LINES IN THE PLANE

问题描述：

用 n 条直线切割平面空间，求切割出的空间的最大数目。

解决方案：

当我们用 n 条直线去切割时，与前面的 n-1 条直线最多有 n-1 个不同的交点，那么最多新增 n 个空间。假定 n 条直线切割的空间最多为 Ln ，则有公式： Ln <= Ln-1 + n
并且当直线间的切割原则是任何两条直线间不平行，且任意三条直线不相交于一个交点时，可易得下面公式： Ln = Ln-1 + n
再由 L0 = 1, L1 = 2 且 Ln = Ln-1 +n,有

Ln=n∗(n−1)/2+1

代码：

时间： 2024-12-24 17:37:15

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