Cognitive AI Manager

Ninja is fond of sequences. He has a set of numbers and wants to make minimum decreasing subsequences such that all numbers are part of exactly one subsequence. Can you help Ninja with this challenge?

You are given an array ‘ARR’ having ‘N’ elements.Your task is to divide all ‘N’ elements of the array into a minimum number of strictly decreasing subsequences. Each number can be in one subsequence only. Find the minimum number of such strictly decreasing subsequences.

For Example

If 'ARR' is [4,2,1,3] ,it can be splitted into two subsequences as [4,2,1] , [3] or [4,3],[2,1].  

You are given an array 'a' of size 'n'.

Print the Next Greater Element(NGE) for every element.

The Next Greater Element for an element 'x' is the first element on the right side of 'x' in the array, which is greater than 'x'.

If no greater elements exist to the right of 'x', consider the next greater element as -1.

For example:

Input: 'a' = [7, 12, 1, 20]

Output: NGE = [12, 20, 20, -1]

Explanation: For the given array,

- The next greater element for 7 is 12.

- The next greater element for 12 is 20. 

- The next greater element for 1 is 20. 

- There is no greater element for 20 on the right side. So we consider NGE as -1.

Given a binary tree having ‘N’ number of nodes. Your task is to find the sum of all left nodes present in the input binary tree. That is, you need to take the sum of all nodes which are the left child of some node.

Note :

1. A binary tree is a tree in which each node can have at most two children. 
2. The given tree will be non-empty i.e the number of non-NULL nodes will always be greater than or equal to 1.
3. Multiple nodes in the tree can have the same values, all values in the tree will be positive.

You have been given a Binary Search Tree of integers. You are supposed to convert it to a greater sum tree such that the value of every node in the given BST is replaced with the sum of the values of all the nodes which are greater than the value of the current node in the tree.

A Binary Search Tree is a tree, whose internal nodes each store a value greater than all the values in the node's left subtree and less than those in its right subtree.

Note :

You need to modify the given tree only. You are not allowed to create a new tree.

For example:

For the given binary search tree

11 will be replaced by {15 + 29 + 35 + 40}, i.e. 119.
2 will be replaced by {7 + 11 + 15 + 29 + 35 + 40}, i.e. 137.
29 will be replaced by {35 + 40}, i.e. 75.
1 will be replaced by {2 + 7 + 11 + 15 + 29 + 35 + 40}, i.e. 139.
7 will be replaced by {11 + 15 + 29 + 35 + 40}, i.e. 130.
15 will be replaced by {15 + 29 + 35 + 40}, i.e. 104.
40 will be replaced by 0 {as there is no node with a value greater than 40}.
35 will be replaced by {40}, i.e. 40.

You have been given a Binary Tree of integers. You are supposed to return the level order traversal of the given tree.

For example:

For the given binary tree

The level order traversal will be {1,2,3,4,5,6,7}.

Given a binary tree and the value of two nodes, find the distance between the given two nodes of the Binary Tree.

Distance between two nodes is defined as the minimum number of edges in the path from one node to another.