update

chapterBalancedSearchTree.tex

@@ -101,3 +101,4 @@ \section{B-Tree}
 \end{figure}
 
 \section{AVL Tree}
+TODO

chapterDynamicProgramming.tex

@@ -11,7 +11,7 @@ \section{Introduction}
 
 The so called concept dp as memoization of recursion does not grasp the core philosophy of dp. 
 
-The formula in the following section are unimportant. What is important is the definition of dp array and transition function derivation.
+The formula in the following section are unimportant. Instead, what is important is the definition of dp array and transition function derivation.
 \subsection{Common practice}
 \rih{Dummy.} Use dummies to avoid using if-else conditional branch.
 \begin{enumerate}

chapterGraph.tex

@@ -97,6 +97,7 @@ \subsection{Undirected Graph}
     visited.add(k)
     return True
 \end{python}
+
 \section{Topological Sorting}
 For a graph $G=\{V, E\}$, $ A \rightarrow B $, then $A$ is before $B$ in the ordered list. 
 \subsection{Algorithm}

chapterGreedy.tex

@@ -6,5 +6,5 @@ \section{Introduction}
 
 
 \subsection{Summarizing properties}
-
+TODO
 

chapterSearch.tex

@@ -1,8 +1,5 @@
 \chapter{Search}
 
-
-\section{Introduction}
-
 \section{Binary Search}
 Variants:
 \begin{enumerate}

chapterSort.tex

@@ -109,7 +109,7 @@ \subsubsection{3-way pivoting}
     return lt+1, gt
 \end{python}
 
-\section{Stability}
+\subsection{Stability}
 Definition: a stable sort preserves the \textbf{relative order of items with equal keys} (scenario: sorted by time then sorted by location). 
 
 Algorithms:
@@ -135,7 +135,7 @@ \section{Stability}
 \label{fig:trie} 
 \end{figure}
 
-\section{Applications}
+\subsection{Applications}
 \begin{enumerate}
 \item Sort
 \item Partial quick sort (selection), k-th largest elements 
@@ -145,12 +145,44 @@ \section{Applications}
 \item Data compression
 \end{enumerate}
 
+\subsection{Considerations}
+\begin{enumerate}
+\item Stable?
+\item Distinct keys?
+\item Need guaranteed performance?
+\item Linked list or arrays?
+\item Caching system? (reference to neighboring cells in the array? 
+\item Usually randomly ordered array?
+(or partially sorted?)\item Parallel?
+\item Deterministic?
+\item Multiple key types?
+\end{enumerate}
+
+$O(N\lg N)$ is the lower bound of comparison-based sorting; but for other
+contexts, we may not need $O(N \lg N)$:
+\begin{enumerate}
+\item Partially-ordered arrays: insertion sort to achieve $O(N)$. \textbf{Number of inversions}: 1 inversion $=$ 1 pair of keys that are out
+of order.
+\item Duplicate keys
+\item Digital properties of keys: radix sort to achieve $O(N)$.
+\end{enumerate}
+
+\subsection{Summary}
+\begin{figure}[hbtp]
+\centering
+\subfloat{\includegraphics[scale=0.80]{sort_summary}}
+\caption{Sort summary}
+\label{fig:trie} 
+\end{figure}
+
 
 \section{Reversion}
 If $a_i > a_j$ but $i<j$, then this is considered as 1 reversion. 
 
 \subsection{Calculation}
-MergeSort to calculate the \#reverse-ordered paris. The only difference from a normal merge sort is that - when pushing the 2nd half of the array to the place, you calculate the reversion generated by the element $A_2[i_2]$ compared to $A_1[i_1:]$.
+MergeSort to calculate the \#reverse-ordered paris. The only difference from a normal
+merge sort is that - when pushing the 2nd half of the array to the place, you calculate
+the reversion generated by the element $A_2[i_2]$ compared to $A_1[i_1:]$.
 
 \begin{python}
 def merge(A1, n1, A2, n2, A, n):
@@ -196,34 +228,3 @@ \subsection{Calculation}
     return count
 \end{python}
 
-
-
-\section{Considerations}
-\begin{enumerate}
-\item Stable?
-\item Distinct keys?
-\item Need guaranteed performance?
-\item Linked list or arrays?
-\item Caching system? (reference to neighboring cells in the array? 
-\item Usually randomly ordered array?
-(or partially sorted?)\item Parallel?
-\item Deterministic?
-\item Multiple key types?
-\end{enumerate}
-
-$O(N\lg N)$ is the lower bound of comparison-based sorting; but for other
-contexts, we may not need $O(N \lg N)$:
-\begin{enumerate}
-\item Partially-ordered arrays: insertion sort to achieve $O(N)$. \textbf{Number of inversions}: 1 inversion $=$ 1 pair of keys that are out
-of order.
-\item Duplicate keys
-\item Digital properties of keys: radix sort to achieve $O(N)$.
-\end{enumerate}
-
-\section{Summary}
-\begin{figure}[hbtp]
-\centering
-\subfloat{\includegraphics[scale=0.90]{sort_summary}}
-\caption{Sort summary}
-\label{fig:trie} 
-\end{figure}