846 lines
24 KiB
C++
846 lines
24 KiB
C++
#pragma once
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#include <iostream>
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#include <vector>
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#include <stack>
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#include <queue>
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namespace Lenyiin
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{
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enum Colour
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{
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RED,
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BLACK
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};
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template <class K, class V>
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struct RBTreeNode
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{
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RBTreeNode<K, V>* _left;
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RBTreeNode<K, V>* _right;
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RBTreeNode<K, V>* _parent;
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std::pair<K, V> _kv;
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Colour _colour;
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RBTreeNode(const std::pair<K, V>& kv)
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: _left(nullptr), _right(nullptr), _parent(nullptr), _kv(kv), _colour(RED)
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{
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}
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};
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template <class K, class V>
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class RBTree
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{
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private:
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typedef RBTreeNode<K, V> Node;
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// 左单旋
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void RotateL(Node* parent)
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{
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Node* ppNode = parent->_parent;
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Node* subR = parent->_right;
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Node* subRL = subR->_left;
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parent->_right = subRL;
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if (subRL)
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{
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subRL->_parent = parent;
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}
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subR->_left = parent;
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parent->_parent = subR;
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// 1. 原来 parent 是这棵树的根, 现在 subR 是根
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if (parent == _root)
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{
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_root = subR;
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subR->_parent = nullptr;
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}
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// 2. parent 为根的树只是整棵树中的子树, 改变链接关系, 那么 subR 要顶替他的位置
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else
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{
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if (ppNode->_left == parent)
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{
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ppNode->_left = subR;
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}
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else
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{
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ppNode->_right = subR;
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}
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subR->_parent = ppNode;
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}
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}
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// 右单旋
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void RotateR(Node* parent)
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{
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Node* ppNode = parent->_parent;
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Node* subL = parent->_left;
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Node* subLR = subL->_right;
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parent->_left = subLR;
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if (subLR)
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{
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subLR->_parent = parent;
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}
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subL->_right = parent;
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parent->_parent = subL;
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if (parent == _root)
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{
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_root = subL;
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subL->_parent = nullptr;
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}
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else
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{
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if (ppNode->_left == parent)
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{
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ppNode->_left = subL;
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}
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else
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{
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ppNode->_right = subL;
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}
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subL->_parent = ppNode;
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}
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}
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// 删除整个红黑树
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void DeleteTree(Node* root)
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{
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if (root == nullptr)
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{
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return;
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}
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// 递归删除左子树
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DeleteTree(root->_left);
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// 递归删除右子树
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DeleteTree(root->_right);
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// 删除当前节点
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delete root;
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}
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public:
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RBTree(Node* root = nullptr)
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: _root(root)
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{
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}
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~RBTree()
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{
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DeleteTree(_root);
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}
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// 1. 空树。插入结点做根,把他变黑。
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// 2. 插入红色节点,他的父亲是黑色的,结束。
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// 3. 插入红色节点,他的父亲是红色的,可以推断他的祖父存在且一定为黑色。关键看叔叔
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// a. 如果叔叔存在且为红,把父亲和叔叔变黑,祖父变红,继续往上处理。
