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# P3476 [POI2008]TRO-Triangles

• 44通过
• 202提交
• 题目提供者 洛谷OnlineJudge
• 评测方式 云端评测
• 标签 叉积 深度优先搜索,DFS 计算几何 POI 2008 高性能
• 难度 提高+/省选-
• 时空限制 1000ms / 128MB
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## 题目描述

pairwise disjoint points in the plane are given ().

There are triangles whose vertices are some pairwise different points among them (including degenerate triangles, i.e. ones whose vertices are collinear).

We want to calculate the sum of areas of all the triangles with vertices in the given points.

Those parts of the plane that belong to many triangles are to be calculated multiple times. We assume that the area of degenerate triangles (i.e. those with collinear vertices) is zero.

reads from the standard input the coordinates of the points in the plane, determines the sum of the areas of all the triangles with vertices in the given points, prints out the result to the standard output.

给定平面上的一些点，求这些点能组成的所有三角形的面积之和

## 输入输出格式

输入格式：

In the first line of the standard input there is one integer () denoting the number of selected points.

Each of the following lines contains two integers and () separated by a single space and denoting the coordinates of the point (for ).

No pair (ordered) of coordinates appears more than once.

输出格式：

In the first and only line of the standard output there should be one real number equal to the sum of the areas of all the triangles with vertices in the given points. The outcome should be printed out with exactly one digit after dot and should not differ from the correct value by more than .

## 输入输出样例

输入样例#1： 复制
5
0 0
1 2
0 2
1 0
1 1

输出样例#1： 复制
7.0

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