SDE - 1

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”.

You are given an array ‘ARR’ of length ‘N’. There are two operations, ‘FIRST_SUM’ and ‘LAST_SUM’ for every index ‘i’ (1 <= i <= N) in the array,

i) FIRST_SUM(i) calculates the sum of first i numbers.

ii) LAST_SUM(i) calculates the sum of last N-i+1 numbers.

Also for every ‘i’, SPECIAL_SUM(i) can be calculated as:

SPECIAL_SUM(i) = FIRST_SUM(i) + LAST_SUM(i)

Your task is to return the minimum SPECIAL_SUM for 0 <= i <= N - 1.

For example:

Given ‘N’ = 4 and ‘ARR’ = [1, 2, 3, 4].
Then the minimum special sum will be 5 for i = 0 (0-based indexing), which is (1 + 4) = 5.Sum of 1 integer from beginning and end.
For i = 1 it will be (1 + 2) + (3 + 4) = 10
For i = 2 it will be (1 + 2 + 3) + (2 + 3 + 4) = 15
For i = 3 it will be (1 + 2 + 3 + 4) + (1 + 2 + 3 + 4) = 20
All of which are greater than 5.  

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