红黑树C++源码, 有详细注释
2013-05-31 21:22
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'7?" '< .< ')=) .1´ `[)3}[; =« ^ ^_` }»` ]} ~7$= `´´< ;« ~«7«()//)´ ~7` `%11\2. 4000 ,[' ="' :?}`':` ~&^ `3= ´<'< /? ````` »« <1~=[! !; `-´ "} ´. }7» /* !2: ~/[^ :"<´ ` => »" ~? ^\^ `"*/ ///> 1. 每个结点要么是红的,要么是黑的。 ///> 2. 根结点是黑的。 ///> 3. 每个叶结点,即空结点(NIL)是黑的。 ///> 4. 如果一个结点是红的,那么它的俩个儿子都是黑的。 ///> 5. 对每个结点,从该结点到其子孙结点的所有路径上包含相同数目的黑结点。 #include <iostream> #include <ctime> enum COLOR { black = 0, red = 1, }; struct RBNode { COLOR color; RBNode* pParent; RBNode* pLeft; RBNode* pRight; int val; RBNode(int nVal = 0) : color(red) , pLeft(NULL) , pRight(NULL) , pParent(NULL) , val(nVal) { } RBNode(RBNode* left, RBNode* right, RBNode* parent, int nVal, COLOR enumColor = red) : color(enumColor) , pLeft(left) , pRight(right) , pParent(parent) , val(nVal) { } }; class RBTree { public: RBTree(); ~RBTree(); public: bool Insert(int keyVal); bool DeleteNode(int keyVal); void DisplayNode(); int GetNodeSize() const; RBNode* TreeFind(int keyVal); void DisplayTree(); int GetSize(); private: RBNode* _SearchNode(int keyVal); RBNode* _MinimumNode(int kevVal); RBNode* _MaximumNode(int kevVal); RBNode* _MinimumNode(RBNode* pNode); RBNode* _MaximumNode(RBNode* pNode); RBNode* _SuccessorNode(int keyVal); RBNode* _SuccessorNode(RBNode* pNode); RBNode* _SearchNode(RBNode* pNode, int keyVal); void _InsertFixedUp(RBNode* pNode); ///> _InsertFixedUp2和上面的运算结果一样的, 虽然代码不一样 void _InsertFixedUp2(RBNode* pNode); void _DelFixedUp(RBNode* pNode); bool _LeftRotate(RBNode* pNode); bool _RightRotate(RBNode* pNode); void _DisplayTree(RBNode* pNode); private: RBNode* m_root; RBNode* m_Nil; int m_size; }; RBTree::RBTree() { m_root = m_Nil; m_Nil = new RBNode(0x0fffffff); m_Nil->color = black; m_size = 0; } RBTree::~RBTree() { if(m_root != m_Nil && m_root != NULL){ delete m_root; m_root = NULL; } if(m_Nil != NULL){ delete m_Nil; m_Nil = NULL; } } bool RBTree::_LeftRotate(RBNode* pNode) { if(pNode == m_Nil || pNode->pRight == m_Nil) { return false; } RBNode* pRightChild = pNode->pRight; ///> 此时右孩子parent指针已指向了node的父节点 pRightChild->pParent = pNode->pParent; ///> 所谓左旋就是右孩子的左节点成为node的右结点 pNode->pRight = pRightChild->pLeft; if(pRightChild->pLeft != m_Nil) { ///> 所谓左旋就是右孩子的左节点成为node的右结点 pRightChild->pLeft->pParent = pNode; } ///> 如果node就是root节点 if(pNode->pParent == m_Nil) { ///>··则让root节点为pRightChild m_root = pRightChild; m_Nil->pLeft = m_root; m_Nil->pRight = m_root; } ///> 如果node不是root节点 else { ///> 如果位于右边 if(pNode == pNode->pParent->pLeft) { ///> 则让node的父节点把指向node的指针改为 ///> 指向pRightChild pNode->pParent->pLeft = pRightChild; } ///> 反之······ else { pNode->pParent->pRight = pRightChild; } } ///> 所谓左旋就是右孩子的左节点成为node的右结点 ///> node的父节点把指向node的指针改为指向pRightChild ///> 并且node成为自己右孩子的孩子 pNode->pParent = pRightChild; pRightChild->pLeft = pNode; return true; } bool RBTree::_RightRotate(RBNode* pNode) { if(pNode == m_Nil || pNode->pLeft == m_Nil) { return false; } RBNode* pLeftChild = pNode->pLeft; pNode->pLeft = pLeftChild->pRight; pLeftChild->pParent = pNode->pParent; if(pLeftChild->pRight != m_Nil) { pLeftChild->pRight->pParent = pNode; } if(pNode->pParent == m_Nil) { m_root = pLeftChild; m_Nil->pLeft = m_root; m_Nil->pRight = m_root; } else { if(pNode == pNode->pParent->pRight) { pNode->pParent->pRight = pLeftChild; } else { pNode->pParent->pLeft = pLeftChild; } } pNode->pParent = pLeftChild; pLeftChild->pRight = pNode; return true; } RBNode* RBTree::TreeFind(int keyVal) { RBNode* pNode = _SearchNode(keyVal); if(pNode == m_Nil) { ///> 作为对外接口则返回NULL而不是m_Nil return NULL; } return pNode; } RBNode* RBTree::_SearchNode(int keyVal) { RBNode* pNode = _SearchNode(m_root, keyVal); return pNode; } RBNode* RBTree::_SearchNode(RBNode* pNode, int keyVal) { if(pNode == m_Nil || keyVal == pNode->val) { return pNode; } if(keyVal < pNode->val) { return _SearchNode(pNode->pLeft, keyVal); } else { return _SearchNode(pNode->pRight, keyVal); } } RBNode* RBTree::_MinimumNode(int kevVal) { RBNode* pNode = _SearchNode(kevVal); return _MinimumNode(pNode); } RBNode* RBTree::_MaximumNode(int kevVal) { RBNode* pNode = _SearchNode(kevVal); return _MaximumNode(pNode); } RBNode* RBTree::_MinimumNode(RBNode* pNode) { if(pNode == m_Nil) { return m_Nil; } while(pNode->pLeft != m_Nil) { pNode = pNode->pLeft; } return pNode; } RBNode* RBTree::_MaximumNode(RBNode* pNode) { if(pNode == m_Nil) { return m_Nil; } while(pNode->pRight != m_Nil) { pNode = pNode->pRight; } return pNode; } RBNode* RBTree::_SuccessorNode(int keyVal) { RBNode* pNode = _SearchNode(keyVal); return _SuccessorNode(pNode); } RBNode* RBTree::_SuccessorNode(RBNode* pNode) { if(pNode->pRight != m_Nil) { return _MinimumNode(pNode->pRight); } RBNode* pParNode = pNode->pParent; ///> 沿着父节点扶摇直上, 如果转向左边, ///> 则说明那个节点是后继. 不多解释, 请在网上看例图 while(pParNode != m_Nil && pNode == pParNode->pRight) { pNode = pParNode; pParNode = pParNode->pParent; } return pParNode; } bool RBTree::Insert(int keyVal) { RBNode* pInsertPoint = m_root; RBNode* pIndex = m_root; if(m_root != NULL) { ///> 循环结束后, pIndex降为空, ///> pInsertPoint则为要插入节点的父节点 while(pIndex != m_Nil) { pInsertPoint = pIndex; if(keyVal < pIndex->val) { pIndex = pIndex->pLeft; } else if(keyVal > pIndex->val) { pIndex = pIndex->pRight; } else { return false; } } ///> 已经找到插入节点的位置, 按值大小来插入 if(keyVal < pInsertPoint->val) { pInsertPoint->pLeft = new RBNode( m_Nil, m_Nil, pInsertPoint, keyVal); ///> 以上都是常规的二叉树代码. ///> 在红黑树中, 为了保持红黑性质, 则要进行整理 _InsertFixedUp(pInsertPoint->pLeft); } else { pInsertPoint->pRight = new RBNode( m_Nil, m_Nil, pInsertPoint, keyVal); ///> 不解释 _InsertFixedUp(pInsertPoint->pRight); } m_size++; } ///> 如果root节点为空, 则新建一个节点给root else { ///> 如果只有一个颜色为black的root节点, 则不需要整理 m_root = new RBNode(m_Nil, m_Nil, m_Nil, keyVal, black); m_size++; } } ///> 插入一个红结点会破坏性质2(根结点为空的情况下) ///> 或者性质4(根结点不为空的情况下) void RBTree::_InsertFixedUp(RBNode* pNode) { ///> 如果满足父节点为红色. 