容斥原理

定理

$$\left| S_{1}\cup S_{2}\ldots \cup S_{n}\right|$$

$$=\sum_{i} |S_i| - \sum_{i<j} |S_{i_1}\cap S_{i_2}| + \sum_{i<j<k} |S_{i_1}\cap S_{i_2}\cap S_{i_2}| + \dots + (-1)^{n-1}|S_{i_1}\cap S_{i_2}\cap \dots \cap S_{i_k}|$$

posted @ 2018-01-07 22:16  自为风月马前卒  阅读(...)  评论(...编辑  收藏

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