day2/session1.tex
author Santosh G. Vattam <vattam.santosh@gmail.com>
Thu, 22 Oct 2009 15:54:42 +0530
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%Tutorial slides on Python.
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%
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% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
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% Copyright (c) 2005-2009, Prabhu Ramachandran
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\documentclass[14pt,compress]{beamer}
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%\documentclass[draft]{beamer}
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%\documentclass[compress,handout]{beamer}
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%\usepackage{pgfpages} 
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%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
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% Modified from: generic-ornate-15min-45min.de.tex
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\mode<presentation>
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{
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  \usetheme{Warsaw}
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  \useoutertheme{split}
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  \setbeamercovered{transparent}
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}
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\usepackage[english]{babel}
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\usepackage[latin1]{inputenc}
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%\usepackage{times}
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\usepackage[T1]{fontenc}
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% Taken from Fernando's slides.
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\usepackage{ae,aecompl}
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\usepackage{mathpazo,courier,euler}
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\usepackage[scaled=.95]{helvet}
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\definecolor{darkgreen}{rgb}{0,0.5,0}
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\usepackage{listings}
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\lstset{language=Python,
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    basicstyle=\ttfamily\bfseries,
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    commentstyle=\color{red}\itshape,
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  stringstyle=\color{darkgreen},
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  showstringspaces=false,
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  keywordstyle=\color{blue}\bfseries}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Macros
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\setbeamercolor{emphbar}{bg=blue!20, fg=black}
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\newcommand{\emphbar}[1]
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{\begin{beamercolorbox}[rounded=true]{emphbar} 
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      {#1}
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 \end{beamercolorbox}
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}
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\newcounter{time}
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\setcounter{time}{0}
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\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
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\newcommand{\typ}[1]{\texttt{#1}}
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\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
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%%% This is from Fernando's setup.
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% \usepackage{color}
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% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}
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% % Use and configure listings package for nicely formatted code
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% \usepackage{listings}
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% \lstset{
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%    language=Python,
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%    basicstyle=\small\ttfamily,
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%    commentstyle=\ttfamily\color{blue},
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%    stringstyle=\ttfamily\color{orange},
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%    showstringspaces=false,
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%    breaklines=true,
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%    postbreak = \space\dots
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% }
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Title page
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\title[Basic Python]{Python:\\A formal approach}
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\author[FOSSEE Team] {The FOSSEE Group}
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\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
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\date[] {1, November 2009\\Day 2, Session 1}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
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%\logo{\pgfuseimage{iitmlogo}}
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%% Delete this, if you do not want the table of contents to pop up at
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%% the beginning of each subsection:
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\AtBeginSubsection[]
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{
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  \begin{frame}<beamer>
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    \frametitle{Outline}
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    \tableofcontents[currentsection,currentsubsection]
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  \end{frame}
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}
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\AtBeginSection[]
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{
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  \begin{frame}<beamer>
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    \frametitle{Outline}
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    \tableofcontents[currentsection,currentsubsection]
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  \end{frame}
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}
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% If you wish to uncover everything in a step-wise fashion, uncomment
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% the following command: 
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%\beamerdefaultoverlayspecification{<+->}
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%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DOCUMENT STARTS
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\begin{document}
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\begin{frame}
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  \titlepage
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\end{frame}
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\begin{frame}
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  \frametitle{Outline}
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  \tableofcontents
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  % You might wish to add the option [pausesections]
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\end{frame}
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\section{Data types}
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\begin{frame}
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  \frametitle{Primitive Data types}
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  \begin{itemize}
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    \item Numbers: float, int, complex
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    \item Strings
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    \item Boolean
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  \end{itemize}
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\end{frame}
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\subsection{Numbers}
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\begin{frame}[fragile]
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  \frametitle{Numbers}
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  \begin{itemize}
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    \item \kwrd{int}\\ Any whole number is an \kwrd{int}, no matter what the size!
