AGGRCOW - Aggressive cows


Farmer John has built a new long barn, with N (2 <= N <= 100,000) stalls. The stalls are located along a straight line at positions x1,...,xN (0 <= xi <= 1,000,000,000).

His C (2 <= C <= N) cows don't like this barn layout and become aggressive towards each other once put into a stall. To prevent the cows from hurting each other, FJ wants to assign the cows to the stalls, such that the minimum distance between any two of them is as large as possible. What is the largest minimum distance?

Input

t – the number of test cases, then t test cases follows.
* Line 1: Two space-separated integers: N and C
* Lines 2..N+1: Line i+1 contains an integer stall location, xi

Output

For each test case output one integer: the largest minimum distance.

Example

Input:

1
5 3
1
2
8
4
9

Output:

3

Output details:

FJ can put his 3 cows in the stalls at positions 1, 4 and 8,
resulting in a minimum distance of 3.


hide comments
garrykevin: 2018-01-09 13:10:51

For those who are wondering about , why the cows should be placed in positions 1 4 8. Why couldnt it be 1 4 9 since it indicates largest distance as possible.

" If you are wondering why 1,4,8 instead of 1,4,9 then do not. For me its actually a subtle hint for applying binary search. You will understand it when you apply the algo.
Also if you are confused by the "minimum largest" terminology think of it as this:
if you put cows at 1,2,8. Distance btw stalls is 1, 6 resp. but if you keep at 1,4,8 distance is 3, 4. In first case minimum distance is 1 while 2nd case its 3. You can never put cows that gives a minimum that is larger than 3 i.e. distance cannot be 4,5 or 6,7 (where mins 4 and 6 > 3) so the largest minimum is 3. Just keep that in mind and Farmer John will be happy with you! ;D "

source:
https://www.commonlounge.com/discussion/
2be51c96907e4449a8cd25dd557a2067/all/ba989a8548c8480b8c174112395e8900#_=_

Last edit: 2018-01-10 15:04:39
kkarthikeyan98: 2018-01-08 17:29:49

In the example test case, why the cows should be placed in positions 1 4 8. Why couldnt it be 1 4 9 since it indicates largest distance as possible. Please help!

anup2raj: 2018-01-04 09:00:11

good one

Last edit: 2018-01-04 09:01:21
code0monkey1: 2017-12-27 10:05:52

Struggled with it for almost A FULL MONTH ( On and Off ). Did many similar problems to get a hang of the logic before approaching the question again ( Read the topcoder binary search tutorial ).

Finally solved the question myself before the year ended !! :D

This stack overflow post post provides a more general ( and clearer ) way of looking at this problem ( and other problems like this ) : https://stackoverflow.com/questions/28095662/algorithm-help-how-to-divide-array-into-n-segments-with-least-possible-largest

This quora link is totally dedicated to the Aggressive cows problem : https://www.quora.com/What-is-the-correct-approach-to-solve-the-SPOJ-problem-Aggressive-cow

Similar problems you guys might want to try ( apart from the FairWorkLoad problem mentioned in the topcoder tutorial ) :
https://www.codechef.com/problems/PRPR5
https://articles.leetcode.com/the-painters-partition-problem/
https://practice.geeksforgeeks.org/problems/allocate-minimum-number-of-pages/0

Last edit: 2017-12-27 10:07:50
true_idiot: 2017-12-20 14:16:02

took 2 whole days for me to come up with the solution!
tpcoder is lit af!!! :D

v_pp_27: 2017-12-03 19:40:13

Topcoder tutorial on binary search helped

Radha Krishna: 2017-11-24 13:52:50

any similar kind of problems available out there to get the practice?

Shubham Aggarwal: 2017-11-20 22:18:05

I tested it on a lot of cases, it runs fine, but here I'm getting NZEC in python

Last edit: 2017-11-21 06:10:01
balakrishna21: 2017-11-19 06:43:57

could any one give any some more test cases for this "AGGRCOW - Aggressive cows
" problem

themast3r: 2017-11-01 16:59:04

Possibly the finest problem I solved on SPOJ.

Last edit: 2017-11-01 16:59:18

Added by:Roman Sol
Date:2005-02-16
Time limit:2s
Source limit:10000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:USACO February 2005 Gold Division