This C++ project provides an implementation of a Binary Search Tree (BST) data structure with a variety of operations such as insert, search, remove, select, split, and join. It also includes a unique function insert_random that inserts nodes randomly.

The code contains the following functions:

• fix_size(Node *T): Updates the size of a node based on the number of its child nodes.
• insert(Node *T, int k): Inserts a node with key k into the BST.
• inorder_traversal(Node *T): Returns a vector of key values from an inorder traversal of the BST.
• find(Node *T, int k): Searches for a node with key k in the BST and returns it if found.
• select(Node *T, int r): Returns a node of rank r in the BST.
• join(Node *L, Node *R): Joins two trees, where all keys in L are less than or equal to keys in R.
• remove(Node *T, int k): Removes a node with key k from the BST.
• **split(Node *T, int k, Node **L, Node R): Splits the tree T into two trees L and R based on key k.
• insert_random(Node *T, int k): Inserts a node with key k into the BST at a random position.
• printVector(vector v): Prints the elements of a vector.

You can compile the program with a C++ compiler, e.g., g++ or clang++. The main function is currently commented out, but it contains a series of tests that you can use to verify the functionality of the BST operations.

Uncomment the main function and then compile and run the program with:

$ g++ -o bst binarySearchTree.cpp
$ ./bst