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  \begin{lstlisting}
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In []: a = 13
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In []: a = 99999999999999999999
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  \end{lstlisting}
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    \item \kwrd{float}
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  \begin{lstlisting}
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In []: fl = 3.141592
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  \end{lstlisting}
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  \end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Complex numbers}
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  \begin{lstlisting}
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In []: cplx = 3+4j
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In []: abs(cplx)
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Out[]: 5.0
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In []: cplx.imag
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Out[]: 4.0
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In []: cplx.real
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Out[]: 3.0
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  \end{lstlisting}
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\end{frame}
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\subsection{Boolean}
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\begin{frame}{Boolean}
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  \begin{itemize}
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    \item \kwrd{True}
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    \item \kwrd{False}
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    \item \kwrd{not}
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    \item \kwrd{and}
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    \item \kwrd{or}
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  \end{itemize}
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\end{frame}
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\subsection{Strings}
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\begin{frame}[fragile]
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  \frametitle{String methods}
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Strings were introduced previously, let us now look at them in a little more detail.
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  \begin{lstlisting}
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In []: a = 'hello world'
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In []: a.startswith('hell')
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Out[]: True
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In []: a.endswith('ld')
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Out[]: True
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  \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Still with strings}
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We saw split() previously. join() is the opposite of split()
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  \begin{lstlisting}
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In []: ''.join(['a', 'b', 'c'])
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Out[]: 'abc'
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  \end{lstlisting}
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  \begin{block}{Note:}
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Strings are immutable.\\ That is string variables cannot be changed.
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  \end{block}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{String formatting}
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  \begin{lstlisting}
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In []: x, y = 1, 1.234
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In []: 'x is %s, y is %s' %(x, y)
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Out[]: 'x is 1, y is 1.234'
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  \end{lstlisting}
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  \small
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\url{docs.python.org/lib/typesseq-strings.html}\\
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\inctime{10}
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\end{frame}
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\section{Relational and logical operators}
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\begin{frame}[fragile]
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  \frametitle{Relational and logical operators}
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  \begin{lstlisting}
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In []: pos, zer, neg = 1, 0, -1
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In []: pos == neg
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Out[]: False
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In []: pos >= neg
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Out[]: True
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In []: neg < zer < pos
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Out[]: True
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In []: pos + neg != zer
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Out[]: False
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  \end{lstlisting}
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\inctime{5}
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\end{frame}
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\begin{frame}
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  {A classic problem}
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  \begin{block}
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    {Interchange values}
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    How to interchange values of two variables? 
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  \end{block}
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  \pause
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  \begin{block}{Note:}
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    This Python idiom works for all types of variables.\\
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They need not be of the same type!
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  \end{block}
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  \inctime{}
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\end{frame}
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\section{Control flow}
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\begin{frame}
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  \frametitle{Control flow constructs}  
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  \begin{itemize}
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  \item \kwrd{if/elif/else}: branching
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  \item \kwrd{while}: looping
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  \item \kwrd{for}: iterating 
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  \item \kwrd{break, continue}: modify loop 
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  \item \kwrd{pass}: syntactic filler
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  \end{itemize}
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\end{frame}
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\subsection{Basic Conditional flow}
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\begin{frame}[fragile]
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  \frametitle{\typ{If...elif...else} example}
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\begin{lstlisting}
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x = int(raw_input("Enter an integer:"))
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if x < 0:
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     print 'Be positive!'
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elif x == 0:
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     print 'Zero'
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elif x == 1:
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     print 'Single'
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else:
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     print 'More'
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\end{lstlisting}
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\end{frame}
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\begin{frame}{Simple IO}
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  \begin{block}
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    {Console Input}
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    \texttt{raw\_input()} waits for user input.\\Prompt string is optional.\\
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    All keystrokes are Strings!\\\texttt{int()} converts string to int.
