Software Developer

You are given ‘N’ binary tree nodes numbered from 0 to N - 1 where node ‘i’ has two children LEFT_CHILD[i] and RIGHT_CODE[i]. Return ‘True’ if and only if all the given nodes form exactly one valid binary tree. If node ‘i’ has no left child then 'LEFT_CHILD[i]' will equal -1, similarly for the right child.

Example:

Let’s say we have n=4 nodes, 'LEFT_CHILD' = {1, -1, 3, -1} and 
RIGHT_CHILD = {2, -1, -1, -1}. So the resulting tree will look like this:

It will return True as there is only one valid binary tree and each node has only one parent and there is only one root.

You are given an integer 'H'. Your task is to count and print the maximum number of balanced binary trees possible with height 'H'.

The balanced binary tree is one in which, for every node, the difference between the left and right subtree heights is less than or equal to 1.

You have to print the answer with modulo 1e9+7.

For Example:

Input:
H = 2

Output: 
3

There will be a total 3 different balanced binary trees with height 2. 
One node as a root and other nodes on one of the two sides.
One with root and left subtree with one more node than right.
One with root and right subtree with one more node than left. 

You have been given an unsorted array ‘ARR’.

Your task is to sort the array in such a way that the array looks like a wave array.

Example:

If the given sequence ‘ARR’ has ‘N’ elements then the sorted wave array looks like - 
‘ARR[0] >= ARR[1]’ and ‘ARR[1] <= ARR[2]’
‘ARR[2] >= ARR[3]’ and ‘ARR[3] <= ARR[4]’
‘ARR[4] >= ARR[5]’ and ‘ARR[5] <= ARR[6]’  And so on.

Note:

1. ‘ARR[0]’ must be greater than or equal to ‘ARR[1]’.

2. There can be multiple arrays that look like a wave array but you have to return only one.

3. We have an internal function that will check your solution and return 'True' in case your array is one of the solutions otherwise return 'False'.

Explanation

The given array ‘ ARR = { 4, 3, 5, 2, 3, 1, 2 } ’
The below figure is a visual representation of the given ‘ARR’ and you can see we can express ‘ARR’ in a waveform array because 
4>3 and 3<5 
5>2 and 2<3
3>1 and 1<2
And it follows the condition of wave array.

Follow up:

Try to solve this problem in linear time complexity.

You are given a Binary Tree ‘root’. The given Binary Tree may or may not be a Binary Search Tree(BST) itself. Your task is to find the maximum sum of node values of any subtree that is a Binary Search Tree(BST).

Binary Search Tree is defined as follows:

1) If the left subtree exists it should contain only nodes with values less than the current node's value.

2) If the right subtree exists it should contain only nodes with values greater than the current node's value.

3) Both the left and right subtrees should also be Binary Search Tree.

Example :

For the above binary tree, the BST with the maximum possible sum is marked with RED colour, the sum of this BST is equal to 6.

You are given a Binary Search Tree (BST) and a target value ‘K’. Your task is to return true if there exist two nodes in the given BST such that the sum of their values is equal to the given target ‘K’, else return false.

A binary search tree (BST) is a binary tree data structure which has the following properties.

• The left subtree of a node contains only nodes with data less than the node’s data.

• The right subtree of a node contains only nodes with data greater than the node’s data.

• Both the left and right subtrees must also be binary search trees.

Note:

1. All the elements of the Binary Search Tree are unique.

2. You can’t use the same node value/element of BST twice.

For example:

tree: 8 5 10 2 6 -1 -1 -1 -1 -1 7 -1 -1
'K' = 13,

The nodes with values 8 and 5 as shown in the above figure gives sum equal to the given target 13. 

Therefore, the output will be “true” i.e it is possible to find a pair in the given BST having sum equal to ‘K’.

You are given an arbitrary binary tree, a node of the tree, and an integer 'K'. You need to find all such nodes which have a distance K from the given node and return the list of these nodes.

Distance between two nodes in a binary tree is defined as the number of connections/edges in the path between the two nodes.

Note:

1. A binary tree is a tree in which each node has at most two children. 
2. The given tree will be non-empty.
3. The given tree can have multiple nodes with the same value.
4. If there are no nodes in the tree which are at distance = K from the given node, return an empty list.
5. You can return the list of values of valid nodes in any order. For example if the valid nodes have values 1,2,3, then you can return {1,2,3} or {3,1,2} etc.

Example :

Consider this tree above. The target node is 5 and K = 3. The nodes at distance 1 from node 5 are {2}, nodes at distance 2 from node 5 are {1, 4} and nodes at distance 3 from node 5 are {6, 3}.

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