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// b. 如果叔叔存在且为黑,或者不存在。旋转(单旋 or 双旋)+ 变色
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bool Insert(const std::pair<K, V>& kv)
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{
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// 1. 按照搜索树的规则进行插入
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// 如果树为空,直接将新节点设为根节点,并染成黑色
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if (_root == nullptr)
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{
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_root = new Node(kv);
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_root->_colour = BLACK; // 根节点是黑色的
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return true;
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}
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// 遍历树找到插入位置
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Node* parent = nullptr;
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Node* cur = _root;
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while (cur)
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{
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if (cur->_kv.first > kv.first)
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{
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parent = cur;
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cur = cur->_left;
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}
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else if (cur->_kv.first < kv.first)
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{
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parent = cur;
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cur = cur->_right;
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}
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else
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{
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return false; // 待插入的节点已经存在
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}
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}
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// 找到位置 插入新节点
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cur = new Node(kv);
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if (parent->_kv.first > kv.first)
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{
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parent->_left = cur;
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cur->_parent = parent;
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}
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else
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{
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parent->_right = cur;
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cur->_parent = parent;
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}
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// 插入调整
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InsertFixUp(parent, cur);
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return true;
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}
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void InsertFixUp(Node* parent, Node* cur)
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{
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// 调整结点颜色
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// 新结点给红的还是黑的? 红色
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// 1. 空树。插入结点做根, 把他变黑。
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// 2. 插入红色节点, 他的父亲是黑色的, 结束。
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// 3. 插入红色节点, 他的父亲是红色的, 可以推断他的祖父存在且一定为黑色。关键看叔叔
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// a. 如果叔叔存在且为红, 把父亲和叔叔变黑, 祖父变红, 继续往上处理。
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// b. 如果叔叔存在且为黑, 或者不存在。旋转(单旋 or 双旋)+ 变色
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while (parent && parent->_colour == RED)
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{
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// 关键看叔叔
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Node* grandfather = parent->_parent;
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if (grandfather->_left == parent)
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{
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Node* uncle = grandfather->_right;
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// 情况1: uncle 存在, 且为红
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if (uncle && uncle->_colour == RED)
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{
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parent->_colour = uncle->_colour = BLACK;
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grandfather->_colour = RED;
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// 继续向上调整
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cur = grandfather;
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parent = cur->_parent;
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}
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// 情况 2 or 情况 3 : uncle 不存在 or uncle 存在且为黑
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else
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{
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// 情况 3: 双旋 -> 变成单旋
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if (cur == parent->_right)
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{
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RotateL(parent);
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std::swap(parent, cur);
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}
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// 第二种情况 (ps: 有可能是第三种情况变过来的)
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RotateR(grandfather);
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grandfather->_colour = RED;
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parent->_colour = BLACK;
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break;
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}
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}
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else
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{
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Node* uncle = grandfather->_left;
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// 情况1: uncle 存在, 且为红
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if (uncle && uncle->_colour == RED)
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{
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parent->_colour = BLACK;
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uncle->_colour = BLACK;
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grandfather->_colour = RED;
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// 继续向上调整
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cur = grandfather;
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parent = cur->_parent;
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}
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// 情况2 or 情况3: uncle 不存在 or uncle 存在且为黑
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else
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{
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// 情况3: 双旋 -> 变为单旋
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if (cur == parent->_left)
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{
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RotateR(parent);
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std::swap(parent, cur);
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}
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// 第二种情况 (ps: 有可能是第三种情况变来的)
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RotateL(grandfather);
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grandfather->_colour = RED;
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parent->_colour = BLACK;
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break;
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}
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}
