C++ 基于红黑树封装 map 与 set 详解

同时需要在迭代器类中添加接受普通迭代器的构造函数，以完成隐式转换。

三、Map 的 operator[] 实现

有了上述基础，Map 的 operator[] 实现就很简单了：

V& operator[](const K& key) {
    // 尝试插入 key-value，value 默值构造
    pair<iterator, bool> ret = insert(make_pair(key, V()));
    // 返回 value 的引用
    return ret.first->second;
}

测试代码验证了插入和修改的功能均正常。对于 Set，我们同样验证了迭代器遍历和插入功能，确保 key 无法被修改。

四、完整源码参考

以下是整理后的核心代码结构，包含红黑树、Set 和 Map 的封装。

RBTree.h

#pragma once
#include <iostream>
using namespace std;

enum Colour { RED, BLACK };

template<class T>
struct RBTreeNode {
    RBTreeNode<T>* _left;
    RBTreeNode<T>* _right;
    RBTreeNode<T>* _parent;
    Colour _col;
    T _data;

    RBTreeNode(const T& data) : _left(nullptr), _right(nullptr), _parent(nullptr), _col(RED), _data(data) {}
};

template<class T, class Ptr, class Ref>
struct __TreeIterator {
    typedef RBTreeNode<T> Node;
    typedef __TreeIterator<T, Ptr, Ref> Self;
    
    // 解决 insert 中 set 的问题，提供从普通迭代器到 const 迭代器的转换
    typedef __TreeIterator<T, T*, T&> iterator;

    __TreeIterator(const iterator& it) : _node(it._node) {};
    Node* _node;

    __TreeIterator(Node* node) : _node(node) {}

    Ref operator*() { return _node->_data; }
    Ptr operator->() { return &(_node->_data); }

    bool operator!=(const Self& s) { return _node != s._node; }
    bool operator==(const Self& s) const { return _node == s._node; }

    Self& operator++() {
        if (_node->_right != nullptr) {
            Node* curleft = _node->_right;
            while (curleft->_left) curleft = curleft->_left;
            _node = curleft;
        } else {
            Node* cur = _node;
            Node* parent = _node->_parent;
            while (parent) {
                if (parent->_left == cur) break;
                else { cur = parent; parent = parent->_parent; }
            }
            _node = parent;
        }
        return *this;
    }

    Self& operator--() {
        if (_node->_left) {
            Node* subRight = _node->_left;
            while (subRight->_right) subRight = subRight->_right;
            _node = subRight;
        } else {
            Node* cur = _node;
            Node* parent = cur->_parent;
            while (parent && cur == parent->_left) {
                cur = cur->_parent;
                parent = parent->_parent;
            }
            _node = parent;
        }
        return *this;
    }
};

template<class K, class T, class KeyOfT>
class RBTree {
    typedef RBTreeNode<T> Node;
public:
    typedef __TreeIterator<T, T*, T&> iterator;
    typedef __TreeIterator<T, const T*, const T&> const_iterator;

    iterator begin() {
        Node* leftMin = _root;
        while (leftMin && leftMin->_left) leftMin = leftMin->_left;
        return iterator(leftMin);
    }
    iterator end() { return iterator(nullptr); }

    const_iterator begin() const {
        Node* leftMin = _root;
        while (leftMin && leftMin->_left) leftMin = leftMin->_left;
        return const_iterator(leftMin);
    }
    const_iterator end() const { return const_iterator(nullptr); }

    Node* Find(const K& key) {
        Node* cur = _root;
        KeyOfT kot;
        while (cur) {
            if (kot(cur->_data) < key) cur = cur->_right;
            else if (kot(cur->_data) > key) cur = cur->_left;
            else return cur;
        }
        return nullptr;
    }

    pair<iterator, bool> Insert(const T& data) {
        if (_root == nullptr) {
            _root = new Node(data);
            _root->_col = BLACK;
            return make_pair(iterator(_root), true);
        }
        Node* cur = _root;
        Node* parent = nullptr;
        KeyOfT kot;
        while (cur) {
            if (kot(data) < kot(cur->_data)) {
                parent = cur; cur = cur->_left;
            } else if (kot(data) > kot(cur->_data)) {
                parent = cur; cur = cur->_right;
            } else {
                return make_pair(iterator(cur), false);
            }
        }
        cur = new Node(data);
        cur->_col = RED;
        Node* newnode = cur;
        if (kot(cur->_data) < kot(parent->_data)) parent->_left = cur;
        else parent->_right = cur;
        cur->_parent = parent;

        while (parent && parent->_col == RED) {
            Node* grandfather = parent->_parent;
            if (parent == grandfather->_left) {
                Node* uncle = grandfather->_right;
                if (uncle && uncle->_col == RED) {
                    parent->_col = BLACK;
                    uncle->_col = BLACK;
                    grandfather->_col = RED;
                    cur = grandfather;
                    parent = cur->_parent;
                } else {
                    if (cur == parent->_left) {
                        RotateR(grandfather);
                        parent->_col = BLACK;
                        grandfather->_col = RED;
                    } else {
                        RotateL(parent);
                        RotateR(grandfather);
                        cur->_col = BLACK;
                        grandfather->_col = RED;
                    }
                    break;
                }
            } else {
                Node* uncle = grandfather->_left;
                if (uncle && uncle->_col == RED) {
                    parent->_col = BLACK;
                    uncle->_col = BLACK;
                    grandfather->_col = RED;
                    cur = grandfather;
                    parent = cur->_parent;
                } else {
                    if (cur == parent->_right) {
                        RotateL(grandfather);
                        parent->_col = BLACK;
                        grandfather->_col = RED;
                    } else {
                        RotateR(parent);
                        RotateL(grandfather);
                        cur->_col = BLACK;
                        grandfather->_col = RED;
                    }
                    break;
                }
            }
        }
        _root->_col = BLACK;
        return make_pair(iterator(newnode), true);
    }

