完整源代码: http://download.csdn.net/detail/hanqing280441589/8450041
红黑节点设计与实现
template <typename Comparable> class RedBlackNode { friend class RedBlackTree<Comparable>; //所有的成员都是private private: RedBlackNode(const Comparable &theElement = Comparable(), RedBlackNode *theLeft = NULL, RedBlackNode *theRight = NULL, int theColor = RedBlackTree<Comparable>::BLACK) : element(theElement), left(theLeft), right(theRight), color(theColor) {} //数据成员 Comparable element; RedBlackNode *left; RedBlackNode *right; int color; };
红黑树的设计
template <typename Comparable> class RedBlackTree { //类型定义 public: typedef RedBlackNode<Comparable> Node; enum COLOR {RED, BLACK}; //开放的接口 public: explicit RedBlackTree(const Comparable & negInf); ~RedBlackTree(); void insert(const Comparable &x); bool isEmpty() const; void makeEmpty(); Gref<Comparable> find(const Comparable & x) const; Gref<Comparable> findMin() const; Gref<Comparable> findMax() const; //实用的私有操作 private: //自动处理: [1]重新染色; [2]:自动旋转 void handleReorient(const Comparable &item); //自动旋转函数(返回旋转以后的theParent子树的根) Node *rotate(const Comparable & item, Node *theParent); /**单旋转**/ //向右转(带着右孩子) void rotateWithLeftChild(Node *& k2); //向左转(带着左孩子) void rotateWithRightChild(Node *& k1); //递归删除所有节点 void reclainMemory(Node *t) const; private: //指向红黑树的头(伪根节点) Node *header; Node *nullNode; //在insert时使用 Node *current; //当前节点 Node *parent; //父节点 Node *grand; //祖父节点 Node *great; //曾祖父节点 };
红黑树的实现
//红黑树构造函数 template <typename Comparable> RedBlackTree<Comparable>::RedBlackTree(const Comparable & negInf) { nullNode = new RedBlackNode<Comparable>; //nullNode 的左右子节点都指向自己 nullNode->left = nullNode->right = nullNode; header = new RedBlackNode<Comparable>(negInf, nullNode, nullNode); }
//红黑树析构函数: 完善版本 template <typename Comparable> RedBlackTree<Comparable>::~RedBlackTree() { if (!isEmpty()) makeEmpty(); delete nullNode; delete header; }
/**红黑树最复杂的操作 ** insert **/ template <typename Comparable> void RedBlackTree<Comparable>::insert(const Comparable &x) { current = parent = grand = great = header; nullNode->element = x; while (current->element != x) { //让祖父成为曾祖父, 父亲成为祖父, 自己成为父亲 //每个节点都成长一辈 great = grand; grand = parent; parent = current; current = (x < current->element) ? current->left : current->right; //处理1. 如果current节点有两个红色孩子 if ((current->left->color == RED) && (current->right->color == RED)) handleReorient( x ); } //如果树中包含相同的元素 if (current != nullNode) throw DuplicateItemException(); current = new Node(x, nullNode, nullNode); if (x < parent->element) parent->left = current; else parent->right = current; //+ 处理2. 如果新插入的节点破坏了红黑规则 handleReorient( x ); }
/**自动平衡函数: [1]重新染色 [2]自动旋转 */ template <typename Comparable> void RedBlackTree<Comparable>::handleReorient(const Comparable & item) { // 将current节点染成红色 current->color = RED; // 将current的left和right节点染成黑色 current->left->color = current->right->color = BLACK; // 如果current节点的父节点也是红的 -> 单旋转 or 双旋转 if( parent->color == RED ) { //则将其祖父(爷爷)的颜色染成红色 grand->color = RED; //然后判断新插入的节点是否是内部孙子? //如果是, 则增加一次旋转->构成双旋转 //if注释: 如果该节点小于爷爷, 小于爸爸, 这两种情况不同时满足 //则说明其是爷爷的内孙子 if( (item < grand->element) != (item < parent->element) ) { // 则依grand(祖父)节点进行旋转 parent = rotate( item, grand ); // Start double rotate } // 则依great(曾祖父)节点进行旋转 current = rotate( item, great ); //令当前节点为黑色 current->color = BLACK; } //根节点必须是黑色的 header->right->color = BLACK; // Make root black }
// 自动判断并进行旋转函数 template <typename Comparable> typename RedBlackTree<Comparable>::Node * RedBlackTree<Comparable>::rotate(const Comparable &item, Node *theParent ) { //位于theParent的左子树 if( item < theParent->element ) { //如果为真, 则说明theParent->left有左孩子, //否则, 有右孩子 item < theParent->left->element ? //如果theParent左边有一棵子树, 则以theParent->left //为轴, 向右转 rotateWithLeftChild( theParent->left ) : // LL //如果theParent右边有一棵子树, 则以theParent->left //为轴, 向左转 rotateWithRightChild( theParent->left ) ; // LR return theParent->left; //返回左子树 } else //位于右子树 { //如果为真, 则说明theParent->right有左孩子,往右转 //否则, 有右孩子, 往左转 item < theParent->right->element ? rotateWithLeftChild( theParent->right ) : // RL rotateWithRightChild( theParent->right ); // RR return theParent->right; //返回右子树 } }
