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statement is incorrect

23700번 - Counting Polygons

shanlunjiajian 3년 전 0

The statement is incorrect. Please use the version in https://disk.yandex.ru/i/wugBZ_4mv1k9tA .

Sorry about my carelessness!

Mr. Panda loves counting polygons. Today, he wants to count the number of non-isomorphic convex polygons with $m$ sides such that the length of each side is a positive integer, the perimeter is exactly $n$ and no two sides are collinear.
Mr. Panda thinks such a polygon could be described by the sequence $[l_1, l_2, \dots , l_m]$ — lengths of its sides in some order. A polygon may have several describing sequences. Each describing sequence may start at any side of the polygon and go through all the sides in clockwise or counterclockwise such that each side appears exactly once.
Mr. Panda calls two convex polygons $P$ and $Q$ isomorphic if and only if there exists a describing sequence $A = [a_1, a_2, \dots , a_x]$ of $P$ and a describing sequence $B = [b_1, b_2, \dots , b_y]$ of $Q$ such that $x = y$ and $a_i = b_i$ for $i = 1, 2, . . . , x$.
Could you please help Mr. Panda count the number of these polygons? To avoid huge output data, you are only asked the answer modulo $(10^9 + 7)$.
...
Note
For the third sample case, there is only one type of convex polygon, whose describing sequence can be $[1, 2, 2],ドル or $[2, 1, 2],ドル or $[2, 2, 1]$.
For the last sample case, there are three types of convex polygons, whose describing sequences can be $[1, 2, 2, 2],ドル $[1, 1, 2, 3]$ and $[1, 2, 1, 3]$ respectively.
Note that a polygon with describing sequence $[1, 2, 1, 3]$ and a polygon with describing sequence $[1, 3, 1, 2]$ are isomorphic.

jh05013 3년 전 5

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