System Engineer

Given an array/list of integer numbers 'CHOCOLATES' of size 'N', where each value of the array/list represents the number of chocolates in the packet. There are ‘M’ number of students and the task is to distribute the chocolate to their students. Distribute chocolate in such a way that:

1. Each student gets at least one packet of chocolate.

2. The difference between the maximum number of chocolate in a packet and the minimum number of chocolate in a packet given to the students is minimum.

Example :

Given 'N' : 5 (number of packets) and 'M' : 3 (number of students)

And chocolates in each packet is : {8, 11, 7, 15, 2}

All possible way to distribute 5 packets of chocolates among 3 students are -

( 8,15, 7 ) difference of maximum-minimum is ‘15 - 7’ = ‘8’
( 8, 15, 2 ) difference of maximum-minimum is ‘15 - 2’ = ‘13’ 
( 8, 15, 11 ) difference of maximum-minimum is ‘15 - 8’ = ‘7’
( 8, 7, 2 ) difference of maximum-minimum is ‘8 - 2’ = ‘6’
( 8, 7, 11 ) difference of maximum-minimum is ‘11 - 7’ = ‘4’
( 8, 2, 11 ) difference of maximum-minimum is ‘11 - 2’ = ‘9’
( 15, 7, 2 ) difference of maximum-minimum is ‘15 - 2’ = 13’
( 15, 7, 11 ) difference of maximum-minimum is ‘15 - 7’ = ‘8’
( 15, 2, 11 ) difference of maximum-minimum is ‘15 - 2’ = ‘13’
( 7, 2, 11 ) difference of maximum-minimum is ‘11 - 2’ = ‘9’

Hence there are 10 possible ways to distribute ‘5’ packets of chocolate among the ‘3’ students and difference of combination (8, 7, 11) is ‘maximum - minimum’ = ‘11 - 7’ = ‘4’ is minimum in all of the above.

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.

There are ‘N’ cities in Pokeland, and they are connected by ‘N-1’ roads. It is possible to reach from any city to any other city and there is a unique path between each pair of cities.

Each city has one Pokemon represented by an integer between 1 and 10^9. In each city. Given queries in the form of pairs of cities ‘U’ and ‘V’, find the number of Pokemon Ash catches while traveling from city ‘U’ to ‘V’. If he already has a Pokemon ‘X’ and he comes across it again, he does NOT catch it.

Note: Each query is independent, that is, he starts each query with zero Pokemon.

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