The document discusses deleting nodes from a binary search tree (BST). There are three cases to consider when deleting a node: 1) if the node is a leaf, it can be deleted immediately, 2) if the node has one child, its parent pointer is redirected to the child node, 3) if the node has two children, it is replaced with its inorder successor. The algorithm and C++ code for deleting nodes from a BST is presented.

1. Class No.16 Data Structures http://ecomputernotes.com

7. Deleting a node in BST Delete(2): locate inorder successor 6 2 5 3 1 8 4 Inorder successor http://ecomputernotes.com

9. Deleting a node in BST Delete(2): copy data from inorder successor 6 2 5 3 1 8 4  6 3 5 3 1 8 4 http://ecomputernotes.com

10. Deleting a node in BST Delete(2): remove the inorder successor 6 2 5 3 1 8 4  6 3 5 3 1 8 4  6 3 5 3 1 8 4 http://ecomputernotes.com

11. Deleting a node in BST Delete(2)  6 3 5 4 1 8  6 3 5 3 1 8 4 http://ecomputernotes.com

13. C++ code for delete TreeNode<int>* remove(TreeNode<int>* tree, int info) { TreeNode<int>* t; int cmp = info - *(tree->getInfo()); if( cmp < 0 ){ t = remove(tree->getLeft(), info); tree->setLeft( t ); } else if( cmp > 0 ){ t = remove(tree->getRight(), info); tree->setRight( t ); }  http://ecomputernotes.com

14. C++ code for delete TreeNode<int>* remove(TreeNode<int>* tree, int info) { TreeNode<int>* t; int cmp = info - *(tree->getInfo()); if( cmp < 0 ){ t = remove(tree->getLeft(), info); tree->setLeft( t ); } else if( cmp > 0 ){ t = remove(tree->getRight(), info); tree->setRight( t ); }  http://ecomputernotes.com

15. C++ code for delete TreeNode<int>* remove(TreeNode<int>* tree, int info) { TreeNode<int>* t; int cmp = info - *(tree->getInfo()); if( cmp < 0 ){ t = remove(tree->getLeft(), info); tree->setLeft( t ); } else if( cmp > 0 ){ t = remove(tree->getRight(), info); tree->setRight( t ); }  http://ecomputernotes.com

16. C++ code for delete TreeNode<int>* remove(TreeNode<int>* tree, int info) { TreeNode<int>* t; int cmp = info - *(tree->getInfo()); if( cmp < 0 ){ t = remove(tree->getLeft(), info); tree->setLeft( t ); } else if( cmp > 0 ){ t = remove(tree->getRight(), info); tree->setRight( t ); }  http://ecomputernotes.com

17. C++ code for delete //two children, replace with inorder successor else if(tree->getLeft() != NULL && tree->getRight() != NULL ){ TreeNode<int>* minNode; minNode = findMin(tree->getRight()); tree->setInfo( minNode->getInfo() ); t = remove(tree->getRight(), *(minNode->getInfo())); tree->setRight( t ); }  http://ecomputernotes.com

18. C++ code for delete //two children, replace with inorder successor else if(tree->getLeft() != NULL && tree->getRight() != NULL ){ TreeNode<int>* minNode; minNode = findMin(tree->getRight()); tree->setInfo( minNode->getInfo() ); t = remove(tree->getRight(), *(minNode->getInfo())); tree->setRight( t ); }  http://ecomputernotes.com

19. C++ code for delete //two children, replace with inorder successor else if(tree->getLeft() != NULL && tree->getRight() != NULL ){ TreeNode<int>* minNode; minNode = findMin(tree->getRight()); tree->setInfo( minNode->getInfo() ); t = remove(tree->getRight(), *(minNode->getInfo())); tree->setRight( t ); }  http://ecomputernotes.com

20. C++ code for delete //two children, replace with inorder successor else if(tree->getLeft() != NULL && tree->getRight() != NULL ){ TreeNode<int>* minNode; minNode = findMin(tree->getRight()); tree->setInfo( minNode->getInfo() ); t = remove(tree->getRight(), *(minNode->getInfo())); tree->setRight( t ); }  http://ecomputernotes.com

21. C++ code for delete //two children, replace with inorder successor else if(tree->getLeft() != NULL && tree->getRight() != NULL ){ TreeNode<int>* minNode; minNode = findMin(tree->getRight()); tree->setInfo( minNode->getInfo() ); t = remove(tree->getRight(), *(minNode->getInfo())); tree->setRight( t ); }  http://ecomputernotes.com

22. C++ code for delete else { // case 1 TreeNode<int>* nodeToDelete = tree; if( tree->getLeft() == NULL ) // will handle 0 children tree = tree->getRight(); else if( tree->getRight() == NULL ) tree = tree->getLeft(); else tree = NULL; delete nodeToDelete; } return tree; }  http://ecomputernotes.com

