# CIRKILL - Non-official editorial describing my approach

@bruno: good work man, keep it up

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This solution looks good.

I would like to show my approach.

Equn. of circle passing through 3 points using System of Circles:

When P(x1, y1), Q(x2, y2) and R(x3, y3) are the points:

Equn. of PQ: L: (y-y2 / x-x2) - (y1-y2 / x1-x2) = 0

Equn of Circle with PQ as diameter: C: (x-x1)(x-x2) + (y-y1)(y-y2) = 0

System of circles through the intersection of C and L:

C + kL = 0

=> k = -C/L (if L equals 0 then k = C)

substitute R in C and L to get k.

Now, you get the equation of Circle as C + kL = 0

For any other value D(x, y) (call this guy Ash).

put D in C + kL = 0
if the value is negative (inside the circle) or zero (on the circle) Ash gets killed.

For this approach, we need 4 points P, Q, R => Team Rocket, D => Ash

For each P, Q, R iterate D (find positions for Ash that gets him killed).

Got this idea form here http://www.qc.edu.hk/math/Advanced%20Level/circle%20given%203%20points.htm (method 5).

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Good Work! You should remove the tag ājul13ā, which will be removed anyways by the admins some time later. The tag is reserved for editorials.

I think that the tag jul13 is reserved for all questions related to the contestā¦ But, I can also easily remove it

I can recognize some mathematical expressions there very similar to the ones I have used yes It seems you also used the 3 points of the triangle and possibly exploited some mathematical and/or geometrical facts that I havenāt used! Nontheless, thanks for showing me a solution without any divisions I was curious during contest to see how this was done and now I know

@vineetpaliwal : I saw your solution and I myself employed a similar kind of approach but the center coordinates were being computed differently if the order of points was changed.

Hello @sanchit_h, Yes, after contest I was also told that general equation of circle could be used in the solution, but, I couldnt remember Cramerās rule at the time So I ended up using this more geometric approach :(( I still have much, much to learnā¦ Thatās why I am here for Thanks for you explanation!

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Thatās what I did. Great & simple approach, isnāt it?

@kuruma Awesome work . Really appreciate your time and dedication to help fellow coders. Keep up the good work buddy !!

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@ani94, As I said before, itās really a pleasure to be able to learn and grow up as a coder with this community and I hope I can stick around for many years to come

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@vpyati, Thank you very much!! It means a lot to me that people appreciate my work here as a member of Codechef community and if I managed to inspire at least one person with my work, then I am really, really happy!!

Thank you very much @i_wanna_rokk, I always try to give my best in everything and if its something I love, like Algorithms, even more

But, above all I am here to learn

Best regards,
Bruno

Hello @hrculiz, If you have learnt something new from my text, then it means I am doing things right!! And itās my pleasure!

Good work bruno, it was painful to watch you struggle with this problem for 2-3 days, but I am really happy for you that you pulled it off, and also hats off to your determination

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Thank you very much @v_akshay, your words of motivation also helped me a lot And this problem only proves I need to learn many, many new things like Graphs, DP, Treesā¦ I know itās a long road, but Im also sure I will get there with time and hard work

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Awesome work!! man ,keep it up @kuruma

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Thanks @faiz, itās what I plan to do and I plan to learn lots of new things Thank you very much!

Thank you very much @ravi itās really wonderful to see that people enjoyed this text And ofc my own personal goal is to keep learning more and more so I can write texts like this for a wider range of problems!! My personal goal now is to work on DP and graphs in a more specfic way and study new data structures so I can implement classic algorithms like LCS, suffix array, etc

Good job @arjunc I have came across that website during contest but actually failed to use the ideas described there and I chose this method instead, so, congratulations