一些取整技巧
-
\(-\lceil r \rceil = \lfloor -r \rfloor,-\lfloor r \rfloor = \lceil -r \rceil\),\(\forall n\in Z,\lceil x + n\rceil = \lceil x \rceil + n,\lfloor x + n\rfloor = \lfloor x \rfloor + n\)
-
\(\lceil \dfrac{a}{b} \rceil = \lfloor \dfrac{a-1}{b} \rfloor + 1\)
-
\(\lfloor \dfrac{n}{xy} \rfloor = \lfloor \dfrac{\lfloor \frac{n}{x} \rfloor}{y} \rfloor\)
-
广义鸽巢原理：\(N\) 件物品分 \(M\) 个集合，至少有一个集合内的元素个数 \(\ge \lceil \dfrac{N}{M} \rceil\) 。
-
\(\dfrac{a}{b} < s < \dfrac{c}{d} \Leftrightarrow \lceil \dfrac{a+1}{b} \rceil \le s < \lfloor \dfrac{c-1}{d} \rfloor\)
-
\( \lceil \dfrac{\lfloor \dfrac{a}{x} \rfloor}{y} \rceil = \lceil \dfrac{a}{xy} \rceil \)
