System Engineer

There is an array ‘A’ of length ‘N’. You can perform the following operation on the array, select ‘i’, ‘1< i <= N - 1’ and replace ‘A[i]’ with ‘A[i] | A[i - 2]’, where ‘|’ represents bitwise OR operation.

Your task is to find the maximum element ‘X’ you can obtain by operating zero or more times.

Example:

‘A’ = [1, 3, 2, 5]

A[3] = A[3] or A[1] = 3 | 5 = 7    
‘A’ = [1, 3, 2, 7]
Hence the maximum element we can obtain is 7.
Therefore, the answer is 7.

Given a string "pattern", which contains only two types of characters ‘(’, ‘)’.

Your task is to find the minimum number of parentheses either ‘(’, ‘)’ we must add the parentheses in string ‘pattern’ and the resulted string is valid.

Condition for valid string-

Every opening parenthesis ‘(’ must have a correct closing parenthesis ‘)’.

Example - ‘(()(()))’, ‘()()()’, ‘((()))’ are valid string, and ‘(((’, ‘(()’, ‘)(())’ are invalid string.

Note:

1. You are not required to print the output explicitly, it has already been taken care of. Just implement the function and return the minimum number of parentheses required to make a string valid.

You have been given the preorder and inorder traversal of a binary tree. Your task is to construct a binary tree using the given inorder and preorder traversals.

Note:

You may assume that duplicates do not exist in the given traversals.

For example :

For the preorder sequence = [1, 2, 4, 7, 3] and the inorder sequence = [4, 2, 7, 1, 3], we get the following binary tree.