Secret Room

Hmm, now why would someone break into a mundane software company?
After looking at the building blueprints (to place cameras), you've noticed the suspicious room at the top.
Investigating a little, you find no visible entrance - but there's a strange humming noise emanating from the room.

Upon asking your manager you are ushered into the conference room where a confidential meeting seems to be taking place.
It seems that this secret room holds a certain treasure: the thishasbeencensored
Now, they want to secure this room with lethal green laser beams.
The lasers are very thin, but they have the ability to burn a hole through an intruder instantly.

The company engineers have built several laser designs, and they'd like to choose the best one.
To make a laser design effective, they want to minimize the freedom a thief would have while in the room.
As an estimate, they'd like to find the largest circle that could fit anywhere without hitting a laser.
Now, doing this by hand would be quite tedious - so write a program to do it for them!


Two positive integers, W and H (W,H ≤ 10,000) representing the width and height of the room.
Then, an integer N ≤ 50, representing the number of laser beams.
For each laser beam:
4 integers, (x1,y1),(x2,y2) representing one laser beam.
A laser beam will travel between those two points (they are guaranteed to be on the wall).
The room will be modeled as a 2-D grid - (0,0) being the lower left and (W,H) the upper right.


The radius of the largest circle that could fit without being cut by lasers.
Your answer should be correct to 4 decimal places.

Sample Input

7 7
0 0 7 7
0 7 7 0
0 6 7 2
2 0 2 7
5 0 5 7

Sample Output


The exact answer is 3.5(√2 - 1) = 1.449747...
(Try calculating it! Please don't try coordinate geometry :P)


All Submissions
Best Solutions

Point Value: 25 (partial)
Time Limit: 2.00s
Memory Limit: 16M
Added: Feb 15, 2009
Author: hansonw1

Languages Allowed:

Comments (Search)

Actually it was a bug - when I resubmitted test data the old submission didn't get updated properly.

Parallel lines are from HELL.

That's why you use the PUGA (Plachta Universal Geometry Algorithm) for all geometry problems.

If it helps, you can use this python program to draw test cases. (I used this to check my test data)
(It is pretty picky with how you input your data - use the same format as the sample input)

import Tkinter, os 
from Tkinter import *

W, H = map(int, raw_input("Width and height? (W H) ").split(" "))

wscale = 1. * W / max(W, H) * 800
hscale = 1. * H / max(W, H) * 800

def pt(x, y):
x = 5 + 1. * x / W * wscale
y = 5 + hscale - 1. * y / H * hscale
return x,y

root = Tk()

canvas = Canvas(root, width=wscale+10, height=hscale+10)

canvas.create_line(pt(0,0), pt(0,H))
canvas.create_line(pt(0,H), pt(W,H))
canvas.create_line(pt(W,H), pt(W,0))
canvas.create_line(pt(W,0), pt(0,0))

N = int(raw_input("Number of lines? (N) "))
for i in range(N):
x1,y1,x2,y2 = map(int, raw_input("Line: (x1 y1 x2 y2) ").split(" "))
canvas.create_line(pt(x1,y1), pt(x2,y2), fill="red")

#If you want, you can draw a circle to see if it lines up
sz = float(raw_input("Radius of the circle? (R) "))

x, y = map(float, raw_input("Centre of the circle (x y)? ").split(" "))
canvas.create_oval(pt(x-sz,y-sz), pt(x+sz,y+sz))