent = pNode->pParent; if (pNode->pParent == m_pSentryNULL) { m_pRoot = pNode->pLeft; } else { if (pNode == pNode->pParent->pLeft) { pNode->pParent->pLeft = pNode->pLeft; } else { pNode->pParent->pRight = pNode->pLeft; } } pNode->pParent = pNode->pLeft; if (pNode->pParent->pRight == m_pSentryNULL) { pNode->pLeft = m_pSentryNULL; } else { pNode->pLeft->pRight->pParent = pNode; pNode->pLeft = pNode->pParent->pRight; } pNode->pParent->pRight = pNode; } //插入调整; void RB_Insert_Fixup(tNode* pNode) { while (pNode->pParent->iColor == _Red) { if (pNode->pParent == pNode->pParent->pParent->pLeft) { tNode* pUncleNode = pNode->pParent->pParent->pRight; if (pUncleNode->iColor == _Red)//叔结点为红色; { pUncleNode->iColor = _Black; pNode->pParent->iColor = _Black; pNode->pParent->pParent->iColor = _Red; pNode = pNode->pParent->pParent; } else//叔结点为黑色; { if (pNode == pNode->pParent->pRight) { pNode = pNode->pParent; left_Rotate(pNode); } pNode->pParent->iColor = _Black; pNode->pParent->pParent->iColor = _Red; right_Rotate(pNode->pParent->pParent); } } else//对称操作 { tNode* pUncleNode = pNode->pParent->pParent->pLeft; if (pUncleNode->iColor == _Red)//叔结点为红色; { pUncleNode->iColor = _Black; pNode->pParent->iColor = _Black; pNode->pParent->pParent->iColor = _Red; pNode = pNode->pParent->pParent; } else//叔结点为黑色; { if (pNode == pNode->pParent->pLeft) { pNode = pNode->pParent; right_Rotate(pNode); } pNode->pParent->iColor = _Black; pNode->pParent->pParent->iColor = _Red; left_Rotate(pNode->pParent->pParent); } } } m_pRoot->iColor = _Black; } //删除调整; void RB_Delete_Fixup(tNode* pNode) { while (pNode!=m_pRoot&&pNode->iColor == _Black) { if (pNode == pNode->pParent->pLeft) { tNode* pBrotherNode = pNode->pParent->pRight; //兄弟结点; if (pBrotherNode->iColor == _Red) { pNode->pParent->iColor = _Red; pBrotherNode->iColor = _Black; left_Rotate(pNode->pParent); pBrotherNode = pBrotherNode->pParent->pRight; } if (pBrotherNode->iColor == _Black) { if (pBrotherNode->pLeft->iColor == _Black&&pBrotherNode->pRight->iColor == _Black) { pBrotherNode->iColor = _Red; pNode = pNode->pParent; } else { if(pBrotherNode->pRight->iColor == _Black) { pBrotherNode->iColor = _Red; pBrotherNode->pLeft->iColor = _Black; right_Rotate(pBrotherNode); pBrotherNode = pNode->pParent->pRight; } pBrotherNode->iColor = pNode->pParent->iColor; pNode->pParent->iColor = _Black; pBrotherNode->pRight->iColor = _Black; left_Rotate(pNode->pParent); pNode = m_pRoot; } } } else//对称操作; { tNode* pBrotherNode = pNode->pParent->pLeft; //兄弟结点; if (pBrotherNode->iColor == _Red) { pNode->pParent->iColor = _Red; pBrotherNode->iColor = _Black; right_Rotate(pNode->pParent); pBrotherNode = pBrotherNode->pParent->pLeft; } if (pBrotherNode->iColor == _Black) { if (pBrotherNode->pRight->iColor == _Black&&pBrotherNode->pLeft->iColor == _Black) { pBrotherNode->iColor = _Red; pNode = pNode->pParent; } else { if(pBrotherNode->pLeft->iColor == _Black) { pBrotherNode->iColor = _Red; pBrotherNode->pRight->iColor = _Black; left_Rotate(pBrotherNode); pBrotherNode = pNode->pParent->pLeft; } pBrotherNode->iColor = pNode->pParent->iColor; pNode->pParent->iColor = _Black; pBrotherNode->pLeft->iColor = _Black; right_Rotate(pNode->pParent); pNode = m_pRoot; } } } } pNode->iColor = _Black; } //返回最小关键字元素; tNode* minNode(tNode* rootNode) { if(rootNode == m_pSentryNULL) return m_pSentryNULL; while (rootNode->pLeft!=m_pSentryNULL) { rootNode = rootNode->pLeft; } return rootNode; } //返回最大关键字元素; tNode* maxNode(tNode* rootNode) { if(rootNode == m_pSentryNULL) return m_pSentryNULL; while (rootNode->pRight!=m_pSentryNULL) { rootNode = rootNode->pRight; } return rootNode; } //替换子树; void transplantNode(tNode* pDesNode,tNode* pSrcNode) { if (pDesNode->pParent == m_pSentryNULL) { m_pRoot = pSrcNode; } else if(pDesNode == pDesNode->pParent->pLeft) { pDesNode->pParent->pLeft = pSrcNode; } else { pDesNode->pParent->pRight = pSrcNode; } pSrcNode->pParent = pDesNode->pParent; }public: //查询数据; tNode* search(int iKey) { tNode* pTemp = m_pRoot; while(pTemp!