数据结构基础(24) --红黑树的设计与实现(下)

完整源代码: http://download.csdn.net/detail/hanqing280441589/8450041



红黑节点设计与实现

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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

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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

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//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);
}

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//红黑树析构函数: 完善版本
template <typename Comparable>
RedBlackTree<Comparable>::~RedBlackTree()
{
if (!isEmpty())
makeEmpty();

delete nullNode;
delete header;
}

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/**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 );
}

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/**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
}

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// 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
}
}

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/** 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;
}

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/** 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;
}

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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>();
}
}

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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);
}

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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);
}

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template <typename Comparable>
bool RedBlackTree<Comparable>::isEmpty() const
{
if (header->right == nullNode)
return true;
return false;
}

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template <typename Comparable>
void RedBlackTree<Comparable>::makeEmpty()
{
reclainMemory(header->right);
header->right = nullNode;
}

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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

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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

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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

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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;
}

原文地址：/article/1333384.html