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2024-04-23 17:33:58 -07:00
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Advanced/Compression/parts/0 intro.tex
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@ -9,7 +9,7 @@ A \textit{string} is a sequence of symbols from an alphabet. \par
For example, \texttt{CBCAADDD} is a string over the alphabet $\{\texttt{A}, \texttt{B}, \texttt{C}, \texttt{D}\}$.
\problem{}
Say we want to store a length-$n$ string over the alphabet $\{\texttt{A}, \texttt{B}, \texttt{C}, \texttt{D}\}$ as a binary blob. \par
Say we want to store a length-$n$ string over the alphabet $\{\texttt{A}, \texttt{B}, \texttt{C}, \texttt{D}\}$ as a binary sequence. \par
How many bits will we need? \par
\hint{
Our alphabet has four symbols, so we can encode each symbol using two bits, \par
@ -32,6 +32,6 @@ using $n \times \lceil \log_2k \rceil$ bits. Convince yourself that this is true
\vfill
Of course, this isn't ideal---we can do much better than $n \times \lceil \log_2k \rceil$.
As you might expect, this isn't ideal: we can do much better than $n \times \lceil \log_2k \rceil$.
We will spend the rest of this handout exploring more efficient ways of encoding such sequences of symbols.
\pagebreak