|시간 제한||메모리 제한||제출||정답||맞힌 사람||정답 비율|
|서브태스크 참고 (추가 시간 없음)||1024 MB (추가 메모리 없음)||47||37||34||85.000%|
A matryoshka is a type of doll that originated in Russia over a century ago. Their defining characteristic is that they consist of a set of dolls, all of a different size, with smaller dolls fitting nicely inside larger dolls.
In this problem, we work with matrygons, which are sets of regular convex polygons that follow a similar nesting pattern. A matrygon consists of a set of regular convex polygons with positive area p1, p2, …, pk such that, for all i, the vertices of pi+1 overlap with a proper subset of the vertices of pi (pi+1 has strictly less vertices than pi).
For example, the following pictures illustrates two matrygons. The first one contains 3 regular convex polygons: a regular icositetragon (24 sides), a regular hexagon (6 sides), and an equilateral triangle (3 sides). The second one contains 2 regular convex polygons: a regular icosidigon (22 sides) and a regular hendecagon (11 sides). Each of these matrygons has 33 total sides among all polygons in it.
Given a fixed total number of sides N, calculate the largest number of polygons that can be part of a matrygon such that the total number of sides among all polygons in it is exactly N.
The first line of the input gives the number of test cases, T. T lines follow. Each line represents a test case and contains a single integer N, the target total number of sides.
For each test case, output one line containing
Case #x: y, where x is the test case number (starting from 1) and y is the maximum number of polygons in a matrygon such that the total number of sides among all polygons in it is exactly N.
시간 제한: 20 초
시간 제한: 40 초
3 33 15 41
Case #1: 3 Case #2: 2 Case #3: 1
The first matrygon pictured in the problem statement is an optimal solution for Sample Case #1.
In Sample Case #2, we can get to two polygons by fitting a regular pentagon (5 sides) inside a regular decagon (10 sides).
In Sample Case #3, there is no way to create a matrygon with multiple regular polygons, so our only option is to use a single regular tetracontahenagon (41 sides).