SPOJ.com - Problem AGGRCOW

AGGRCOW - Aggressive cows

#binary-search

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:

Output:

Output details:

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

Submit solution!

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	kapilgm: 2018-03-27 08:49:43 AC in 12th go!! I used my own implementation of quicksort, which gave TLE. Using qsort of stdlib.h solved my problem.
	yaswanth desu: 2018-03-21 15:19:32 Hello Everyone, I have figured out a DP solution for this problem which is working for all available test cases from spojtoolkit. but i have got Time Limit Exceeded. For my dp case, i used a map for the cache purpose. Here is the code https://ideone.com/1IC8BL Can any one check and help me regarding how to make much more efficient to run in 2sec.
	amitboss: 2018-03-16 18:54:10 good problem , 100th on spoj
	prasoon_07: 2018-03-14 03:51:34 topcoder is awesome :)
	kkislay20: 2018-03-12 15:14:05 This was one of the finest problems I had come across on spoj. It gave me more insights for binary search, topcoder and quora helped a lot.
	zephyr_96: 2018-02-26 14:23:56 @shobit1998, It works with high=mid-1 too. Maybe there is some fault in your implementation.
	shobhit1998: 2018-02-14 16:32:31 in else part of binary search why does high = mid and high = mid-1 make a difference in answer
	rob_in_1: 2018-01-22 12:43:07 Last edit: 2018-02-28 19:52:33
	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!

Submit solution!

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