=m_pSentryNULL&&iKey!=pTemp->iKey) { if (iKey<pTemp->iKey) { pTemp = pTemp->pLeft; } else { pTemp = pTemp->pRight; } } return pTemp; } //插入; void RB_Insert(tNode* pNode) { if(pNode == m_pSentryNULL) { return; } //二叉搜索树插入操作; tNode* pTemp = m_pRoot; tNode* pTempParent = m_pSentryNULL; while (pTemp!=m_pSentryNULL) { pTempParent = pTemp; if (pNode->iKey<pTemp->iKey) { pTemp = pTemp->pLeft; } else { pTemp = pTemp->pRight; } } pNode->pParent = pTempParent; if (m_pRoot == m_pSentryNULL) { m_pRoot = pNode; } else { if (pNode->iKey < pTempParent->iKey) { pTempParent->pLeft = pNode; } else { pTempParent->pRight = pNode; } } pNode->pLeft = m_pSentryNULL; pNode->pRight = m_pSentryNULL; pNode->iColor = _Red; m_iCount++; //调整以保持红黑性质; RB_Insert_Fixup(pNode); } //删除; void RB_Delete(tNode* pNode) { if (m_pRoot == m_pSentryNULL||pNode == m_pSentryNULL) { return; } int iDeleteColor = pNode->iColor; //要删除的结点颜色; tNode* pSrcNode = nullptr; //纪录替换删除位置的结点; if(pNode->pLeft == m_pSentryNULL)//左子结点不存在; { pSrcNode = pNode->pRight; transplantNode(pNode,pNode->pRight); cout<<"delete success!"<<endl; } else if(pNode->pRight == m_pSentryNULL)//左子结点存在,右子结点不存在; { pSrcNode = pNode->pLeft; transplantNode(pNode,pNode->pLeft); cout<<"delete success!"<<endl; } else//左右子结点都存在; { tNode* pSuccessor =minNode(pNode->pRight);//后继; iDeleteColor = pSuccessor->iColor; pSrcNode = pSuccessor->pRight; if (pSuccessor!=pNode->pRight) { transplantNode(pSuccessor, pSuccessor->pRight); pSuccessor->pRight = pNode->pRight; pSuccessor->pRight->pParent = pSuccessor; } transplantNode(pNode,pSuccessor); pSuccessor->pLeft = pNode->pLeft; pSuccessor->pLeft->pParent = pSuccessor; pSuccessor->iColor = pNode->iColor; cout<<"delete success!"<<endl; } m_iCount--; if (iDeleteColor == _Black) { RB_Delete_Fixup(pSrcNode); } delete pNode; pNode = nullptr; } //前驱; tNode* predecessorNode(tNode* pNode) { if (pNode->pLeft!=m_pSentryNULL) { return maxNode(pNode->pLeft); } tNode* pTemp = pNode->pParent; while (pTemp!=m_pSentryNULL&&pTemp->pLeft == pNode) { pNode = pTemp; pTemp = pTemp->pParent; } return pTemp; } //后继; tNode* successorNode(tNode* pNode) { if (pNode->pRight!=m_pSentryNULL) { return minNode(pNode->pRight); } tNode* pTemp = pNode->pParent; while (pTemp!=m_pSentryNULL&&pTemp->pRight == pNode) { pNode = pTemp; pTemp = pTemp->pParent; } return pTemp; } //获得最小的元素值; const int& getMinValue() { tNode* pTemp = minNode(m_pRoot); if (pTemp!=m_pSentryNULL) { return pTemp->iKey; } else { return NULL; } } //获得最大的元素值; const int& getMaxValue() { tNode* pTemp = maxNode(m_pRoot); if (pTemp!=m_pSentryNULL) { return pTemp->iKey; } else { return NULL; } } //判断红黑树是否为空; bool empty() { if (m_iCount == 0) { return true; } return false; } //插入元素; void push(int iData) { tNode* pNode = new tNode; if (pNode) { pNode->iKey = iData; RB_Insert(pNode); } } //获得元素数目; const int& size() { return m_iCount; } //遍历; void traversal() { //中序遍历; if (m_pRoot == m_pSentryNULL) { return; } stack<tNode*> _stack; tNode* pTemp = m_pRoot; while (m_pSentryNULL!=pTemp||!_stack.empty()) { if (m_pSentryNULL!=pTemp) { _stack.push(pTemp); pTemp = pTemp->pLeft; } else { pTemp = _stack.top(); cout<<pTemp->iKey<<" "<<pTemp->iColor<<endl; _stack.pop(); pTemp = pTemp->pRight; } } }};//测试代码;RBTree _rbTree;cout<<"empty "<<_rbTree.empty()<<endl;_rbTree.push(11);_rbTree.push(7);_rbTree.push(5);_rbTree.push(12);_rbTree.push(6);cout<<"empty "<<_rbTree.empty()<<endl;//cout<<"size "<<_rbTree.size()<<endl;//_rbTree.traversal();_rbTree.RB_Delete(_rbTree.search(7));cout<<"size "<<_rbTree.size()<<endl;_rbTree.traversal();//测试代码输出;empty 1empty 0delete success!size 45 26 111 212 2 0 0
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