索引二叉搜索树

// linked binary tree implementation of a binary search tree

// implements all dictionary and bsTree methods

#ifndefindexedBinarySearchTree_

#define indexedBinarySearchTree_

#include "indexedBSTree.h"

#include "linkedBinaryTree.h"

using namespace std;

template

class indexedBinarySearchTree : public indexedBSTree,

public linkedBinaryTree> {

public:

// methods of dictionary

bool empty() const {return this->treeSize == 0;}

intsize() const {return this->treeSize;}

pair* get(int ) const;

void insert(const pair&thePair);

void erase(const K&theKey);

void delete2(int);

// additional method of bsTree

void ascend() {this->inOrderOutput();}

// void makeBst(constint a[]);

void eraseMax();//删除关键字最大的元素

};

template

pair* indexedBinarySearchTree::get(int Index)const {

binaryTreeNode> *p =this->root;

while (p != NULL)

{

if (Index < p->leftSize)

{

p = p->leftChild;

}

else

{

if (Index > p->leftSize)

{

Index = Index-(p->leftSize+1);

p = p->rightChild;

}

else // found matching pair

return &p->element;

}

}

// no matching pair

return NULL;

}

template

void indexedBinarySearchTree::insert(const pair&thePair) {// Insert thePair into the tree. Overwrite existing

// pair, if any, with same key.

// find place to insert

binaryTreeNode> *p = this->root, *pp = NULL;

while (p != NULL)

{// examine p->element

pp = p;

// pp作为p的双亲结点

if (thePair.first< p->element.first)

{

p->leftSize++;//索引加1

p = p->leftChild;

}

else

{

if (thePair.first> p->element.first)

p = p->rightChild;

else//如果相同

{//替换原来的value

p->element.second = thePair.second;//不对

return;

}

}

}

// get a node for thePair and attach to pp

binaryTreeNode> *newNode

= new binaryTreeNode> (thePair);

if (this->root != NULL) // the tree is not empty

{

if (thePair.first< pp->element.first)

{

pp->leftChild = newNode;

//pp->leftSize = 1;//索引为1

}

else

pp->rightChild = newNode;

}

else

{

this->root = newNode;

//this->root->leftSize = 0;//索引为0

} // insertion into empty tree

this->treeSize++;

}

template

void indexedBinarySearchTree::erase(const K&theKey)//根据关键字删除{// Delete the pair, if any, whose key equals theKey.

// search for node with key theKey

binaryTreeNode> *p = this->root,

*pp = NULL;

while (p != NULL && p->element.first != theKey)

{// move to a child of p

pp = p;

if (theKey< p->element.first)

p = p->leftChild;

else

p = p->rightChild;

}

if (p == NULL)

return; // no pair with key theKey

// restructure tree

// handle case when p has two children

if (p->leftChild != NULL && p->rightChild != NULL)

{// two children

// convert to zero or one child case

// find largest element in left subtree of p

binaryTreeNode> *s = p->leftChild,

*ps = p; // parent of s while (s->rightChild != NULL)

{// move to larger element

ps = s;

s = s->rightChild;

}

// move largest from s to p, can't do a simple move

// p->element = s->element as key is const binaryTreeNode> *q =

new binaryTreeNode>

(s->element, p->leftChild, p->rightChild);

if (pp == NULL)

this->root = q;

else if (p == pp->leftChild)

pp->leftChild = q;

else

pp->rightChild = q;

if (ps == p) pp = q;

else pp = ps;

delete p;

p = s;

}

// p has at most one child

// save child pointer in c binaryTreeNode> *c;

if (p->leftChild != NULL)

c = p->leftChild;

else

c = p->rightChild;

// delete p

if (p == this->root)

this->root = c;

else

{// is p left or right child of pp?

if (p == pp->leftChild)

pp->leftChild = c;

else pp->rightChild = c;

}

this->treeSize--;

delete p;

}

template

void indexedBinarySearchTree::delete2(int Index)

{// Delete the pair, if any, whose key equals theKey.