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}
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// 保证根节点为黑色
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_root->_colour = BLACK;
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}
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// 删除操作
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bool Erase(const K& key)
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{
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// 查找节点
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Node* nodeToDelete = _root;
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while (nodeToDelete)
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{
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if (nodeToDelete->_kv.first > key)
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{
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nodeToDelete = nodeToDelete->_left;
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}
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else if (nodeToDelete->_kv.first < key)
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{
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nodeToDelete = nodeToDelete->_right;
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}
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else
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{
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break; // 找到待删除的节点
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}
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}
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// 如果未找到节点
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if (nodeToDelete == nullptr)
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{
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return false;
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}
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// 执行删除操作
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Node* parent, * child;
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Colour originalColour = nodeToDelete->_colour;
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if (nodeToDelete->_left == nullptr)
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{
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child = nodeToDelete->_right;
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parent = nodeToDelete->_parent;
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Transplant(nodeToDelete, nodeToDelete->_right);
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}
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else if (nodeToDelete->_right == nullptr)
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{
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child = nodeToDelete->_left;
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parent = nodeToDelete->_parent;
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Transplant(nodeToDelete, nodeToDelete->_left);
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}
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else
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{
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Node* successor = Minimum(nodeToDelete->_right);
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originalColour = successor->_colour;
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child = successor->_right;
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if (successor->_parent == nodeToDelete)
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{
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parent = successor;
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}
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else
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{
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Transplant(successor, successor->_right);
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successor->_right = nodeToDelete->_right;
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successor->_right->_parent = successor;
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parent = successor->_parent;
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}
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Transplant(nodeToDelete, successor);
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successor->_left = nodeToDelete->_left;
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successor->_left->_parent = successor;
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successor->_colour = nodeToDelete->_colour;
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}
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delete nodeToDelete;
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// 如果删除的节点是黑色,需要进行调整
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if (originalColour == BLACK)
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{
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EraseFixUp(child, parent);
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}
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return true;
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}
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void EraseFixUp(Node* x, Node* parent)
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{
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while (x != _root && (x == nullptr || x->_colour == BLACK))
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{
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if (x == parent->_left)
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{
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Node* w = parent->_right;
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// 情况1: x的兄弟节点w是红色的
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if (w->_colour == RED)
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{
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w->_colour = BLACK;
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parent->_colour = RED;
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RotateL(parent);
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w = parent->_right;
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}
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// 情况2: x的兄弟节点w是黑色的,且w的两个子节点都是黑色的
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if ((w->_left == nullptr || w->_left->_colour == BLACK) &&
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(w->_right == nullptr || w->_right->_colour == BLACK))
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{
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w->_colour = RED;
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x = parent;
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parent = x->_parent;
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}
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else
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{
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// 情况3: w是黑色的,并且w的左子节点是红色,右子节点是黑色
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if (w->_right == nullptr || w->_right->_colour == BLACK)
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{
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if (w->_left)
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w->_left->_colour = BLACK;
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w->_colour = RED;
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RotateR(w);
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w = parent->_right;
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}
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// 情况4: w是黑色的,并且w的右子节点是红色
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if (w)
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{
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w->_colour = parent->_colour;
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parent->_colour = BLACK;
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if (w->_right)
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w->_right->_colour = BLACK;
