Software Engineer

You have been given a root node of the binary search tree and a positive integer value. You need to perform an insertion operation i.e. inserting a new node with the given value in the given binary search tree such that the resultant tree is also a binary search tree.

If there can be more than one possible tree, then you can return any.

Note :

A binary search tree is a binary tree data structure, with the following properties :

    a. The left subtree of any node contains nodes with a value less than the node’s value.

    b. The right subtree of any node contains nodes with a value equal to or greater than the node’s value.

    c. Right, and left subtrees are also binary search trees.
It is guaranteed that,

    d. All nodes in the given tree are distinct positive integers.

    e. The given BST does not contain any node with a given integer value.

Example, below the tree, is a binary search tree.

Below the tree is not a BST as node ‘2’ is less than node ‘3’ but ‘2’ is the right child of ‘3’, and node ‘6’ is greater than node ‘5’ but it is in the left subtree of node ‘5’.

Design a data structure that stores a mapping of a key to a given value and supports the following operations in constant time.

1. INSERT(key, value): Inserts an integer value to the data structure against a string type key if not already present. If already present, it updates the value of the key with the new one. This function will not return anything.

2. DELETE(key): Removes the key from the data structure if present. It doesn't return anything.

3. SEARCH(key): It searches for the key in the data structure. In case it is present, return true. Otherwise, return false.

4. GET(key): It returns the integer value stored against the given key. If the key is not present, return -1. 

5. GET_SIZE(): It returns an integer value denoting the size of the data structure. 

6. IS_EMPTY(): It returns a boolean value, denoting whether the data structure is empty or not. 

Note :

1. Key is always a string value.
2. Value can never be -1.

Operations Performed :

First(Denoted by integer value 1):  Insertion to the Data Structure. It is done in a pair of (key, value).

Second(Denoted by integer value 2):  Deletion of a key from the Data Structure.

Third(Denoted by integer value 3): Search a given key in the Data Structure.

Fourth(Denoted by integer value 4): Retrieve the value for a given key from the Data Structure.

Fifth(Denoted by integer value 5): Retrieve the size of the Data Structure.

Sixth(Denoted by integer value 6): Retrieve whether the Data Structure is empty or not.

Q: What is the most efficient way to store a sorted array in a tree?