/** 右(单)旋转 **/ template <typename Comparable> void RedBlackTree<Comparable>::rotateWithLeftChild(Node *& k2) { Node *k1 = k2->left; k2->left = k1->right; k1->right = k2; k2 = k1; }
/** 左(单)旋转 **/ template <typename Comparable> void RedBlackTree<Comparable>::rotateWithRightChild(Node *& k1) { Node * k2 = k1->right; k1->right = k2->left; k2->left = k1; k1 = k2; }
template <typename Comparable> Gref<Comparable> RedBlackTree<Comparable>::find(const Comparable &x) const { if (isEmpty()) return Gref<Comparable>(); nullNode->element = x; Node *iter = header->right; while (true) { if (x < iter->element) iter = iter->left; else if (x > iter->element) iter = iter->right; //如果 x == iter->element else if (iter != nullNode) return Gref<Comparable>(iter->element) ; else return Gref<Comparable>(); } }
template <typename Comparable> Gref<Comparable> RedBlackTree<Comparable>::findMax() const { if (isEmpty()) return Gref<Comparable>(); Node *iter = header->right; while (iter->right != nullNode) { // 一直向右走 iter = iter->right; } return Gref<Comparable>(iter->element); }
template <typename Comparable> Gref<Comparable> RedBlackTree<Comparable>::findMin() const { if (isEmpty()) return Gref<Comparable>(); Node *iter = header->right; while (iter->left != nullNode) { // 一直向左走 iter = iter->left; } return Gref<Comparable>(iter->element); }
template <typename Comparable> bool RedBlackTree<Comparable>::isEmpty() const { if (header->right == nullNode) return true; return false; }
template <typename Comparable> void RedBlackTree<Comparable>::makeEmpty() { reclainMemory(header->right); header->right = nullNode; }
template <typename Comparable> void RedBlackTree<Comparable>::reclainMemory(Node *t) const { //t == t->left的时候, 是当t==nullNode时 if (t != t->left) { reclainMemory(t->left); reclainMemory(t->right); delete t; } }
Gref包装器的设计与实现
template <typename Object> class Gref { public: Gref(): obj(NULL) {} explicit Gref(const Object &x) : obj(& x) {} const Object &get() const { if (isNull()) throw NullPointerException(); else return * obj; } bool isNull() const { if (obj == NULL) return true; return false; } private: const Object * obj; };
Exception的设计与实现
class DSException { public: typedef std::string string; public: DSException(const string &_msg = string()) :message(_msg) {} virtual ~DSException() {} virtual string what() const { return message; } virtual string toString() const { return "Exception " + message; } private: string message; }; class DuplicateItemException : public DSException { public: DuplicateItemException(const string &_msg = string()) : DSException(_msg) {} }; class NullPointerException : public DSException { public: NullPointerException(const string &_msg = string()) : DSException(_msg) {} };
测试代码
int main() { const int NEG_INF = -999999; RedBlackTree<int> tree(NEG_INF); tree.insert(50); tree.insert(40); tree.insert(30); tree.insert(10); tree.insert(55); tree.insert(88); tree.insert(200); tree.insert(100); tree.insert(70); tree.insert(80); tree.insert(650); Gref<int> g = tree.findMin(); cout << "Min = " << g.get() << endl; g = tree.findMax(); cout << "Max = " << g.get() << endl; int searchVal; while (cin >> searchVal) { g = tree.find(searchVal); if (g.isNull()) cout << "not found" << endl; else cout << g.get() << " founded" << endl; } tree.makeEmpty(); if (tree.isEmpty()) { cout << "is Empty" << endl; } else { cout << "not Empty" << endl; } return 0; }