Kth Largest Element in BST

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Problem statement

Given the root node of a Binary Search Tree (BST), you have to return the Kth largest element in the BST.

For Example:

If K is 4 and the tree is depicted by the following image then,

The 4th largest element in the given BST is 1. So the output will be 1.

Follow-up :

 Try to do it in O(1) space without using recursion.

Detailed explanation ( Input/output format, Notes, Images )

Input Format :

The first line contains an Integer 'T' which denotes the number of test cases or queries to be run. Then the test cases follow.

The first line of each test case contains the elements of the tree in the level order form separated by a single space.
If any node does not have a left or right child, take -1 in its place. Refer to the example below.

The second line of each test case contains a single integer ‘K’, denoting ‘K’ as explained in the problem statement.

Example :

Elements are in the level order form. The input consists of values of nodes separated by a single space in a single line. In case a node is null, we take -1 in its place.

For example, the input for the tree depicted in the below image would be :

1
2 3
4 -1 5 6
-1 7 -1 -1 -1 -1
-1 -1

Explanation :
Level 1 :
The root node of the tree is 1

Level 2 :
Left child of 1 = 2
Right child of 1 = 3

Level 3 :
Left child of 2 = 4
Right child of 2 = null (-1)
Left child of 3 = 5
Right child of 3 = 6

Level 4 :
Left child of 4 = null (-1)
Right child of 4 = 7
Left child of 5 = null (-1)
Right child of 5 = null (-1)
Left child of 6 = null (-1)
Right child of 6 = null (-1)

Level 5 :
Left child of 7 = null (-1)
Right child of 7 = null (-1)

The first not-null node (of the previous level) is treated as the parent of the first two nodes of the current level. The second not-null node (of the previous level) is treated as the parent node for the next two nodes of the current level and so on.

The input ends when all nodes at the last level are null (-1).

Note: The above format was just to provide clarity on how the input is formed for a given tree. 

The sequence will be put together in a single line separated by a single space. Hence, for the above-depicted tree, the input will be given as:

1 2 3 4 -1 5 6 -1 7 -1 -1 -1 -1 -1 -1

Output Format :

For each test case, print a single integer value representing the Kth largest value of the given BST.

Output for each test case will be printed in a separate line.

Note:

You are not required to print anything, it has already been taken care of. Just implement the function.

Constraints :

1 <= T <= 100
1 <= N <= 5 * 10^3
1 <= K <= N
0 <= X <= 10^9

Where ‘X’ is the value at the node and ‘N’ is the no. of nodes in given BST.

Time Limit: 1 sec.

Sample Input 1 :

2
2 1 4 -1 -1 3 -1 -1 -1
4
2 1 7 -1 -1 3 -1 -1 4 -1 -1
3

Sample Output 1 :

1
3

Explanation For Sample Input 1 :

For First Case - Same as explained in above example.

For the second case - 
K is 3 and the tree is depicted by the following image then,

The 3rd largest element in the given BST is 3. So the output will be 3.

Sample Input 2 :

2
4 3 -1 2 -1 1 -1 -1 -1
1
3 1 8 -1 2 -1 -1 -1 -1
3

Sample Output 2 :

4
2

Console