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  \end{block}
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  \begin{block}
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    {Console output}
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    \texttt{print} is straight forward. Note the distinction between \texttt{print x} and \texttt{print x,}
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  \end{block}
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\end{frame}
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\subsection{Basic Looping}
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\begin{frame}[fragile]
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  \frametitle{\kwrd{while}}
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Example: Fibonacci series
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  \begin{lstlisting}
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# the sum of two elements
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# defines the next
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a, b = 0, 1
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while b < 10:
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    print b,
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    a, b = b, a + b 
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\end{lstlisting}
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\typ{1 1 2 3 5 8}\\  
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{\kwrd{range()}}
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\kwrd{range([start,] stop[, step])}\\
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\begin{itemize}
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  \item \alert {range() returns a list of integers}
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  \item \alert {The start and the step arguments are optional}  
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   315
\end{itemize}
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   316
\end{frame}
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\begin{frame}[fragile]
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   319
  \frametitle{\kwrd{for}}
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   320
Example: print squares of first \typ{n} numbers
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   321
  \begin{lstlisting}
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In []: for i in range(5):
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 ....:     print i, i * i
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   324
 ....:     
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 ....:     
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   326
0 0
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1 1
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2 4
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3 9
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4 16
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   331
\end{lstlisting}
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\inctime{15}
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   333
\end{frame}
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   334
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   335
\section{Lists}
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\begin{frame}[fragile]
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\frametitle{More List methods}
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   338
\begin{lstlisting}
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In []: lst = [1,2,3,4,5,6,7,8]
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In []: lst.reverse()
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   341
In []: lst
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   342
Out[]: [8, 7, 6, 5, 4, 3, 2, 1]
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   343
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   344
In []: lst.extend([0, -1, -2])
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   345
In []: lst
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   346
Out[]: [8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2]
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   347
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Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   348
In []: lst.remove(0)
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   349
In []: lst
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   350
Out[]: [8, 7, 6, 5, 4, 3, 2, 1, -1, -2]
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   351
\end{lstlisting}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   352
\end{frame}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   353
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   354
\begin{frame}[fragile]
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   355
\frametitle{List containership}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   356
\begin{lstlisting}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   357
In []: a = 8
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   358
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   359
In []: a in lst
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   360
Out[]: True
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   361
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   362
In []: b = 10
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   363
In []: b in lst
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   364
Out[]: False
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   365
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   366
In []: b not in lst
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   367
Out[]: True
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   368
\end{lstlisting}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   369
\inctime{10}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   370
\end{frame}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   371
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   372
\section{Tuples}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   373
\begin{frame}[fragile]
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   374
\frametitle{Tuples: Immutable lists}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   375
\begin{lstlisting}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   376
In []: tup = (1,2,3,4,5,6,7,8)
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   377
In []: tup[0]+tup[3]+tup[-1]
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   378
Out[]: 13
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   379
\end{lstlisting}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   380
\begin{block}{Note:}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   381
\begin{itemize}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   382
\item Tuples are immutable - cannot be changed
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   383
\item Multiple return values in a function are actually tuples
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   384
\item Tuples are working behind the scenes in exchanging values - Tuple Unpacking
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   385
\end{itemize}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   386
\end{block}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   387
\inctime{5}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   388
\end{frame}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   389
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   390
\section{Dictionaries}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   391
\begin{frame}[fragile]
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   392
\frametitle{Dictionaries}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   393
  \alert {lists and tuples: integer indexes :: dictionaries: string indexes}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   394
\begin{lstlisting}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   395
In []: player = {'Mat': 134, 'Inn': 233, 'Runs': 10823, 'Avg': 52.53}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   396
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   397
In []: player['Avg']
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   398
Out[]: 52.530000000000001
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   399
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   400
In []: player.keys()
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   401
Out[]: ['Runs', 'Inn', 'Avg', 'Mat']
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   402
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   403
In []: player.values()
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   404
Out[]: [10823, 233, 52.530000000000001, 134]
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   405
\end{lstlisting}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   406
\end{frame}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   407
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   408
\begin{frame}{Dictionaries}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   409
\begin{itemize}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   410
\item Duplicate keys are not allowed!
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   411
\item Dictionaries are iterable through keys.
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   412
\end{itemize}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   413
\inctime{5}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   414
\end{frame}
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   415
a5da7607ab14 Added Session 1, Day 2 - "Formal approach to Python" slides.
Santosh G. Vattam <vattam.santosh@gmail.com>
parents:
diff changeset
   416
\end{document}