当前位置：首页 > news >正文

手把手实现红黑树Set和Map

news 2026/3/27 4:09:17

好的，我们来手把手实现一个简化版的红黑树（RB-Tree），并基于此封装Set和Map容器。整个过程会分为几个步骤：

步骤1: 红黑树基础

红黑树是一种自平衡二叉搜索树，满足以下性质：

每个节点是红色或黑色
根节点是黑色
叶子节点（NIL节点）是黑色
红色节点的子节点必须是黑色（不能有连续红色节点）
从任一节点到其叶子节点的路径包含相同数量的黑色节点

步骤2: 节点结构设计

enum Color { RED, BLACK }; template<typename T> struct RBTreeNode { T data; // 节点存储的数据 Color color; RBTreeNode* parent; RBTreeNode* left; RBTreeNode* right; RBTreeNode(T val, Color c = RED) : data(val), color(c), parent(nullptr), left(nullptr), right(nullptr) {} };

http://my.tv.sohu.com/us/441548290/698245990.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NTk5MC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247253.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzI1My5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247332.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzMzMi5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247513.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzUxMy5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247336.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzMzNi5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247340.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzM0MC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247343.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzM0My5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247424.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzQyNC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247349.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzM0OS5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247351.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzM1MS5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247534.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzUzNC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247537.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzUzNy5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247286.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzI4Ni5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247443.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzQ0My5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247451.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzQ1MS5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247454.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzQ1NC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247557.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzU1Ny5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247567.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzU2Ny5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247608.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzYwOC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247387.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzM4Ny5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247624.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzYyNC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247593.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzU5My5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247486.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzQ4Ni5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247600.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzYwMC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247646.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzY0Ni5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247916.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzkxNi5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247921.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzkyMS5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247500.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzUwMC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247929.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzkyOS5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247931.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzkzMS5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247736.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0NzczNi5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247992.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0Nzk5Mi5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698247997.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0Nzk5Ny5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248025.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODAyNS5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248105.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODEwNS5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248216.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODIxNi5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248234.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODIzNC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248316.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODMxNi5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248068.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODA2OC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248246.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODI0Ni5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248254.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODI1NC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248333.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODMzMy5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248085.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODA4NS5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248262.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODI2Mi5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248164.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODE2NC5zaHRtbA==.html
http://my.tv.sohu.com/us/441548290/698248339.shtml
https://tv.sohu.com/v/dXMvNDQxNTQ4MjkwLzY5ODI0ODMzOS5zaHRtbA==.html

步骤3: 核心操作实现

3.1 左旋（Left Rotate）

template<typename T> void RBTree<T>::leftRotate(RBTreeNode<T>* x) { RBTreeNode<T>* y = x->right; x->right = y->left; if (y->left) y->left->parent = x; y->parent = x->parent; if (!x->parent) root = y; else if (x == x->parent->left) x->parent->left = y; else x->parent->right = y; y->left = x; x->parent = y; }

3.2 右旋（Right Rotate）

template<typename T> void RBTree<T>::rightRotate(RBTreeNode<T>* y) { RBTreeNode<T>* x = y->left; y->left = x->right; if (x->right) x->right->parent = y; x->parent = y->parent; if (!y->parent) root = x; else if (y == y->parent->left) y->parent->left = x; else y->parent->right = x; x->right = y; y->parent = x; }

步骤4: 插入修复（Fixup）

插入后可能破坏红黑树性质，需通过颜色翻转和旋转修复：

template<typename T> void RBTree<T>::insertFixup(RBTreeNode<T>* z) { while (z->parent && z->parent->color == RED) { if (z->parent == z->parent->parent->left) { RBTreeNode<T>* uncle = z->parent->parent->right; if (uncle && uncle->color == RED) { // Case 1: 叔节点为红 z->parent->color = BLACK; uncle->color = BLACK; z->parent->parent->color = RED; z = z->parent->parent; } else { if (z == z->parent->right) { // Case 2: 三角型 z = z->parent; leftRotate(z); } // Case 3: 直线型 z->parent->color = BLACK; z->parent->parent->color = RED; rightRotate(z->parent->parent); } } else { // 对称操作（略） } } root->color = BLACK; // 根节点始终为黑 }

步骤5: 封装Set容器

template<typename Key> class Set { private: RBTree<Key> tree; // 红黑树实例 public: void insert(const Key& key) { tree.insert(key); } bool contains(const Key& key) { return tree.find(key) != nullptr; } // 迭代器、删除等操作（略） };

步骤6: 封装Map容器

通过存储键值对实现：

template<typename Key, typename Value> class Map { private: struct MapNode { Key key; Value value; bool operator<(const MapNode& other) const { return key < other.key; } }; RBTree<MapNode> tree; // 存储键值对 public: void insert(const Key& key, const Value& val) { tree.insert({key, val}); } Value& operator[](const Key& key) { auto node = tree.find({key, Value()}); if (!node) { insert(key, Value()); node = tree.find({key, Value()}); } return node->data.value; } };