23. C++ code for delete else { // case 1 TreeNode<int>* nodeToDelete = tree; if( tree->getLeft() == NULL ) // will handle 0 children tree = tree->getRight(); else if( tree->getRight() == NULL ) tree = tree->getLeft(); else tree = NULL; delete nodeToDelete; } return tree; }  http://ecomputernotes.com

24. C++ code for delete else { // case 1 TreeNode<int>* nodeToDelete = tree; if( tree->getLeft() == NULL ) // will handle 0 children tree = tree->getRight(); else if( tree->getRight() == NULL ) tree = tree->getLeft(); else tree = NULL; delete nodeToDelete; } return tree; }  http://ecomputernotes.com

25. C++ code for delete TreeNode<int>* findMin(TreeNode<int>* tree) { if( tree == NULL ) return NULL; if( tree->getLeft() == NULL ) return tree; // this is it. return findMin( tree->getLeft() ); }  http://ecomputernotes.com

26. C++ code for delete TreeNode<int>* findMin(TreeNode<int>* tree) { if( tree == NULL ) return NULL; if( tree->getLeft() == NULL ) return tree; // this is it. return findMin( tree->getLeft() ); }  http://ecomputernotes.com

27. C++ code for delete TreeNode<int>* findMin(TreeNode<int>* tree) { if( tree == NULL ) return NULL; if( tree->getLeft() == NULL ) return tree; // this is it. return findMin( tree->getLeft() ); }  http://ecomputernotes.com

28. BinarySearchTree.h Let us design the BinarySearchTree class (factory). http://ecomputernotes.com

29. BinarySearchTree.h #ifndef _BINARY_SEARCH_TREE_H_ #define _BINARY_SEARCH_TREE_H_ #include <iostream.h> // For NULL // Binary node and forward declaration template <class EType> class BinarySearchTree;  http://ecomputernotes.com

30. BinarySearchTree.h #ifndef _BINARY_SEARCH_TREE_H_ #define _BINARY_SEARCH_TREE_H_ #include <iostream.h> // For NULL // Binary node and forward declaration template <class EType> class BinarySearchTree;  http://ecomputernotes.com

31. BinarySearchTree.h template <class EType> class BinaryNode { EType element; BinaryNode *left; BinaryNode *right; BinaryNode( const EType & theElement, BinaryNode *lt, BinaryNode *rt ) : element( theElement ), left( lt ), right( rt ) { } friend class BinarySearchTree<EType>; };  http://ecomputernotes.com

32. BinarySearchTree.h template <class EType> class BinaryNode { EType element; BinaryNode *left; BinaryNode *right; BinaryNode( const EType & theElement, BinaryNode *lt, BinaryNode *rt ) : element( theElement ), left( lt ), right( rt ) { } friend class BinarySearchTree<EType>; };  http://ecomputernotes.com

33. BinarySearchTree.h template <class EType> class BinaryNode { EType element; BinaryNode *left; BinaryNode *right; BinaryNode( const EType & theElement, BinaryNode *lt, BinaryNode *rt ) : element( theElement ), left( lt ), right( rt ) { } friend class BinarySearchTree<EType>; };  http://ecomputernotes.com

34. BinarySearchTree.h template <class EType> class BinaryNode { EType element; BinaryNode *left; BinaryNode *right; BinaryNode( const EType & theElement, BinaryNode *lt, BinaryNode *rt ) : element( theElement ), left( lt ), right( rt ) { } friend class BinarySearchTree<EType>; };  http://ecomputernotes.com

35. BinarySearchTree.h template <class EType> class BinarySearchTree { public: BinarySearchTree( const EType& notFound ); BinarySearchTree( const BinarySearchTree& rhs ); ~BinarySearchTree( ); const EType& findMin( ) const; const EType& findMax( ) const; const EType& find( const EType & x ) const; bool isEmpty( ) const; void printInorder( ) const; http://ecomputernotes.com

36. BinarySearchTree.h void insert( const EType& x ); void remove( const EType& x ); const BinarySearchTree & operator= ( const BinarySearchTree & rhs ); http://ecomputernotes.com

37. BinarySearchTree.h private: BinaryNode<EType>* root; // ITEM_NOT_FOUND object used to signal failed finds const EType ITEM_NOT_FOUND; const EType& elementAt( BinaryNode<EType>* t ); void insert(const EType& x, BinaryNode<EType>* & t); void remove(const EType& x, BinaryNode<EType>* & t); BinaryNode<EType>* findMin(BinaryNode<EType>* t); BinaryNode<EType>* findMax(BinaryNode<EType>* t); BinaryNode<EType>* find(const EType& x, BinaryNode<EType>* t ); void makeEmpty(BinaryNode<EType>* & t); void printInorder(BinaryNode<EType>* t); }; #endif http://ecomputernotes.com