When storing big text contents in a database, it is better to store after compressing the data. The following is an example storing HTML contents in a database cache. We first create a table mapping URLs to HTML contents. The…
When storing big text contents in a database, it is better to store after compressing the data. The following is an example storing HTML contents in a database cache. We first create a table mapping URLs to HTML contents. The…
PHP provides str_pad() to add a string to a certain length with another string. Another way is to use sprintf() with formatting patterns. Pad leading zeros to get exactly 3 digits:
Let \(S\) be a family of subsets of \(\{1,\ldots,n\}\) such that no set in \(S\) contains another. This is often called an antichain. Theorem. [Sperner’s Theorem] \[ |S| \leq {n \choose \lfloor n/2 \rfloor}. \] The proof of Sperner’s Theorem…