Chocolate Problem
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.
Input format :
The first line of input contains an integer ‘T’ denoting the number of test cases.
The next ‘2*T’ lines represent the ‘T’ test cases.
The first line of each test case contains two space-separated integers ‘N’ denoting the number of packets of chocolate and ‘M’ denotes the number of students.
The second line of each test case contains ‘N’ space-separated integers denoting the number of chocolate in each of ‘N’ packets.
Output Format :
For each test case, print the minimum difference of the chocolates contained in the packets distributed to the students.
Note :
You don't need to print anything, it has already been taken care of. Just implement the given function.
Constraints:
1 <= T <= 50
2 <= M <= N <= 10^4
1 <= CHOCOLATES[i] <= 10^9
Time Limit : 1 sec
CodingNinjas
author
2y
Recursion
The idea is that generate all the possible subsets of size ‘M’ and checks the minimum difference that can be possible from all subsets.
- This problem can be solved using recursion and the ide...read more
CodingNinjas
author
2y
Sliding Window
The idea is based on the observation that to minimize the difference between a maximum number of chocolate in a packet and a minimum number of chocolate in the packet is that, always cho...read more
Anonymous
3mo
15
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