Overlapping discs

Problem code: M5

All submissions for this problem are available.

The problem statement has been updated.

The time limit for this problem is now 5 seconds.

You are given n discs on plane, of the same radius (r=1). Output the area of the part of the plane which is covered by each disc.

Input

First, 1<=t<=10, the number of tests. Each testcase is of the following form: 1<=n<=100000, then n pairs of floating point coordinates follow: -1000<=xi,yi<=1000, representing the location of the i-th disc.

Output

For each testcase, output the total area covered by the intersection of all discs. Round the answer to 6 decimal digits after the point.

Example

Input:
1
2
0 0
0 1

Output:
1.228370
Author: admin
Date Added: 29-01-2010
Time Limit: 2 - 5 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TEXT, WSPC


Comments

Hi, I have some doubts. How

Aravind J @ 15 Apr 2010 10:35 PM

Hi,

I have some doubts.

How the overlapping pattern would be? Whether a third circle can overlap in the region where 2 circles already overlap?

Also.. Its is difficult to generalize the solution.. So it will be nice if we get sample output for atleast 3 circles.

There is no restraint on the

triplem @ 16 Apr 2010 02:48 AM

There is no restraint on the locations of the circles. The intersection could be formed by any number of them.

There is no need for additional test cases; the sample output is solely there to make sure the problem is understandable.

" output the total area

wolfdarrigan @ 4 Nov 2011 07:55 PM
" output the total area covered by the intersection of all discs" Is this asking for the total area of all intersections? (disc 1 overlaps 2, 2 overlaps 3, 3 does not overlap 1; area is 1-2 overlap + 2-3 overlap) OR Is this asking for the area of the region where EVER disc overlaps? (disc 1 overlaps 2, 2 overlaps 3, 3 does not overlap 1; area is 0)

There is ambiguity between

moawalling @ 29 Nov 2011 10:08 PM
There is ambiguity between the problem statement and the output statement. "Output the area of the part of the plane which is covered by each disc" is different from "output the total area covered by the intersection of all discs". Intersected area could be different from union area.

output should be the common

manisshhh @ 14 Mar 2012 12:11 AM
output should be the common area among all the disks.

SUCCESSFUL SUBMISSIONS FOR THIS PROBLEM:

HELP

Program should read from standard input and write to standard output. After you submit a solution you can see your results by clicking on the [My Submissions] tab on the problem page. Below are the possible results:

 

  • Accepted Your program ran successfully and gave a correct answer. If there is a score for the problem, this will be displayed in parenthesis next to the checkmark.
  • Time Limit Exceeded Your program was compiled successfully, but it didn't stop before time limit. Try optimizing your approach.
  • Wrong Answer Your program compiled and ran succesfully but the output did not match the expected output.
  • Runtime Error Your code compiled and ran but encountered an error. The most common reasons are using too much memory or dividing by zero. For the specific error codes see the help section.
  • Compilation Error Your code was unable to compile. When you see this icon, click on it for more information.

    • If you are still having problems, see a sample solution here.

CodeChef is a global programming communityCodeChef hosts online programming competitions