Part A$-$ Consider a binary search tree $($BST$).$ Assume that the keys are integers and no value $($objects$)$ other than the key is stored in each node. By following the explanations and examples given in class, design an algorithm in pseudo$-$code for operation remove$($k$).$ Use java programming language, implement the BST ADT in a linked structure, along with the following operations: search, insert and remove.

Part B$-$ Implement the InOrder traversal strategy, which shows the keys of the BST in increasing order.

$$ Following the InOrder traversal strategy, write a program $($or a method$)$ that draws the BST and shows it on the screen $($either console or GUI screen is acceptable$).$

Part C$-$Insert $1,2,3,4,5,6,7,8,9,10,11,12,13,14,15$ in the tree $($in that order$).$ Show all keys in the tree $($for this and the following, use the InOrder traversal method you implemented in Part B$).$

$$ Perform search$(1)$ and search$(15)100,000$ times and record the CPU time taken by each of these.

$$ Remove key $5.$ Show all keys in Inorder traversal. Remove $15.$ Show all the keys in Inorder traversal. Remove $1.$ Show all the keys in Inorder traversal. Insert key $2.$ Show all keys in Inorder traversal.