just noticed your link .. sorry .. ignore previous mail 2009/9/30 Bharath Raghavendran <[email protected]>
> what is inversion? :D > > 2009/9/29 Zx.MYS <[email protected]> > > >> I got it!Thank you Takaki! >> >> Takaki wrote: >> > 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 -~----------~----~----~----~------~----~------~--~---