则继续循环直到满足5条性质 while(pNode->pParent->color == red) { RBNode* pNodeParent = pNode->pParent; RBNode* pNodePaBro; ///> 得到叔父节点, 赋值给pNodePaBro. if(pNodeParent->pParent->pLeft == pNodeParent) { pNodePaBro = pNodeParent->pParent->pRight; } else { pNodePaBro = pNodeParent->pParent->pLeft; } ///> 父节点和叔父节点都是红色,(父节点为红在while循环里判断了) ///> 全部赋值为黑. 并且祖父节点赋值为红. ///> 这样符合性质4, 性质5. if(pNodePaBro->color == red) { pNodeParent->color = black; pNodePaBro->color = black; pNodeParent->pParent->color = red; ///> 将pNode节点赋值为它的祖父节点 pNode = pNode->pParent->pParent; pNode = pNodeParent->pParent; } ///> 当前父节点是祖父节点的左子节点, ///> 节点的父节点是红色,叔叔节点是黑色, ///> 当前节点是其父节点的左子节点 ///> 解法:父节点变为黑色,祖父节点变为红色,以祖父节点为支点右旋. else if(pNodeParent->pParent->pLeft == pNodeParent && pNodeParent->pLeft == pNode ) { pNodeParent->color = black; pNodeParent->pParent->color = red; _RightRotate(pNode->pParent->pParent); break; } ///> 当前父节点是祖父节点的左子节点, ///> 节点的父节点是红色,叔叔节点是黑色, ///> 当前节点是其父节点的左子节点 ///> 解法:当前节点的父节点做为新的当前节点,以新当前节点为支点左旋. else if(pNodeParent->pParent->pLeft == pNodeParent && pNodeParent->pRight == pNode ) { pNode = pNode->pParent; _LeftRotate(pNode); } ///> 当前父节点是祖父节点的右子节点, ///> 节点的父节点是红色,叔叔节点是黑色, ///> 当前节点是其父节点的左子节点 ///> 解法:当前节点的父节点做为新的当前节点,以新当前节点为支点右旋. else if(pNodeParent->pParent->pRight == pNodeParent && pNodeParent->pLeft == pNode ) { pNode = pNode->pParent; _RightRotate(pNode); } ///> 当前父节点是祖父节点的右子节点, ///> 节点的父节点是红色,叔叔节点是黑色, ///> 当前节点是其父节点的右子节点 ///> 解法:当前节点的父节点做为新的当前节点,以祖父节点为支点左旋. else { pNodeParent->color = black; pNodeParent->pParent->color = red; _LeftRotate(pNode->pParent->pParent); break; } }///> while(pNode->pParent->color == red) ///> 性质2: 根节点必须为黑色 m_root->color = black; } ///> _InsertFixedUp2和上面的_InsertFixedUp运算结果一样的, 虽然代码不一样 void RBTree::_InsertFixedUp2(RBNode* pNode) { RBNode* pUncleNode = m_Nil; ///> 如果满足父节点为红色. 则继续循环直到满足5条性质 while(pNode->pParent->color == red) { if(pNode->pParent == pNode->pParent->pParent->pLeft) { pUncleNode = pNode->pParent->pParent->pRight; ///> 父节点和叔父节点都是红色,(父节点为红在while循环里判断了) d001 ///> 全部赋值为黑. 