STL 容器 map 与 set 的红黑树封装及迭代器实现原理

set 实现示例

namespace stl_impl {
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;

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

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

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

红黑树模拟实现

红黑树节点定义及核心操作如下：

enum Colour { RED, BLACK };

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

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

template<class K, class T, class KeyOfT>
struct 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;
    }

    std::pair<iterator, bool> Insert(const T& data) {
        if (_root == nullptr) {
            _root = new Node(data);
            _root->_col = BLACK;
            return make_pair(iterator(_root), true);
        }

        Node* parent = nullptr;
        Node* cur = _root;
        KeyOfT kot;
        while (cur) {
            if (kot(cur->_data) < kot(data)) {
                parent = cur;
                cur = cur->_right;
            } else if (kot(cur->_data) > kot(data)) {
                parent = cur;
                cur = cur->_left;
            } else {
                return make_pair(iterator(cur), false);
            }
        }

        cur = new Node(data);
        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 (parent == grandfather->_left) {
                Node* uncle = grandfather->_right;
                // u 存在且为红
                if (uncle && uncle->_col == RED) {
                    parent->_col = uncle->_col = BLACK;
                    grandfather->_col = RED;
                    cur = grandfather;
                    parent = cur->_parent;
                } else {
                    // u 不存在 或 存在且为黑
                    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;
                // u 存在且为红
                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);
                        grandfather->_col = RED;
                        parent->_col = BLACK;
                    } else {
                        RotateR(parent);
                        RotateL(grandfather);
                        cur->_col = BLACK;
                        grandfather->_col = RED;
                    }
                    break;
                }
            }
        }
        _root->_col = BLACK;
        return make_pair(iterator(cur), true);
    }

private:
    Node* _root = nullptr;
    // 旋转相关代码参考 AVL 树实现
    void RotateL(Node* parent) {} // Placeholder
    void RotateR(Node* parent) {} // Placeholder
};

注意：需区分头节点与根节点。库实现中通常包含头节点，其父亲是红黑树根节点，left 指向最小数，right 指向最大数。

迭代器模拟实现

迭代器的 begin 指向最左节点，end 指向 nullptr（逻辑上的尾后位置）。

++ 操作逻辑

1. 当前节点的右子树不为空，则访问右子树的最左节点。
2. 当前节点的右子树为空，如果当前节点是其父亲的左孩子，就访问当前节点的父亲；否则向上回溯直到找到满足条件的父节点或到达根节点的父亲。

-- 操作逻辑

1. 当前节点的左子树不为空，则访问左子树的最右节点。
2. 当前节点的左子树为空，如果当前节点是其父亲的右孩子，就访问当前节点的父亲；否则向上回溯直到找到满足条件的父节点或到达根节点的父亲。

补充：普通迭代器可隐式转换为 const 迭代器。

template<class T, class Ptr, class Ref>
struct __TreeIterator {
    typedef RBTreeNode<T> Node;
    typedef __TreeIterator<T, Ptr, Ref> Self;
    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) const {
        return _node != s._node;
    }

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

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