C++ 红黑树封装实战：从零实现 Map 与 Set

2.2 迭代器 iterator 的实现

迭代器的核心是用一个类型封装结点指针，并通过重载运算符实现类似指针的行为。难点在于 operator++ 和 operator-- 的实现，这依赖于中序遍历的逻辑。

迭代器 ++ 的核心逻辑

中序遍历顺序为：左子树 -> 根结点 -> 右子树。

1. 若当前结点的右子树不为空：下一个访问的结点是右子树的中序第一个结点（即右子树的最左结点）。
2. 若当前结点的右子树为空：需要向上回溯到祖先结点。
   • 如果当前结点是父亲的左孩子，则父亲就是下一个结点。
   • 如果当前结点是父亲的右孩子，说明当前子树已访问完，需继续向上找，直到找到一个结点是它父亲的左孩子为止。

end() 的表示

使用 nullptr 充当 end() 标记。当迭代器移动到末尾时，将内部指针置为 nullptr。在 --end() 时需特殊处理，使其指向最右结点。

Iterator End() { return Iterator(nullptr); }

对于 set，迭代器不支持修改，可将模板参数设为 const K；对于 map，key 不可修改但 value 可改，故设为 pair<const K, V>。

2.3 map 支持 [] 运算符

map 要支持 [] 操作符，主要涉及两点：

1. 修改 Insert 返回值，返回 pair<Iterator, bool>。
2. 利用 Insert 的结果，若插入成功则构造默认值，若存在则直接返回引用。

V& operator[](const K& key) {
    auto [it, flag] = _t.Insert({ key, V() });
    return it->second;
}

完整代码示例与实践演示

RBTree.h

#include <utility>
using namespace std;

template<class T, class Ref, class Ptr> struct RBTreeIterator {
    typedef RBTreeNode<T> Node;
    typedef RBTreeIterator<T, Ref, Ptr> Self;
    Node* _node;
    RBTreeIterator(Node* node) :_node(node) { }
    Ref operator*() { return _node->_data; }
    Ptr operator->() { return &_node->_data; }
    Self& operator++() {
        if (_node->_right) {
            Node* minRight = _node->_right;
            while (minRight->_left) { minRight = minRight->_left; }
            _node = minRight;
        } else {
            Node* cur = _node;
            Node* parent = cur->_parent;
            while (parent && cur == parent->_right) {
                cur = parent;
                parent = parent->_parent;
            }
            _node = parent;
        }
        return *this;
    }
    bool operator!=(const Self& s) { return _node != s._node; }
    bool operator==(const Self& s) { return _node == s._node; }
};

template<class K, class T, class KeyOfT> struct RBTree {
    typedef RBTreeNode<T> Node;
public:
    typedef RBTreeIterator<T, T&, T*> Iterator;
    typedef RBTreeIterator<T, const T&, const T*> ConstIterator;
    ~RBTree() { Destroy(_root); _root = nullptr; }
    Iterator Begin() {
        Node* minLeft = _root;
        while (minLeft && minLeft->_left) { minLeft = minLeft->_left; }
        return Iterator(minLeft);
    }
    Iterator End() { return Iterator(nullptr); }
    ConstIterator Begin() const {
        Node* minLeft = _root;
        while (minLeft && minLeft->_left) { minLeft = minLeft->_left; }
        return ConstIterator(minLeft);
    }
    ConstIterator End() const { return ConstIterator(nullptr); }
    pair<Iterator, bool> Insert(const T& data) {
        if (_root == nullptr) {
            _root = new Node(data);
            _root->_col = BLACK;
            return { Iterator(_root), true };
        }
        KeyOfT kot;
        Node* parent = nullptr;
        Node* cur = _root;
        while (cur) {
            if (kot(cur->_data) < kot(data)) {
                parent = cur;
                cur = cur->_right;
            } else if (kot(data) < kot(cur->_data)) {
                parent = cur;
                cur = cur->_left;
            } else {
                return { Iterator(cur), false };
            }
        }
        cur = new Node(data);
        Node* newnode = cur;
        cur->_col = RED;
        if (kot(parent->_data) < kot(data)) {
            parent->_right = cur;
        } else {
            parent->_left = cur;
        }
        cur->_parent = parent;
        while (parent && parent->_col == RED) {
            Node* grandfather = parent->_parent;
            if (grandfather->_left == parent) {
                Node* uncle = grandfather->_right;
                if (uncle && uncle->_col == RED) {
                    parent->_col = 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 = 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 { Iterator(newnode), true };
    }
    void RotateR(Node* parent) {
        Node* subL = parent->_left;
        Node* subLR = subL->_right;
        parent->_left = subLR;
        if (subLR) subLR->_parent = parent;
        Node* parentParent = parent->_parent;
        subL->_right = parent;
        parent->_parent = subL;
        if (parent == _root) {
            _root = subL;
            subL->_parent = nullptr;
        } else {
            if (parentParent->_left == parent) {
                parentParent->_left = subL;
            } else {
                parentParent->_right = subL;
            }
            subL->_parent = parentParent;
        }
    }
    void RotateL(Node* parent) {
        Node* subR = parent->_right;
        Node* subRL = subR->_left;
        parent->_right = subRL;
        if (subRL) subRL->_parent = parent;
        Node* parentParent = parent->_parent;
        subR->_left = parent;
        parent->_parent = subR;
        if (parentParent == nullptr) {
            _root = subR;
            subR->_parent = nullptr;
        } else {
            if (parent == parentParent->_left) {
                parentParent->_left = subR;
            } else {
                parentParent->_right = subR;
            }
            subR->_parent = parentParent;
        }
    }
    Iterator Find(const K& key) {
        KeyOfT kot;
        Node* cur = _root;
        while (cur) {
            if (kot(cur->_data) < key) {
                cur = cur->_right;
            } else if (kot(cur->_data) > key) {
                cur = cur->_left;
            } else {
                return Iterator(cur);
            }
        }
        return End();
    }
    int Height() { return _Height(_root); }
    int Size() { return _Size(_root); }
private:
    int _Size(Node* root) {
        if (root == nullptr) return 0;
        return _Size(root->_left) + _Size(root->_right) + 1;
    }
    int _Height(Node* root) {
        if (root == nullptr) return 0;
        int leftHeight = _Height(root->_left);
        int rightHeight = _Height(root->_right);
        return leftHeight > rightHeight ? leftHeight + 1 : rightHeight + 1;
    }
    void Destroy(Node* root) {
        if (root == nullptr) return;
        Destroy(root->_left);
        Destroy(root->_right);
        delete root;
    }
private:
    Node* _root = nullptr;
};