并且祖父节点赋值为红. ///> 这样符合性质4, 性质5. if(pUncleNode->color == red) { pUncleNode->color = black; pNode->pParent->pParent->color = red; ///> 将pNode节点赋值为它的祖父节点来上移节点以 ///> 从下到上整理使树满足红黑性质 pNode = pNode->pParent->pParent; } ///> 如果叔父节点为黑色 else { ///> 如果node是右孩子, 且父节点为红色 ///> 叔父节点为黑色, 那么进行左旋(左旋是什么我就不多说了) if(pNode == pNode->pParent->pRight) { pNode = pNode->pParent; _LeftRotate(pNode); } ///> 把原本是红色的父节点变为黑色, 祖父节点变为红色 ///> 然后以祖父节点右旋 else { pNode->pParent->color = black; pNode->pParent->pParent->color = red; _RightRotate(pNode->pParent->pParent); } } } else if(pNode->pParent == pNode->pParent->pParent->pRight) { pUncleNode = pNode->pParent->pParent->pLeft; ///> 父节点和叔父节点都是红色,(父节点为红在while循环里判断了) ///> 全部赋值为黑. 并且祖父节点赋值为红. ///> 这样符合性质4, 性质5. if(pUncleNode->color == red) { pNode->pParent->color = black; pUncleNode->color = black; pUncleNode->pParent->color = red; ///> 将pNode节点赋值为它的祖父节点来上移节点以 ///> 从下到上整理使树满足红黑性质 pNode = pNode->pParent->pParent; } else if(pUncleNode->color == black) { if(pNode == pNode->pParent->pLeft) { pNode = pNode->pParent; _RightRotate(pNode); } else { ///> 不解释, 除了旋转什么都没变 (●′ω`●) pNode->pParent->color = black; pNode->pParent->pParent->color = red; _LeftRotate(pNode->pParent->pParent); } } } } ///> 红黑树第二条性质, 不解释~亲 m_root->color = black; } bool RBTree::DeleteNode(int keyVal) { ///> 前大部分是普通的二叉树删除, 删除后, ///> 会进行红黑整理来维持红黑树性质 RBNode* pSubstitute = m_Nil; RBNode* pNodeDel = m_Nil; RBNode* pNode = _SearchNode(keyVal); if(pNode == m_Nil) { return false; } ///> 如果要删除的节点没有2个孩子 if(pNode->pLeft == m_Nil || pNode->pRight == m_Nil) { pNodeDel = pNode; } else { ///> 如果要删除的节点有2个孩子 ///> 那么得到node的后继, 把要后继的val ///> 赋给要被删节点的val, 然后把node删掉, ///> node的孩子则成为node父亲的孩子 pNodeDel = _SuccessorNode(pNode); } ///> 哪一端的孩子有效, 则让那孩子代替被删除的节点 if(pNodeDel->pLeft != m_Nil) { pSubstitute = pNodeDel->pLeft; } else { pSubstitute = pNodeDel->pRight; } ///> 将pSubstitute的parent指针指向将被删除的节点的parent指针 pSubstitute->pParent = pNodeDel->pParent; ///> 如果为空, 那么删除后肯定就只有一颗光秃秃的树根, ///> 那么就直接让root为node if(pNodeDel->pParent == m_Nil) { delete m_root; m_root = pSubstitute; } ///> 用左孩子代替被删节点 else if(pNodeDel == pNodeDel->pParent->pLeft) { pNodeDel->pParent->pLeft = pSubstitute; } ///> 用右孩子代替被删节点 else { pNodeDel->pParent->pRight = pSubstitute; } ///> 如果pNodeDel不等于pNode, 则说明要被删除的节点有两个孩子 ///> 把要后继的val赋给要被删节点的val(前面注释中有说过) if(pNodeDel != pNode) { pNode->val = pNodeDel->val; } ///> 如果被删节点为黑色, 则破坏了性质5, 要FixUp if(pNodeDel->color == black) { _DelFixedUp(pNode); } delete pNodeDel; pNodeDel = NULL; m_size--; return true; } void RBTree::_DelFixedUp(RBNode* pNode) { RBNode* pBroNode; ///> 如果pNode不为root, 并且为黑色, 则破坏了性质5 while(pNode != m_root && pNode->color == black) { ///> 如果位于左边, ///> 兄弟节点则为它的父节点的右孩子 if(pNode->pParent->pLeft == pNode) { pBroNode = pNode->pParent->pRight; ///> 如果兄弟节点为红色, ///> 则把兄弟节点改为黑色, ///> 父节点改为红色, 来维持性质5 if(pBroNode->color == red) { pBroNode->color = black; pNode->pParent->color = red; _LeftRotate(pNode->pParent); } ///> 如果兄弟节点为黑色···↓ else { ///>··且兄弟节点的左右孩子都为黑色 ///>··则要把兄弟节点改为红色来维持性质4,5 if(pBroNode->pLeft->color == black && pBroNode->pRight->color == black ) { pBroNode->color = red; ///> node沿树上移. 