System Engineer

Given a binary tree having a positive integer written on each of its nodes. Your task is to find the vertical sum of node values i.e. the sum of nodes that can be connected by a vertical line.

A binary tree is a tree in which each parent node has at most two children.

You are required to print the sum along vertical lines from the leftmost node and moving to the rightmost node.

For Example :

Consider the following Binary Tree:

So the final answer is
12 9 11 6

You are given two strings 'str1' and 'str1'.

You have to tell whether these strings form an anagram pair or not.

The strings form an anagram pair if the letters of one string can be rearranged to form another string.

Pre-requisites:

Anagrams are defined as words or names that can be formed by rearranging the letters of another word. Such as "spar" can be formed by rearranging letters of "rasp". Hence, "spar" and "rasp" are anagrams. 

Other examples include:

'triangle' and 'integral'
'listen' and 'silent'

Note:

Since it is a binary problem, there is no partial marking. Marks will only be awarded if you get all the test cases correct. 

You are given an N * N binary matrix 'MAT'. You can do two operations in the matrix:

i) Swap any two rows.
ii) Swap any two columns. 

Your task is to find the minimum number of operations needed to convert this matrix into a chessboard matrix.

If the task is impossible print -1.

Note:

A chessboard matrix is a binary matrix where there are no two 0’s and no two 1’s who are adjacent to each other.

For example:

[ [1, 0], [0, 1] ] and [ [0, 1], [1, 0] ]  are chessboard matrix whereas [ [1,0], [1, 1] ] isn’t.

A Derangement is a permutation of ‘N’ elements, such that no element appears in its original position. For example, an instance of derangement of {0, 1, 2, 3} is {2, 3, 1, 0}, because 2 present at index 0 is not at its initial position which is 2 and similarly for other elements of the sequence.

Given a number ‘N’, find the total number of derangements possible of a set of 'N’ elements.

Note:

The answer could be very large, output answer %(10 ^ 9 + 7).

You are given an array 'arr' of length 'n', consisting of integers.

A subarray is a contiguous segment of an array. In other words, a subarray can be formed by removing 0 or more integers from the beginning and 0 or more integers from the end of an array.

Find the sum of the subarray (including empty subarray) having maximum sum among all subarrays.

The sum of an empty subarray is 0.

Example :

Input: 'arr' = [1, 2, 7, -4, 3, 2, -10, 9, 1]

Output: 11

Explanation: The subarray yielding the maximum sum is [1, 2, 7, -4, 3, 2].

You are given an array/list of ‘N’ integers. You are supposed to return the maximum sum of the subsequence with the constraint that no two elements are adjacent in the given array/list.

Note:

A subsequence of an array/list is obtained by deleting some number of elements (can be zero) from the array/list, leaving the remaining elements in their original order.