#P1361. 平面分割问题

平面分割问题

题目描述

设有n条封闭曲线画在平面上,而任何两条封闭曲线恰好相交于两点,且任何三条封闭曲线不相交于同一点,问这些封闭曲线把平面分割成的区域个数。 

![](./4852/file/20240723114425_73287.png)

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)

输入格式

一个整数n(n<=10000),代表封闭曲线的条数

输出格式

n条曲线分割区域的个数

2
4