Hi zx.mys! This is my interpretation of the contest analysis solution:
Originally, you have 3 circles of radii r1, r2 and r3 (say r1 is the smallest). The solution says to subtract the radii of the two larger circles to r2 - r1 and r3 - r1. These circles will be outside the smallest circle, so after inversion, they will be contained within the smallest circle. The tangents mean the straight lines that touch the two inverted circles (they won't necessarily go through the smallest circle's centre). Like this: ____O_o___ When inverted back, the tangents will map to circles which touch the r2-r1 and r3-r1 circles (because tangency is preserved by inversion) and goes through the centre of the smallest circle (lines map to circles that pass through origin), so the radius can be increased by r1 to get a circle which touches all three plants. I hope this helps! If you're not too familiar with inversion, I think wikipedia explains it quite well: http://en.wikipedia.org/wiki/Inversive_geometry On Mon, Sep 28, 2009 at 3:00 PM, Zx.MYS <[email protected]> wrote: > > quoted from Contest Analysis > > "We can subtract from the radius of each of the three plants the > radius of the smallest plant, then compute an inversion about that > plant's center. Then we find appropriate tangents to the two inverted > plants, re-invert to find the corresponding circle, and add back the > radius of the smallest plant. " > > I got puzzled when trying to understand this(may caused by my poor > English). > Why doing all these inversions? Doe "appropriate tangents" mean a > tangents go through the smallest plant's center? > And finally,how does this solution work? > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "google-codejam" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/google-code?hl=en -~----------~----~----~----~------~----~------~--~---
