Design Patterns for Data Structures. Chapter 8. The Composite State Binary Tree BiTreeCS
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1 Design Patterns for Data Structures Chapter 8 The Composite State Binary Tree BiTreeCS
2 Design Patterns for Data Structures Chapter 8 The Composite State Binary Tree BiTreeCS In a nonempty node _left is a binary tree _right is a binary tree
3 _root: AcsNode<T> * BiTreeCS T AcsNode T BiTreeCS(rhs: BiTreeCS<T> const &) BiTreeCS(node: AcsNode<T> *) + BiTreeCS( ) + ~BiTreeCS( ) + clear( ) + contains(data: T const &) const: bool copyroot(rhs: BiTreeCS<T> const &): AcsNode<T> * + equals(rhs: BiTreeCS<T> const &) const: bool equalshelper(data: T const &, left: BiTreeCS<T> const &, right: BiTreeCS<T> const &) const: bool + height( ) const: int + inorder(os: ostream &) const + insertroot(data: T const &) + isempty( ) const: bool + left( ): BiTreeCS<T> & + left( ) const: BiTreeCS<T> & + max( ) const: T const & + numleaves( ) const: int + numnodes( ) const: int + operator=(rhs: BiTreeCS<T> const &): BiTreeCS & + postorder(os: ostream &) const + preorder(os: ostream &) const + remleaves( ) + remroot( ): T + right( ): BiTreeCS<T> & + right( ) const: BiTreeCS<T> const & + root( ): T & + root( ) const: T const & + settree(tree: BiTreeCS<T> &) + tostream(os: ostream &) const tostreamhelper(prright: string, prroot: string prleft: string, os: ostream &) const # ~AcsNode( ) # clear(owner: BiTreeCS<T> &) # contains(data: T const &) const: bool copyroot( ): AcsNode<T> * # equals(rhs: BiTreeCS<T> const &) const: bool # equalshelper(data: T const &, left: BiTreeCS<T> const &, right: BiTreeCS<T> const &) const: bool # height( ) const: int # inorder(os: ostream &) const # insertroot(owner: BiTreeCS<T> &, data: T const &) # isempty( ) const: bool # left( ): BiTreeCS<T> & # max( ) const: T const & # numleaves( ) const: int # numnodes( ) const: int # postorder(os: ostream &) const # preorder(os: ostream &) const # remleaves(owner: BiTreeCS<T> &) # remroot(owner: BiTreeCS<T> &): T # right( ): BiTreeCS<T> & # right( ) const: BiTreeCS<T> const & # root( ): T & # root( ) const: T const & # settree(owner: BiTreeCS<T>, tree: BiTreeCS<T> &) # tostream(os: ostream &) const # tostreamhelper(prright: string, prrootpr: string Left: string, os: ostream &) const Figure 8.24 NEcsNode T MTcsNode T _left: BiTreeCS<T> _data: T _right: BiTreeCS<T> MTcsNode( ) NEcsNode(data: T const &) NEcsNode(leftNode: AcsNode<T> *, data: T, rightnode: AcsNode<T> *) NEcsNode(rhs: const NEcsNode<T> *)
4 Design Patterns for Data Structures BiTreeCS class BiTreeCS { private: AcsNode<T> *_root; class NEcsNode : public AcsNode<T> { private: BiTreeCS<T> _left; T _data; BiTreeCS<T> _right;
5 Design Patterns for Data Structures Figure 8.25 mytree mytree._root->_left mytree._root->_data mytree._root->_right mytree._root->_right._root *mytree._root mytree._root (a) A detailed rendering of a binary tree and a node. (b) An abbreviated rendering.
6 Design Patterns for Data Structures BiTreeCS Methods for output and characterization
7 Design Patterns for Data Structures Figure 8.26 // ========= preorder ========= void BiTreeCS<T>::preOrder(ostream &os) const { _root->preorder(os); void MTcsNode<T>::preOrder(ostream &os) const { void NEcsNode<T>::preOrder(ostream &os) const { os << _data << ; _left.preorder(os); _right.preorder(os);
8 Design Patterns for Data Structures Figure 8.27 // ========= isempty ========= bool BiTreeCS<T>::isEmpty() const { return _root->isempty(); bool MTcsNode<T>::isEmpty() const { return true; bool NEcsNode<T>::isEmpty() const { return false; _root _left _data _right 40 (a) The environment of a binary tree. (b) The environment of an empty node. (c) The environment of a nonempty node.
9 Design Patterns for Data Structures Figure 8.27 // ========= isempty ========= bool BiTreeCS<T>::isEmpty() const { return _root->isempty(); bool MTcsNode<T>::isEmpty() const { return true; bool NEcsNode<T>::isEmpty() const { return false; _root _left _data _right 40 (a) The environment of a binary tree. (b) The environment of an empty node. (c) The environment of a nonempty node.