// search for node with key theKey

binaryTreeNode> *p = this->root,

*pp = NULL;

/* if (p == NULL)

return; // no pair with key theKey*/

if(Index>this->treeSize-1)//如果索引值大于节点数减1，则不存在该索引值return ;

while (p&& p->leftSize != Index)//寻找索引值为Index的结点

{// move to a child of p

/*pp = p;

if (theKey< p->element.first)

p = p->leftChild;

else

p = p->rightChild;*/

if (Index < p->leftSize)

{

pp = p;//p的父节点

p->leftSize--;//每向左移动一次索引值减1

p = p->leftChild;

}

else

{

if (Index > p->leftSize)

{

pp = p;//p的父节点

Index = Index-(p->leftSize+1);

p = p->rightChild;

}

/*else // found matching pair

return &p->element;*/

}

}

if (p->leftChild != NULL && p->rightChild != NULL)//存在左孩子和右孩子的情况{// two children

// convert to zero or one child case

// find largest element in left subtree of p

binaryTreeNode> *s = p->leftChild,

*ps = p; // parent of s

while (s->rightChild != NULL)//寻找左子树中最大的结点

{// move to larger element

ps = s;

//ps->leftSize--;//索引减1

s = s->rightChild;//s为要替换的值

}

// 将最大元素s移动到p但不是简单的移动

binaryTreeNode> *q =

new binaryTreeNode>

(s->element, p->leftChild, p->rightChild);

if (pp == NULL)//如果要删除的结点是根节点，则直接替换根节点this->root = q;

else if (p == pp->leftChild)

pp->leftChild = q;

else

pp->rightChild = q;

if (ps == p) pp = q;

else pp = ps;

delete p;

p = s;

}

// p has at most one child

// save child pointer in c binaryTreeNode> *c;

if (p->leftChild != NULL)

c = p->leftChild;

else

c = p->rightChild;

// delete p

if (p == this->root)

this->root = c;

else

{// is p left or right child of pp?

if (p == pp->leftChild)

pp->leftChild = c;

else pp->rightChild = c;

}

this->treeSize--;

delete p;

}

// overload << for pair

template

ostream& operator<<(ostream& out, const pair& x) {out <

template

void indexedBinarySearchTree::eraseMax()

{

binaryTreeNode> *p =this->root,

*pp = NULL;

while(p != NULL)

{

pp = p;

p = p->rightChild;

}

if(p->leftChild != NULL)

{

pp->leftChild = p->leftChild;

}

this->treeSize--;

delete p;

}

#endif

//测试代码

// test binary search tree class

#include

#include"indexedBinarySearchTree.h"

usingnamespace std;

int main(void)

{

indexedBinarySearchTree y;

y.insert(pair(1, 'a'));

y.insert(pair(6, 'c'));

y.insert(pair(4, 'b'));

y.insert(pair(8, 'd'));

cout<<"Tree size is "<

cout<<"Elements in ascending order are"<

y.ascend();

pair *s = y.get(3);//查找索引为3的结点

cout<<"Search for 3 index "<

cout<< s->first<<' '<< s->second<

// y.erase(4);

y.delete2(2);//删除索引为2的结点

cout<<"2 index deleted "<

cout<<"Tree size is "<

cout<<"Elements in ascending order are"<

y.ascend();

s = y.get(2);//查找索引为2的结点

cout<<"Search for 2 index "<

//cout<< s->first << ' ' << s->second <

y.delete2(2);//删除索引为2的结点

cout<<"2 deleted "<

cout<<"Tree size is "<

cout<<"Elements in ascending order are"<

y.ascend();

/* //s = y.find(6);

cout<< "Search for 6 succeeds " <

//cout<< s->first << ' ' << s->second <

cout<< "6 deleted " <

cout<< "Tree size is " <

cout<< "Elements in ascending order are" <

//s = y.find(1);

cout<< "Search for 1 succeeds " <

// cout<< s->first << ' ' << s->second <

cout<< "1 deleted " <

cout<< "Tree size is " <

cout<< "Elements in ascending order are" <

}