    void RotateL(Node* parent) {
        Node* cur = parent->_right;
        Node* curleft = cur->_left;
        parent->_right = curleft;
        if (curleft) curleft->_parent = parent;
        cur->_left = parent;
        Node* ppnode = parent->_parent;
        parent->_parent = cur;
        if (ppnode == nullptr) {
            _root = cur;
            cur->_parent = nullptr;
        } else {
            if (ppnode->_left == parent) ppnode->_left = cur;
            else ppnode->_right = cur;
            cur->_parent = ppnode;
        }
    }

    void RotateR(Node* parent) {
        Node* cur = parent->_left;
        Node* curright = cur->_right;
        parent->_left = curright;
        if (curright) curright->_parent = parent;
        cur->_right = parent;
        Node* ppnode = parent->_parent;
        parent->_parent = cur;
        if (ppnode == nullptr) {
            cur->_parent = nullptr;
            _root = cur;
        } else {
            if (ppnode->_left == parent) ppnode->_left = cur;
            else ppnode->_right = cur;
            cur->_parent = ppnode;
        }
    }

    bool CheckColour(Node* root, int blacknum, int benchmark) {
        if (root == nullptr) {
            if (blacknum != benchmark) return false;
            return true;
        }
        if (root->_col == BLACK) ++blacknum;
        if (root->_col == RED && root->_parent && root->_parent->_col == RED) {
            cout << "出现连续红色节点" << endl;
            return false;
        }
        return CheckColour(root->_left, blacknum, benchmark) && CheckColour(root->_right, blacknum, benchmark);
    }

    bool IsBalance() { return IsBalance(_root); }
    bool IsBalance(Node* root) {
        if (root == nullptr) return true;
        if (root->_col != BLACK) return false;
        int benchmark = 0;
        Node* cur = _root;
        while (cur) {
            if (cur->_col == BLACK) ++benchmark;
            cur = cur->_left;
        }
        return CheckColour(root, 0, benchmark);
    }

private:
    Node* _root = nullptr;
};

myset.h

#pragma once
#include "RBTree.h"
namespace jyf {
template<class K>
class set {
    struct SetKeyOfT {
        const K& operator()(const K& key) { return key; }
    };
public:
    typedef typename RBTree<K, K, SetKeyOfT>::const_iterator iterator;
    typedef typename RBTree<K, K, SetKeyOfT>::const_iterator const_iterator;

    iterator begin() const { return _t.begin(); }
    iterator end() const { return _t.end(); }

    pair<iterator, bool> insert(const K& key) {
        pair<typename RBTree<K, K, SetKeyOfT>::iterator, bool> ret = _t.Insert(key);
        return pair<iterator, bool>(ret.first, ret.second);
    }

private:
    RBTree<K, K, SetKeyOfT> _t;
};
}

mymap.h

#pragma once
#include "RBTree.h"
namespace jyf {
template<class K, class V>
class map {
    struct MapKeyOfT {
        const K& operator()(const pair<const K, V>& kv) { return kv.first; }
    };
public:
    typedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::iterator iterator;
    typedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::const_iterator const_iterator;

    iterator begin() { return _t.begin(); }
    iterator end() { return _t.end(); }
    const_iterator begin() const { return _t.begin(); }
    const_iterator end() const { return _t.end(); }

    V& operator[](const K& key) {
        pair<iterator, bool> ret = insert(make_pair(key, V()));
        return ret.first->second;
    }

    pair<iterator, bool> insert(const pair<K, V>& kv) {
        return _t.Insert(kv);
    }

private:
    RBTree<K, pair<const K, V>, MapKeyOfT> _t;
};
}

test.cpp

#include <iostream>
#include <string>
using namespace std;
#include "mymap.h"
#include "myset.h"

int main() {
    jyf::map<int, int> m;
    m.insert(make_pair(1, 1));
    m.insert(make_pair(3, 3));
    m.insert(make_pair(2, 2));

    auto mit = m.begin();
    while (mit != m.end()) {
        // 不能修改 key，可以修改 value
        // mit->first = 1; mit->second = 2;
        cout << mit->first << ":" << mit->second << endl;
        ++mit;
    }
    cout << endl;

    for (const auto& kv : m) {
        cout << kv.first << ":" << kv.second << endl;
    }
    cout << endl;

    jyf::set<int> s;
    s.insert(5); s.insert(2); s.insert(2);
    s.insert(12); s.insert(22); s.insert(332); s.insert(7);

    jyf::set<int>::iterator it = s.begin();
    while (it != s.end()) {
        // 不应该允许修改 key
        // if (*it % 2 == 0) { *it += 10; }
        cout << *it << " ";
        ++it;
    }
    cout << endl;

    jyf::map<string, string> dict;
    dict.insert(make_pair("sort", "xxx"));
    dict["left"]; // 插入

    for (const auto& kv : dict) {
        cout << kv.first << ":" << kv.second << endl;
    }
    cout << endl;

    dict["left"] = "左边"; // 修改
    dict["sort"] = "排序"; // 修改
    dict["right"] = "右边"; // 插入 + 修改

    for (const auto& kv : dict) {
        cout << kv.first << ":" << kv.second << endl;
    }
    cout << endl;

    return 0;
}

以上便是红黑树封装 map 与 set 的核心逻辑与完整代码。理解这些细节对于掌握 STL 容器的底层原理非常有帮助。