A14511 | Polygon
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内存限制256MB
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题目描述
You are given a strictly convex polygon with $n$ vertices.
You will make $k$ cuts that meet the following conditions:
- each cut is a segment that connects two different nonadjacent vertices;
- two cuts can intersect only at vertices of the polygon.
Your task is to maximize the area of the smallest region that will be formed by the polygon and those $k$ cuts.
You will make $k$ cuts that meet the following conditions:
- each cut is a segment that connects two different nonadjacent vertices;
- two cuts can intersect only at vertices of the polygon.
Your task is to maximize the area of the smallest region that will be formed by the polygon and those $k$ cuts.
输入格式
The first line contains two integers $n$ , $k$ ( $3 \le n \le 200$ , $0 \le k \le n-3$ ).
The following $n$ lines describe vertices of the polygon in anticlockwise direction. The $i$ -th line contains two integers $x_i$ , $y_i$ ( $|x_i|, |y_i| \le 10^8$ ) — the coordinates of the $i$ -th vertex.
It is guaranteed that the polygon is convex and that no two adjacent sides are parallel.
The following $n$ lines describe vertices of the polygon in anticlockwise direction. The $i$ -th line contains two integers $x_i$ , $y_i$ ( $|x_i|, |y_i| \le 10^8$ ) — the coordinates of the $i$ -th vertex.
It is guaranteed that the polygon is convex and that no two adjacent sides are parallel.
输出格式
Print one integer: the maximum possible area of the smallest region after making $k$ cuts multiplied by $2$ .
输入输出样例
输入 #1
8 4 -2 -4 2 -2 4 2 1 5 0 5 -4 4 -5 0 -5 -1
输出 #1
11
输入 #2
6 3 2 -2 2 -1 1 2 0 2 -2 1 -1 0
输出 #2
3
In the first example, it's optimal to make cuts between the following pairs of vertices:
- $(-2, -4)$ and $(4, 2)$ ,
- $(-2, -4)$ and $(1, 5)$ ,
- $(-5, -1)$ and $(1, 5)$ ,
- $(-5, 0)$ and $(0, 5)$ .
 Points $(-5, -1)$ , $(1, 5)$ , $(0, 5)$ , $(-5, 0)$ determine the smallest region with double area of $11$ . In the second example, it's optimal to make cuts between the following pairs of vertices:
- $(2, -1)$ and $(0, 2)$ ,
- $(2, -1)$ and $(1, 0)$ ,
- $(-1, 0)$ and $(0, 2)$ .
 Points $(2, -2)$ , $(2, -1)$ , $(-1, 0)$ determine one of the smallest regions with double area of $3$ .
- $(-2, -4)$ and $(4, 2)$ ,
- $(-2, -4)$ and $(1, 5)$ ,
- $(-5, -1)$ and $(1, 5)$ ,
- $(-5, 0)$ and $(0, 5)$ .
 Points $(-5, -1)$ , $(1, 5)$ , $(0, 5)$ , $(-5, 0)$ determine the smallest region with double area of $11$ . In the second example, it's optimal to make cuts between the following pairs of vertices:
- $(2, -1)$ and $(0, 2)$ ,
- $(2, -1)$ and $(1, 0)$ ,
- $(-1, 0)$ and $(0, 2)$ .
 Points $(2, -2)$ , $(2, -1)$ , $(-1, 0)$ determine one of the smallest regions with double area of $3$ .
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评测结果：Accepted