System Engineer

There is a wedding ceremony at NinjaLand. The bride and groom want everybody to play a game and thus, they have blindfolded the attendees. The people from the bride’s side are holding odd numbers and people from the groom’s side are holding the even numbers. For the game to start quickly, all the bride’s side people should come first, followed by the groom’s side people in the same order.

The attendees of the wedding with their numbers are given in the form of a Singly Linked List, arranged randomly.

A singly linked list is a type of linked list that is unidirectional; that is, it can be traversed in only one direction from head to the last node (tail).

Example:

The attendees holding numbers from 1, 4, 3 are shown: 

As the organizers are busy, you have to arrange all the people by arranging the bride’s side people first followed by the groom’s side people sequentially.

Note:

For the above example 1 -> 4 -> 3, 1 -> 3 -> 4 is the only correct answer, i.e nodes should be grouped sequentially. Hence, 3 -> 1 -> 4 is the wrong answer as we have to preserve the same order.

You are given an integer ‘N’ and there is a hidden number in the range [0, N] which you have to guess. You are also given a function higherLower(k) to help you in guessing the number. The ‘higherLower(k)’ will return -1, 0 or 1, depending on if ‘k’ is smaller, equal or greater than the hidden number.

For Example:

You are given ‘N’ = 20, and the hidden number is ‘8’. You won't have access to the hidden number and you will have to guess the number ‘8’ using the higherLower function and print it.

You are given an array/list ‘BINARYNUMS’ that consists of ‘N’ distinct strings which represent all integers from 0 to N in binary representation except one integer. This integer between 0 to ‘N’ whose binary representation is not present in list ‘BINARYNUMS’ is called ‘Missing Integer’.

Your task is to find the binary representation of that ‘Missing Integer’. You should return a string that represents this ‘Missing Integer’ in binary without leading zeros.

Note

1. There will be no leading zeros in any string in the list ‘BINARYNUMS’.

Example:

Consider N = 5 and the list ‘binaryNums’=  [“0”, “01”, “010”, “100”, “101”].  This list consists of the binary representation of numbers [0, 1, 2, 4, 5]. Clearly, the missing number is 3 and its binary representation will be “11”. So you should return string “11”.