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RotateL(parent);
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}
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x = _root;
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break;
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}
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}
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else
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{
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Node* w = parent->_left;
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// 情况1: x的兄弟节点w是红色的
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if (w->_colour == RED)
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{
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w->_colour = BLACK;
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parent->_colour = RED;
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RotateR(parent);
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w = parent->_left;
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}
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// 情况2: x的兄弟节点w是黑色的,且w的两个子节点都是黑色的
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if ((w->_left == nullptr || w->_left->_colour == BLACK) &&
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(w->_right == nullptr || w->_right->_colour == BLACK))
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{
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w->_colour = RED;
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x = parent;
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parent = x->_parent;
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}
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else
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{
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// 情况3: w是黑色的,并且w的右子节点是红色,左子节点是黑色
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if (w->_left == nullptr || w->_left->_colour == BLACK)
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{
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if (w->_right)
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{
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w->_right->_colour = BLACK;
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}
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w->_colour = RED;
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RotateL(w);
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w = parent->_left;
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}
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// 情况4: w是黑色的,并且w的左子节点是红色
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if (w)
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{
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w->_colour = parent->_colour;
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parent->_colour = BLACK;
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if (w->_left)
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{
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w->_left->_colour = BLACK;
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}
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RotateR(parent);
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}
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x = _root;
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break;
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}
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}
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}
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if (x)
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{
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x->_colour = BLACK;
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}
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}
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Node* Minimum(Node* node)
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{
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while (node->_left != nullptr)
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{
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node = node->_left;
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}
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return node;
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}
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void Transplant(Node* u, Node* v)
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{
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if (u->_parent == nullptr)
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{
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_root = v;
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}
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else if (u == u->_parent->_left)
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{
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u->_parent->_left = v;
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}
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else
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{
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u->_parent->_right = v;
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}
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if (v != nullptr)
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{
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v->_parent = u->_parent;
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}
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}
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// 查找节点
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Node* Find(const K& key)
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{
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Node* cur = _root;
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while (cur)
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{
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if (cur->_kv.first > key)
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{
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cur = cur->_left;
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}
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else if (cur->_kv.first < key)
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{
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cur = cur->_right;
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}
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else
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{
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return cur;
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}
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}
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return nullptr;
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}
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// 前序遍历的递归实现
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// 辅助函数
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// void _PreOrder(Node *root)
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// {
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// if (root == nullptr)
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// {
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// return;
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// }
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// // 访问根节点
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// std::cout << root->_kv.first << " (" << (root->_colour == RED ? "RED" : "BLACK") << ") ";
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// _PreOrder(root->_left); // 访问左子树
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// _PreOrder(root->_right); // 访问右子树
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// }
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// void PreOrder()
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// {
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// std::cout << "前序遍历: ";
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// _PreOrder(_root);
