MTRIAREA - Maximum Triangle Area

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Given n distinct points on a plane, your task is to find the triangle that have the maximum area, whose vertices are from the given points.

 

Input

 

The input consists of several test cases. The first line of each test case contains an integer n, indicating the number of points on the plane. Each of the following n lines contains two integer xi and yi, indicating the ith points. The last line of the input is an integer −1, indicating the end of input, which should not be processed. You may assume that 1 ≤ n ≤ 50000 and −10^4 ≤ xi, yi ≤ 10^4 for all i = 1 . . . n.

Sample Input
3
3 4
2 6
2 7
5
2 6
3 9
2 0
8 0
6 5
-1

Output

 

For each test case, print a line containing the maximum area, which contains two digits after the decimal point. You may assume that there is always an answer which is greater than zero.

Sample output
0.50
27.00


hide comments
anhkhoa: 2016-05-20 11:40:36

that sample output should be 1.50 and 15.00, right ?

Naman Goyal: 2014-07-26 10:57:21

Don't use float, you'll get WA.

hit_code: 2014-06-13 17:57:17

some more test case?

:D: 2012-11-16 07:10:37

Yes, they seem to rule each other out. Well, strictly speaking 1 <= n <= 50000, doesn't require some n to be 1 or 2, but ranges shouldn't be that unnecessary invalid.

uberness132: 2012-11-16 03:13:50

how can n < 3? "You may assume that 1 ≤ n ≤ 50000 " and "You may assume that there is always an answer which is greater than zero."

Cong Liu: 2010-11-24 09:46:44

My algo is O(n) which I think should be right but not yet proofed.

Last edit: 2009-04-15 15:01:38
[Trichromatic] XilinX: 2010-11-24 09:46:44

O(n^2)(Of course, with many optimizations) CAN get Accepted!

Last edit: 2009-03-26 03:01:49

Added by:~!(*(@*!@^&
Date:2009-02-23
Time limit:0.170s-0.712s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS PERL 6
Resource:Pre Shanghai 2004