下次循环时整理上面的节点 pNode = pNode->pParent; } ///>··否则如果只有兄弟的右孩子为黑色, ///>··则要把兄弟节点改为红色, ///>··则还要把左孩子改为黑色, 来维持性质4,5 else if(pBroNode->pRight->color == black) { pBroNode->color = red; pBroNode->pLeft->color = black; _RightRotate(pBroNode); } ///>··兄弟节点是黑色, 右孩子为红色, ///>··左孩子有可能是红也可能是黑, ///>··则把兄弟节点的颜色改为父节点的颜色 ///>··父节点则改为黑, 这样就平衡了而不违反性质4 else if(pBroNode->pRight->color == red) { pBroNode->color = pBroNode->pParent->color; pBroNode->pParent->color = black; pBroNode->pRight->color = black; _LeftRotate(pBroNode->pParent); pNode = m_root; } } } ///> 否则如果位于右边, ///> 兄弟节点则为它的父节点的左孩子 ///> 跟上面的相反, 就不多做注释了 else if(pNode->pParent->pRight == pNode) { pBroNode = pNode->pParent->pLeft; if(pBroNode->color == red) { pBroNode->color = black; pNode->pParent->color = red; _RightRotate(pNode->pParent); } else { if(pBroNode->pLeft->color == black && pBroNode->pRight->color == black ) { pBroNode->color = red; pNode = pNode->pParent; } else if(pBroNode->pLeft->color == black) { pBroNode->color = red; pBroNode->pRight->color = black; _LeftRotate(pBroNode); } else if(pBroNode->pLeft->color == red) { pBroNode->color = pBroNode->pParent->color; pBroNode->pParent->color = black; pBroNode->pLeft->color = black; _RightRotate(pBroNode->pParent); pNode = m_root; } } } m_Nil->pParent = m_root; } pNode->color = black; } void RBTree::DisplayTree() { _DisplayTree(m_root); } ///> 中序遍历, 递增输出 void RBTree::_DisplayTree(RBNode* pNode) { if(pNode == m_Nil) { return; } _DisplayTree(pNode->pLeft); std::cout<<"node val: "<<pNode->val; if(!pNode->color) { std::cout<<"\tcolor: black"<<std::endl; } else { std::cout<<"\tcolor: red"<<std::endl; } if(pNode->pLeft != m_Nil) { std::cout<<"\tleft node val: "<<pNode->pLeft->val; } else { std::cout<<"\tleft node is Nil"; } if(!pNode->pLeft->color) { std::cout<<"\tcolor: black"<<std::endl; } else { std::cout<<"\tcolor: red"<<std::endl; } if(pNode->pRight != m_Nil) { std::cout<<"\tRight node val: "<<pNode->pLeft->val; } else { std::cout<<"\tRight node is Nil"; } if(!pNode->pRight->color) { std::cout<<"\tcolor: black"<<std::endl; } else { std::cout<<"\tcolor: red"<<std::endl; } if(pNode->pParent != m_Nil) { std::cout<<"\tparent node val: "<<pNode->pLeft->val; } else { std::cout<<"\tparent node is Nil"; } if(!pNode->pParent->color) { std::cout<<"\tcolor: black"<<std::endl; } else { std::cout<<"\tcolor: red"<<std::endl; } std::cout<<std::endl<<std::endl; _DisplayTree(pNode->pRight); } int RBTree::GetSize() { return m_size; } int main() { RBTree* rbTree = new RBTree; srand(time(0)); for(int i = 0; i < 100; ++i) { rbTree->Insert(rand()% 1000); } rbTree->DisplayTree(); std::cout<<rbTree->GetSize(); getchar(); return 0; }
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