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\title{{\bf Lecture 0: Introduction}\\
  \normalsize{(CLRS 1)}}
\date{}

\maketitle

\section{Introduction}

\begin{itemize}
\item Class is about {\em designing} and {\em analyzing} {\em algorithms}

  \begin{itemize}
    
  \item {\em Algorithm}: A well-defined procedure that takes an input
    and computes some output.
    \begin{itemize}
    \item not code, does not contain the low-level details.
    \end{itemize}
    
   \item {\em Design of algorithms}: Methods/ideas for developing
     (efficient) algorithms. There are no recipes, but there exist
     some general techniques and we'll study them.
     
   \item {\em Analysis of algorithms}: Abstract/mathematical
     comparison of algorithms (without actually implementing
     them). Think of analysis as a measure of the quality of your
     algorithm and use it to justify design decisions when you write
     programs.
   \end{itemize}
   
 \item In this class we do all these: 
   \begin{itemize}
   \item come up with solutions for a problem  
   \item prove that it is correct 
   \item analyze its running time
   \end{itemize}
 
 \item Hopefully the class will show that {\bf algorithms matter!}
 \end{itemize}
 
 
 \section{Algorithm warmup: searching and sorting} 
 
The fundamental problems are searching and sorting. 

\begin{itemize} 
\item Searching: Given an input array $A$ consisting of $n$ elements,
  and a target element say $t$, find if $t$ occurs in $A$ (yes/no
  answer).

  \begin{itemize} 
  \item for simplicity we assume integers
  \item variations: find index where it occurs; find all occurences;
    count number of occurences.
  \end{itemize} 
  

\item Sorting: Given an input array $A$ consisting of $n$ elements,
  permute the elements such that the sequence is now sorted,
  i.e. $A[0] \le A[1] \le A[2]  \le ...$.

\end{itemize} 

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We'll discuss the following algorithms: 

\begin{enumerate}
\item linear search  
\item binary search 
\item bubble sort
\item selection sort
\item insertion sort
\end{enumerate}



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