10 Design Patterns for Data Structures Figure 8.28 // ========= left ========= BiTreeCS<T> &BiTreeCS<T>::left() { return _root->left(); BiTreeCS<T> &MTcsNode<T>::left() { cerr << left precondition violated: << An empty tree has has no left subtree. << endl; throw -1; BiTreeCS<T> &NEcsNode<T>::left() { return _left;
11 Design Patterns for Data Structures Figure 8.29 // ========= numnodes ========= int BiTreeCS<T>::numNodes() const { return _root->numnodes(); int MTcsNode<T>::numNodes() const { return 0; _left.numnodes() 1 50 _right.numnodes() int NEcsNode<T>::numNodes() const { return 1 + _left.numnodes() + _right.numnodes();
12 Design Patterns for Data Structures Figure 8.30 // ========= max ========= T const &BiTreeCS<T>::max() const { return _root->max(); T const &MTcsNode<T>::max() const { cerr << max precondition violated: An empty tree has no maximum. << endl; throw -1; T const &NEcsNode<T>::max() const { T const *datatemp = &_data; // To avoid restrictions on T const &_data. T const *leftmax = (_left.isempty())? datatemp : &_left.max(); T const *rightmax = (_right.isempty())? datatemp : &_right.max(); return (*leftmax > *rightmax)? ((*leftmax > *datatemp)? *leftmax : *datatemp) : ((*rightmax > *datatemp)? *rightmax : *datatemp);
13 Design Patterns for Data Structures Figure 8.31 // ========= equals ========= // Post: true is returned if this tree equals tree rhs; // otherwise, false is returned. // Two trees are equal if they contain the same number // of equal elements with the same shape. bool BiTreeCS<T>::equals(const BiTreeCS<T> &rhs) const { cerr << BiTreeCS<T>::equals: Exercise for the student. << endl; throw -1; bool MTcsNode<T>::equals(const BiTreeCS<T> &rhs) const { cerr << MTcsNode<T>::equals: Exercise for the student. << endl; throw -1; bool NEcsNode<T>::equals(const BiTreeCS<T> &rhs) const { cerr << NEcsNode<T>::equals: Exercise for the student. << endl; throw -1;
14 Design Patterns for Data Structures Figure 8.31 bool BiTreeCS<T>::equals(const BiTreeCS<T> &rhs) const { cerr << BiTreeCS<T>::equals: Exercise for the student. << endl; throw -1; _root rhs (a) The environment of a binary tree.
15 Design Patterns for Data Structures Figure 8.31 bool MTcsNode<T>::equals(const BiTreeCS<T> &rhs) const { cerr << MTcsNode<T>::equals: Exercise for the student. << endl; throw -1; rhs (b) The environment of an empty node.
16 Design Patterns for Data Structures Figure 8.31 bool NEcsNode<T>::equals(const BiTreeCS<T> &rhs) const { cerr << NEcsNode<T>::equals: Exercise for the student. << endl; throw -1; _left _data _right rhs (c) The environment of a nonempty node.
17 Design Patterns for Data Structures Figure 8.32 // equalshelper // Post: true is returned if root equals this->root(), // left equals this->left(), and right equals this->right(); // otherwise, false is returned. bool BiTreeCS<T>::equalsHelper(T const &data, const BiTreeCS<T> &left, const BiTreeCS<T> &right) const { cerr << BiTreeCS<T>::equalsHelper: Exercise for the student. << endl; throw -1; bool MTcsNode<T>::equalsHelper(T const &, const BiTreeCS<T> &, const BiTreeCS<T> &) const { cerr << MTcsNode<T>::equalsHelper: Exercise for the student. << endl; throw -1; bool NEcsNode<T>::equalsHelper(T const &data, const BiTreeCS<T> &left, const BiTreeCS<T> &right) const { cerr << NEcsNode<T>::equalsHelper: Exercise for the student. << endl; throw -1;
18 Design Patterns for Data Structures Figure 8.32 bool BiTreeCS<T>::equalsHelper(T const &data, const BiTreeCS<T> &left, const BiTreeCS<T> &right) const { cerr << BiTreeCS<T>::equalsHelper: Exercise for the student. << endl; throw -1; _root data left right (a) The environment of a binary tree.
19 Design Patterns for Data Structures Figure 8.32 bool MTcsNode<T>::equalsHelper(T const &, const BiTreeCS<T> &, const BiTreeCS<T> &) const { cerr << MTcsNode<T>::equalsHelper: Exercise for the student. << endl; throw -1; (b) The environment of an empty node.
20 Design Patterns for Data Structures Figure 8.32 bool NEcsNode<T>::equalsHelper(T const &data, const BiTreeCS<T> &left, const BiTreeCS<T> &right) const { cerr << NEcsNode<T>::equalsHelper: Exercise for the student. << endl; throw -1; _left _data _right data left right (c) The environment of a nonempty node.