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// std::cout << std::endl;
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// }
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// 前序遍历的非递归实现
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void PreOrder()
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{
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if (_root == nullptr)
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{
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return;
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}
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std::stack<Node*> stack;
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stack.push(_root);
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std::cout << "前序遍历: ";
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while (!stack.empty())
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{
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Node* cur = stack.top();
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stack.pop();
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// 访问根节点
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std::cout << cur->_kv.first << " (" << (cur->_colour == RED ? "RED" : "BLACK") << ") ";
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// 先压入右子树再压入左子树(确保左子树先处理)
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if (cur->_right != nullptr)
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{
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stack.push(cur->_right);
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}
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if (cur->_left != nullptr)
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{
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stack.push(cur->_left);
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}
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}
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std::cout << std::endl;
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}
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// 中序遍历
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// void _InOrder(Node *root)
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// {
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// if (root == nullptr)
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// {
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// return;
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// }
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// _InOrder(root->_left);
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// // 访问根节点
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// std::cout << root->_kv.first << " (" << (root->_colour == RED ? "RED" : "BLACK") << ") ";
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// _InOrder(root->_right);
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||
// }
|
||
|
||
// void InOrder()
|
||
// {
|
||
// std::cout << "中序遍历: ";
|
||
// _InOrder(_root);
|
||
// std::cout << std::endl;
|
||
// }
|
||
|
||
// 中序遍历 非递归
|
||
void InOrder()
|
||
{
|
||
std::stack<Node*> stack;
|
||
Node* cur = _root;
|
||
|
||
std::cout << "中序遍历: ";
|
||
while (cur != nullptr || !stack.empty())
|
||
{
|
||
// 找到最左边的节点
|
||
while (cur != nullptr)
|
||
{
|
||
stack.push(cur);
|
||
cur = cur->_left;
|
||
}
|
||
|
||
// 处理当前节点
|
||
cur = stack.top();
|
||
stack.pop();
|
||
// 访问根节点
|
||
std::cout << cur->_kv.first << " (" << (cur->_colour == RED ? "RED" : "BLACK") << ") ";
|
||
|
||
// 转向右子树
|
||
cur = cur->_right;
|
||
}
|
||
std::cout << std::endl;
|
||
}
|
||
|
||
// 后序遍历的递归实现
|
||
// 辅助函数
|
||
// void _PostOrder(Node *root)
|
||
// {
|
||
// if (root == nullptr)
|
||
// {
|
||
// return;
|
||
// }
|
||
|
||
// _PostOrder(root->_left); // 访问左子树
|
||
// _PostOrder(root->_right); // 访问右子树
|
||
// // 访问根节点
|
||
// std::cout << root->_kv.first << " (" << (root->_colour == RED ? "RED" : "BLACK") << ") ";
|
||
// }
|
||
|
||
// void PostOrder()
|
||
// {
|
||
// std::cout << "后序遍历: ";
|
||
// _PostOrder(_root);
|
||
// std::cout << std::endl;
|
||
// }
|
||
|
||
// 后序遍历的非递归实现
|
||
void PostOrder()
|
||
{
|
||
if (_root == nullptr)
|
||
{
|
||
return;
|
||
}
|
||
|
||
std::stack<Node*> st;
|
||
Node* cur = _root;
|
||
Node* lastNode = nullptr; // 最近访问的节点
|
||
std::cout << "后序遍历: ";
|
||
while (cur || !st.empty())
|
||
{
|
||
while (cur)
|
||
{
|
||
st.push(cur);
|
||
cur = cur->_left;
|
||
}
|
||
|
||
Node* top = st.top();
|
||
if ((top->_right == nullptr) || (lastNode == top->_right))
|
||
{
|
||
// 访问当前节点
|
||
std::cout << top->_kv.first << " (" << (top->_colour == RED ? "RED" : "BLACK") << ") ";
|
||
lastNode = top;
|
||
st.pop();
|
||
}
|
||
else
|
||
{
|
||
cur = top->_right;
|
||
}
|
||
}
|
||
std::cout << std::endl;
|
||
}
|
||
|
||
// 层序遍历
|
||
void LevelOrder()
|
||
{
|
||
if (_root == nullptr)
|
||
{
|
||
return;
|
||
}
|
||
|
||
std::queue<Node*> queue;
|
||
queue.push(_root);
|
||
|
||
std::cout << "层序遍历: " << std::endl;
|
||
while (!queue.empty())
|
||
{
|
||
int size = queue.size();
|
||
while (size--)
|
||
{
|
||
Node* cur = queue.front();
|
||
queue.pop();
|
||
// 访问当前节点
|
||
std::cout << cur->_kv.first << " (" << (cur->_colour == RED ? "RED" : "BLACK") << ") ";
|
||
|
||
if (cur->_left != nullptr)
|
||
{
|
||
queue.push(cur->_left); // 将左子树压入队列
|
||
}
|
||
if (cur->_right != nullptr)
|
||
{
|
||
queue.push(cur->_right); // 将右子树压入队列
|
||
}
|
||
}
|
||
std::cout << std::endl;
|
||
}
|
||
std::cout << std::endl;
|
||
}
|
||
|
||
// 查找后继节点
|
||
Node* findMin(Node* node)
|
||
{
|
||
while (node->_left != nullptr)
|
||
{
|
||
node = node->_left;
|
||
}
|
||
return node;
|
||
}
|
||
|
||
Node* FindSuccessor(Node* node)
|
||
{
|
||
if (node->_right != nullptr)
|
||
{
|
||
return findMin(node->_right);
|
||
}
|
||
|
||
Node* cur = _root;
|
||
Node* successor = nullptr;
|
||
while (cur != nullptr)
|
||
{
|
||
if (node->_kv.first < cur->_kv.first)
|
||
{
|
||
successor = cur;
|
||
cur = cur->_left;
|
||
}
|
||
else if (node->_kv.first > cur->_kv.first)
|
||
{
|
||
cur = cur->_right;
|
||
}
|
||
else
|
||
{
|
||
break;
|
||
}
|
||
}
|
||
return successor;
|
||
}
|
||
|
||
// 查找前驱节点
|
||
Node* findMax(Node* node)
|
||
{
|
||
while (node->_right != nullptr)
|
||
{
|
||
node = node->_right;
|
||
}
|
||
return node;
|
||
}
|
||
|
||
Node* FindPredecessor(Node* node)
|
||
{
|
||
if (node->_left != nullptr)
|
||
{
|
||
return findMax(node->_left);
|
||
}
|
||
|
||
Node* cur = _root;
|
||
Node* predecessor = nullptr;
|
||
while (cur != nullptr)
|
||
{
|
||
if (node->_kv.first < cur->_kv.first)
|
||
{
|
||
cur = cur->_left;
|
||
}
|
||
else if (node->_kv.first > cur->_kv.first)
|
||
{
|
||
predecessor = cur;
|
||
cur = cur->_right;
|
||
}
|
||
else
|
||
{
|
||
break;
|
||
}
|
||
}
|
||
return predecessor;
|
||
}
|
||
|
||
// 判断是否是红黑树
|
||
bool IsRBTree()
|
||
{
|
||
// 空树也是红黑树
|
||
if (_root == nullptr)
|
||
{
|
||
return true;
|
||
}
|
||
|
||
// 1. 根是黑色
|
||
if (_root->_colour != BLACK)
|
||
{
|
||
std::cout << "根节点不是黑色" << std::endl;
|
||
return false;
|
||
}
|
||
|
||
// 获取任意一条路径上黑色节点的数量
|
||
size_t blackCount = 0;
|
||
Node* cur = _root;
|
||
while (cur)
|
||
{
|
||
if (cur->_colour == BLACK)
|
||
{
|
||
blackCount++;
|
||
}
|
||
cur = cur->_left;
|
||
}
|
||
|
||
// 判断是否满足红黑树的性质, k 用来记录路径中黑色节点的个数
|
||
size_t k = 0;
|
||
return _IsRBTree(_root, k, blackCount);
|
||
}
|
||
|
||
bool _IsRBTree(Node* root, size_t k, size_t blackCount)
|
||
{
|
||
// 走到 nullptr 之后, 判断 k 和 blackCount 是否相等
|
||
if (root == nullptr)
|
||
{
|
||
// 最终黑色节点个数
|
||
if (blackCount != k)
|
||
{
|
||
std::cout << "违反性质四: 每条路径中黑色节点的个数必须相等" << std::endl;
|
||
return false;
|
||
}
|
||
return true;
|
||
}
|
||
|
||
// 统计黑色节点个数
|
||
if (root->_colour == BLACK)
|
||
{
|
||
k++;
|
||
}
|
||
|
||
// 检测当前节点与其父亲节点是否都为红色
|
||
Node* parent = root->_parent;
|
||
if (parent && parent->_colour == RED && root->_colour == RED)
|
||
{
|
||
std::cout << "违反了性质三: 红色节点的孩子必须是黑色" << std::endl;
|
||
return false;
|
||
}
|
||
|
||
return _IsRBTree(root->_left, k, blackCount) && _IsRBTree(root->_right, k, blackCount);
|
||
}
|
||
|
||
private:
|
||
Node* _root;
|
||
};
|
||
} |