[DMDB] Fix small errors in quick overview

semester4/dmdb/parts/08_quick-overview/03_qp.tex

@@ -15,6 +15,7 @@ Given $B$ frames of memory and $N$ records, we have (typically I/Os in pages to
     \item \bi{File Scan}: $N \div P_F$, with $P_F$ the number of pages, because we need to run through all pages
     \item \bi{B+ Tree}: $\texttt{height}(T) - 1 + \texttt{cnt}(P_L) + \texttt{cnt}(P_F)$, $P_L$ the affected leaf pages and $P_F$ the file pages,
           the minus one comes from the fact that we count the leaf page already using $P_L$.
+          Note that $\texttt{height}(T) = 1 + \ceil{\log_K(P_L)}$, with $K$ the number of elements in the inner nodes
           \begin{itemize}
               \item For a clustered index, $\texttt{cnt}(P_F) = \texttt{cnt}(R') \div (F_L \cdot R_L)$, with $R_L$ the number of records per leaf page and $F_L$ the fill factor.
               \item For an unclustered index, $\texttt{cnt}(P_F) = \texttt{cnt}(R')$, with $\texttt{cnt}(R') = \texttt{cnt}(R) \cdot S$, with $S$ the selectivity of the predicate.
@@ -29,8 +30,8 @@ Given $B$ frames of memory and $N$ records, we have (typically I/Os in pages to
 Remember that we need the sort-based and hash-based approach to eliminate duplicates.
 \begin{itemize}
     \item \bi{Partitioning}: $\texttt{Cost}_\texttt{part}(R) = \texttt{cnt}(R) + \texttt{cnt}(R')$ with
-          $\texttt{cnt}(R') = \texttt{cnt}(R) Q$, with $Q$ the fraction of selected attributes divided by total attributes
-    \item \bi{Sort-Based}: The number of sorted runs are $M = \ceil{\texttt{cnt}(R') \div B}$, with the merge passes $P = \ceil{\log_{B - 1}(M)}$, total cost:
+          $\texttt{cnt}(R') = \texttt{cnt}(R) \cdot Q$, with $Q$ the fraction of selected attributes divided by total attributes
+    \item \bi{Sort-Based}: The number of sorted runs are $M = \ceil{\texttt{cnt}(R') \div B}$, with the merge passes $P = 1 + \ceil{\log_{B - 1}(M)}$, total cost:
           $2 \cdot N \cdot P + \texttt{Cost}_\texttt{part}(R)$
     \item \bi{Hash-Based}:
           \begin{itemize}