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algorithm/ideas needed

Posted: Sun Jun 12, 2005 7:51 pm
by abishek ... php?p=2339

I am completely stumped by this problem :(
any body has any ideas how to proceed? may be very advanced math?

Posted: Thu Jun 23, 2005 2:50 pm
by jakabjr
i have no theorem to back me up, but here's a guess:

if lh is the hexagon's side length, ah it's area, lt1..ltn the triangle sides and atn their areas, then if u can write lh as a sum of lt1..ltn and ah as a sum of at1..atn then i belive the hexagon can be splited.

at = lt*lt*sqrt(3)/4;
ah = lh*lh*sqrt(3)*3/8; (there are 6 lh/2 side length triangles in a hexagon)

just an idea... (it works for the test cases)

what i'm sure of though is u only have to consider triangle sides that are prime: if u have both 2 and 4, u can use just 2 since a 4 side triangle is 4 2 side triangles

PS: i used backtracking to see if the splits are possible and it takes quite some while

Posted: Thu Jun 23, 2005 2:54 pm
by jakabjr
sorry, ah = lh*lh*sqrt(3)*3/2

Posted: Fri Jun 24, 2005 4:11 am
by abishek
it may not be enuf to test primes as 2 and 6 may well produce different results than just 2.

Posted: Fri Jun 24, 2005 10:04 am
by jakabjr
actually, a 6 side triangle can be broken into 9 2-side triangles that cover the exact same area.

So, whatever u can cover with a 6 sider, u can also cover with 2 side triangle.

/\ /\
/ \ /\ /\
/____\ / \/ \/\

something like that, with 5,3 and 1 2 side triangles on the rows.