数据结构拾遗(2) --红黑树的设计与实现(中)

Insert完善

    根据规则4, 新增节点必须为红; 根据规则3, 新增节点之父节点必须为黑.

 

示例:

    (1)插入16(红色)/55(红色), 则既不用旋转, 也不用重新染色

    (2)插入82(红色), 则违反了红黑规则, 需要进行动态的调整;

 

红黑树所需的处理

1.单旋转

     新插入的X与其父P都是红色的, 而且X还是G的外部孙子;

 

2.双旋转

    新插入的X与其父P都是红色的, 而且X还是G的内部孙子;

 

3.还需要处理有两个红色孩子的节点, 将右儿子变成黑色的, 我们只允许左儿子是红色的;方法: 旋转+重新染色

 

insert完整实现代码:

/**注意带有 ++ 注释的为新添加的代码**/ 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//每个人都长了一辈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;elseparent->right = current;// ++//+ 处理2. 如果新插入的节点破坏了红黑规则, 则还需做一次处理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 ) ; // LRreturn 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 ) : // RLrotateWithRightChild( theParent->right ); // RRreturn theParent->right; //返回右子树} }

测试代码:

int main() {//用NEG_INF来代表负无穷大const int NEG_INF = -999999;RedBlackTree<int> tree(NEG_INF);tree.insert(50);cout << tree.header->right->element << " " << tree.header->right->nodeColor() << endl;cout << endl;tree.insert(40);cout << tree.header->right->left->element << " " << tree.header->right->left->nodeColor() << endl << endl;//此时需要进行旋转和重新染色tree.insert(30);cout << tree.header->right->element << " " << tree.header->right->nodeColor() << endl ;cout << tree.header->right->left->element << " " << tree.header->right->left->nodeColor() << endl;cout << tree.header->right->right->element << " " << tree.header->right->right->nodeColor() << endl;return 0; }
//由于需要用到nodeColor成员函数, 因此我们将RedBlackNode类改造如下: template <typename Comparable> class RedBlackNode {friend class RedBlackTree<Comparable>; public:RedBlackNode(const Comparable &theElement = Comparable(),RedBlackNode *theLeft = NULL,RedBlackNode *theRight = NULL,int theColor = RedBlackTree<Comparable>::BLACK): element(theElement), left(theLeft), right(theRight), color(theColor) {}public://返回当前节点的颜色, 以作测试std::string nodeColor() const{return (color == RedBlackTree<Comparable>::BLACK) ? "black" : "red";}public:Comparable element;RedBlackNode *left;RedBlackNode *right;int color; };

红黑树其他操作

template <typename Comparable> class RedBlackTree {...bool isEmpty() const;void makeEmpty();Gref<Comparable> find(const Comparable & x) const;Gref<Comparable> findMin() const;Gref<Comparable> findMax() const;//递归删除所有节点void reclainMemory(Node *t) const;... };

//析构函数完善版本 template <typename Comparable> RedBlackTree<Comparable>::~RedBlackTree() {if (!isEmpty())makeEmpty();delete nullNode;delete header; }
//红黑树查找:与二叉查找树类似 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->elementelse if (iter != nullNode)return Gref<Comparable>(iter->element) ;elsereturn Gref<Comparable>();} }
//查找最大值: 一路向右 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); }
//查找最小值: 一路向左 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设计与实现

//一个包装器: 将指针封装成为引用 template <typename Object> class Gref { public:Gref(): obj(NULL) {}explicit Gref(const Object &x): obj(& x) {}const Object &get() const{if (isNull())throw NullPointerException();elsereturn * obj;}bool isNull() const{if (obj == NULL)return true;return false;}private:const Object * obj; };

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