create the remove method for a threaded binary search tree. here is a description for a binary search tree: Since a binary search tree with N nodes has N + 1 NULL pointers, half the space allocated in a binary search tree for pointer information is wasted. Suppose that if a node has a NULL left child, we make its left child pointer link to its inorder predecessor, and if a node has a NULL right child, we make its right child pointer link to its inorder successor. This is known as a threaded tree and the extra links are called threads. here is my .h file: #ifndef THREADEDBST_H #define THREADEDBST_H #include "Node.cpp" class ThreadedBST { private: Node* root; public: /** * Constructs an empty ThreadedBST object. * Pre-condition: None. * Post-condition: An empty ThreadedBST object is created with a null root. */ ThreadedBST(); /** * Destroys the ThreadedBST object and frees the associated memory. * Pre-condition: None. * Post-condition: The ThreadedBST object is destroyed, and all the associated memory is freed. */ ~ThreadedBST(); /** * Inserts a new key into the threaded binary search tree. * Pre-condition: The key is not already present in the threaded binary search tree. * Post-condition: The key is inserted into the threaded binary search tree in the correct position. */ void insert(int key); /** * Removes a key from the threaded binary search tree. * Pre-condition: The key is present in the threaded binary search tree. * Post-condition: The key is removed from the threaded binary search tree if found, and the tree is modified accordingly. */ void remove(int key); /** * Displays the threaded binary search tree in a human-readable format. * Pre-condition: None. * Post-condition: The threaded binary search tree is displayed on the screen. */ void display(); /** * Performs an inorder traversal of the threaded binary search tree. * Pre-condition: None. * Post-condition: The keys of the threaded binary search tree are printed in ascending order. */ void inorder(); private: /** * Finds the successor of a given node in the threaded binary search tree. * Pre-condition: The given node is not null. * Post-condition: Returns the successor node of the given node, or null if it doesn't have a successor. */ Node* findSuccessor(Node* node); /** * Finds the parent of the successor of a given node in the threaded binary search tree. * Pre-condition: The given node is not null. * Post-condition: Returns the parent node of the successor of the given node, or null if it doesn't have a successor. */ Node* findSuccessorParent(Node* node); /** * Copy constructor for the ThreadedBST class. * Pre-condition: The other ThreadedBST object is valid. * Post-condition: A deep copy of the other ThreadedBST object is created. */ ThreadedBST(const ThreadedBST& other); /** * Recursive helper function to copy a subtree rooted at the given node. * Pre-condition: The given node is not null. * Post-condition: Returns a deep copy of the subtree rooted at the given node. */ Node* copyTree(Node* node); }; #endif // THREADEDBST_H
create the remove method for a threaded binary search tree. here is a description for a binary search tree:
Since a binary search tree with N nodes has N + 1 NULL pointers, half the space allocated in a binary search tree for pointer information is wasted. Suppose that if a node has a NULL left child, we make its left child pointer link to its inorder predecessor, and if a node has a NULL right child, we make its right child pointer link to its inorder successor. This is known as a threaded tree and the extra links are called threads.
here is my .h file:
#ifndef THREADEDBST_H
#define THREADEDBST_H
#include "Node.cpp"
class ThreadedBST {
private:
Node* root;
public:
/**
* Constructs an empty ThreadedBST object.
* Pre-condition: None.
* Post-condition: An empty ThreadedBST object is created with a null root.
*/
ThreadedBST();
/**
* Destroys the ThreadedBST object and frees the associated memory.
* Pre-condition: None.
* Post-condition: The ThreadedBST object is destroyed, and all the associated memory is freed.
*/
~ThreadedBST();
/**
* Inserts a new key into the threaded binary search tree.
* Pre-condition: The key is not already present in the threaded binary search tree.
* Post-condition: The key is inserted into the threaded binary search tree in the correct position.
*/
void insert(int key);
/**
* Removes a key from the threaded binary search tree.
* Pre-condition: The key is present in the threaded binary search tree.
* Post-condition: The key is removed from the threaded binary search tree if found, and the tree is modified accordingly.
*/
void remove(int key);
/**
* Displays the threaded binary search tree in a human-readable format.
* Pre-condition: None.
* Post-condition: The threaded binary search tree is displayed on the screen.
*/
void display();
/**
* Performs an inorder traversal of the threaded binary search tree.
* Pre-condition: None.
* Post-condition: The keys of the threaded binary search tree are printed in ascending order.
*/
void inorder();
private:
/**
* Finds the successor of a given node in the threaded binary search tree.
* Pre-condition: The given node is not null.
* Post-condition: Returns the successor node of the given node, or null if it doesn't have a successor.
*/
Node* findSuccessor(Node* node);
/**
* Finds the parent of the successor of a given node in the threaded binary search tree.
* Pre-condition: The given node is not null.
* Post-condition: Returns the parent node of the successor of the given node, or null if it doesn't have a successor.
*/
Node* findSuccessorParent(Node* node);
/**
* Copy constructor for the ThreadedBST class.
* Pre-condition: The other ThreadedBST object is valid.
* Post-condition: A deep copy of the other ThreadedBST object is created.
*/
ThreadedBST(const ThreadedBST& other);
/**
* Recursive helper function to copy a subtree rooted at the given node.
* Pre-condition: The given node is not null.
* Post-condition: Returns a deep copy of the subtree rooted at the given node.
*/
Node* copyTree(Node* node);
};
#endif // THREADEDBST_H
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