21 Design Patterns for Data Structures BiTreeCS Methods for construction and insertion
22 Design Patterns for Data Structures Figure 8.33 Two constructors for BiTreeCS // ========= Constructors ========= BiTreeCS<T>::BiTreeCS(): _root(new MTcsNode<T>()) { // Post: _root points to node with no allocation. BiTreeCS<T>::BiTreeCS(AcsNode<T> *node): _root(node) { Empty node The empty tree created by BiTreeCS().
23 Design Patterns for Data Structures Figure 8.34 Three constructors for NEcsNode // Post: _data is data. NEcsNode<T>::NEcsNode(T const &data): _data(data) {
24 Design Patterns for Data Structures Figure 8.34 Three constructors for NEcsNode // Post: _left._root and _right._root point to leftnode // and rightnode, and _data is data. // _left and _right own their nodes and are responsible // for garbage collection. NEcsNode<T>::NEcsNode(AcsNode<T> *leftnode, T data, AcsNode<T> *rightnode): _data(data) { _left._root = leftnode; _right._root = rightnode;
25 Design Patterns for Data Structures Figure 8.34 Three constructors for NEcsNode // Post: _left is rhs->_left, _data is rhs->_data, // and _right is rhs->_right. NEcsNode<T>::NEcsNode(const NEcsNode *rhs): _left(rhs->_left), _data(rhs->_data), _right(rhs->_right) {
26 Design Patterns for Data Structures Figure 8.35 // ========= insertroot ========= void BiTreeCS<T>::insertRoot(T const &data) { _root->insertroot(*this, data); void MTcsNode<T>::insertRoot(BiTreeCS<T> &owner, T const &data) { owner._root = new NEcsNode<T>(data); delete this; void NEcsNode<T>::insertRoot(BiTreeCS<T> &owner, T const &data) { cerr << insertroot precondition violated: << Cannot insert root into a nonempty tree << endl; throw -1; mytree
27 Design Patterns for Data Structures Figure 8.35 mytree mytree 80 Empty node Empty node Empty node (a) Initial tree. (b) mytree.insertroot(80);
28 Design Patterns for Data Structures Figure 8.36 // ========= settree ========= void BiTreeCS<T>::setTree(BiTreeCS<T> &tree) { _root->settree(*this, tree); void MTcsNode<T>::setTree(BiTreeCS<T> &owner, BiTreeCS<T> &tree) { delete owner._root; owner._root = tree._root; tree._root = new MTcsNode<T>(); void NEcsNode<T>::setTree(BiTreeCS<T> &owner, BiTreeCS<T> &tree) { delete owner._root; owner._root = tree._root; tree._root = new MTcsNode<T>();
29 Design Patterns for Data Structures Figure 8.36 mytree yourtree 20 mytree 20 yourtree (a) Initial trees. (b) mytree.settree(yourtree);
30 Design Patterns for Data Structures Figure 8.37 // ========= operator= ========= BiTreeCS<T> &BiTreeCS<T>::operator=(const BiTreeCS<T> &rhs) { if (this!= &rhs) { // In case someone writes mytree = mytree; delete _root; _root = copyroot(rhs); return *this;
31 Design Patterns for Data Structures Figure 8.37 // ========= copyroot ========= AcsNode<T> *BiTreeCS<T>::copyRoot(const BiTreeCS<T> &rhs) { return rhs._root->copyroot(); AcsNode<T> *MTcsNode<T>::copyRoot() { return new MTcsNode<T>(); AcsNode<T> *NEcsNode<T>::copyRoot() { return new NEcsNode<T>( _left._root->copyroot(), _data, _right._root->copyroot());
32 Design Patterns for Data Structures Figure 8.37 mytree 60 yourtree mytree yourtree (a) Initial trees. (b) mytree = yourtree;
33 Design Patterns for Data Structures BiTreeCS Methods for destruction and removal
34 Design Patterns for Data Structures Figure 8.38 // ========= Destructors ========= // Recursively deletes this tree. BiTreeCS<T>::~BiTreeCS() { delete _root; virtual ~AcsNode() { // Virtual destructor necessary for subclassing.
35 Design Patterns for Data Structures Figure 8.39 // ========= clear ========= void BiTreeCS<T>::clear() { cerr << BiTreeCS<T>::clear: Exercise for the student. << endl; throw -1; void MTcsNode<T>::clear(BiTreeCS<T> &) { cerr << MTcsNode<T>::clear: Exercise for the student. << endl; throw -1; void NEcsNode<T>::clear(BiTreeCS<T> &owner) { cerr << NEcsNode<T>::clear: Exercise for the student. << endl; throw -1;
36 Design Patterns for Data Structures Figure 8.39 The clear() operation for BiTreeCS owner owner owner (a) Original. (b) Clear left. (c) Clear right. owner owner Empty node Empty node (d) Change owner. (e) Delete node.
37 Design Patterns for Data Structures Figure 8.40 The remroot() operation for BiTreeCS owner owner owner owner Empty node Empty node Empty node (a) Original. (b) Link owner. (c) Set to nil. (d) Delete node.
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