Map.h

#pragma once
#include"RBTree.h"
namespace jqj {
template<class K, class V> class map {
    struct MapKeyOfT {
        const K& operator()(const pair<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>::ConstIterator 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(); }
    pair<iterator, bool> insert(const pair<K, V>& kv) { return _t.Insert(kv); }
    iterator find(const K& key) { return _t.Find(key); }
    V& operator[](const K& key) {
        auto [it, flag] = _t.Insert({ key, V() });
        return it->second;
    }
private:
    RBTree<K, pair<const K, V>, MapKeyOfT> _t;
};
}

Set.h

#pragma once
#include"RBTree.h"
namespace jqj {
template<class K> class set {
    struct SetKeyOfT {
        const K& operator()(const K& key) { return key; }
    };
public:
    typedef typename RBTree<K, const K, SetKeyOfT>::Iterator iterator;
    typedef typename RBTree<K, const K, SetKeyOfT>::ConstIterator 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(); }
    pair<iterator, bool> insert(const K& key) { return _t.Insert(key); }
    iterator find(const K& key) { return _t.Find(key); }
private:
    RBTree<K, const K, SetKeyOfT> _t;
};
}

Test.cpp

#define _CRT_SECURE_NO_WARNINGS 1
#include<iostream>
#include<vector>
using namespace std;
#include"RBTree.h"
#include"Map.h"
#include"Set.h"

template<class T> void func(const jqj::set<T>& s) {
    typename jqj::set<T>::const_iterator it = s.begin();
    while (it != s.end()) {
        cout << *it << " ";
        ++it;
    }
    cout << endl;
}

void Test_set() {
    jqj::set<int> s;
    s.insert(1); s.insert(2); s.insert(1); s.insert(5);
    s.insert(0); s.insert(10); s.insert(8);
    jqj::set<int>::iterator it = s.begin();
    while (it != s.end()) {
        cout << *it << " ";
        ++it;
    }
    cout << endl;
    func(s);
}

void Test_map() {
    jqj::map<string, string> dict;
    dict.insert({ "sort", "排序" });
    dict.insert({ "left", "左边" });
    dict.insert({ "right", "右边" });
    dict["string"] = "字符串";
    dict["left"] = "左边 xxx";
    auto it = dict.begin();
    while (it != dict.end()) {
        it->second += 'x';
        cout << it->first << ":" << it->second << endl;
        ++it;
    }
    cout << endl;
    for (auto& [k, v] : dict) {
        cout << k << ":" << v << endl;
    }
    cout << endl;
    string arr[] = { "苹果", "西瓜", "苹果", "西瓜", "苹果", "苹果", "西瓜", "苹果", "香蕉", "苹果", "香蕉" };
    jqj::map<string, int> countMap;
    for (auto& e : arr) {
        countMap[e]++;
    }
    for (auto& [k, v] : countMap) {
        cout << k << ":" << v << endl;
    }
    cout << endl;
}

int main() {
    Test_set();
    Test_map();
    return 0;
}

运行结果

程序输出展示了 set 的有序去重特性以及 map 的键值对统计功能，验证了封装的正确性。