path: root/day1/Session-2.tex

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% Tutorial slides on Python.
%
% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
% Copyright (c) 2005-2009, Prabhu Ramachandran
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% Title page
\title[Basic Python]{Python:\\Functions and basic data structures}

\author[FOSSEE Team] {Asokan Pichai\\Prabhu Ramachandran}

\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
\date[] {10, October 2009\\Day 1, Session 2}
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%% the beginning of each subsection:
\AtBeginSection[]
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  \begin{frame}<beamer>
    \frametitle{Outline}
    \tableofcontents[currentsection,subsections]
  \end{frame}
}


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% DOCUMENT STARTS
\begin{document}

\begin{frame}
  \titlepage
\end{frame}

\section{Control Flow}

\subsection{Exercises}
\begin{frame}
  \frametitle{Problem set 1}
  \begin{itemize}
    \item All the problems can be\\
      solved using \kwrd{if} and \kwrd{while} 
  \end{itemize}
\end{frame}

\begin{frame}{Problem 1.1}
  Write a program that displays all three digit numbers that are equal to the sum of the cubes of their digits. That is, print numbers $abc$ that have the property $abc = a^3 + b^3 + c^3$\\
\vspace*{0.2in}
\emphbar{These are called $Armstrong$ numbers.}
\end{frame}
  
\begin{frame}{Problem 1.2 - Collatz sequence}
\begin{enumerate}
  \item Start with an arbitrary (positive) integer. 
  \item If the number is even, divide by 2; if the number is odd, multiply by 3 and add 1.
  \item Repeat the procedure with the new number.
  \item It appears that for all starting values there is a cycle of 4, 2, 1 at which the procedure loops.
\end{enumerate}
    Write a program that accepts the starting value and prints out the Collatz sequence.

\end{frame}

\begin{frame}[fragile]{Problem 1.4}
  Write a program that prints the following pyramid on the screen. 
  \begin{lstlisting}
1
2  2
3  3  3
4  4  4  4
  \end{lstlisting}
The number of lines must be obtained from the user as input.\\
\pause
\emphbar{When can your code fail?}
\only<2->{\inctime{20}}
\end{frame}

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% TIME: 20 m, running 20m 
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\section{Functions}
\subsection{Defining}
\begin{frame}[fragile]
\frametitle{Functions: examples}
  \begin{lstlisting}
def signum( r ):
    """returns 0 if r is zero
    -1 if r is negative
    +1 if r is positive"""
    if r < 0:
        return -1
    elif r > 0:
        return 1
    else:
        return 0
  \end{lstlisting}
\end{frame}

\begin{frame}[fragile]
  \frametitle{Functions: examples}
  \begin{lstlisting}
def pad( n, size ): 
    """pads integer n with spaces
    into a string of length size
    """
    SPACE = ' '
    s = str( n )
    padSize = size - len( s )
    return padSize * SPACE + s
  \end{lstlisting}
\pause
\emphbar{What about \% formatting?}
\end{frame}

\begin{frame}[fragile]
  {What does this function do?}
  \begin{lstlisting}
def what( n ):
    if n < 0: n = -n
    while n > 0:
        if n % 2 == 1:
            return False
        n /= 10
    return True
  \end{lstlisting}
\end{frame}

\begin{frame}[fragile]
  {What does this function do?}
\begin{lstlisting}
def what( n ):
    i = 1    
    while i * i < n:
        i += 1
    return i * i == n, i
  \end{lstlisting}
\end{frame}

\begin{frame}[fragile]
  {What does this function do?}
  \begin{lstlisting}
def what( n, x ):
    z = 1.0
    if n < 0:
        x = 1.0 / x
        n = -n
    while n > 0:
        if n % 2 == 1:
            z *= x
        n /= 2
        x *= x
    return z
  \end{lstlisting}
\end{frame}

\subsection{Built-in functions}
\begin{frame}
  {Before writing a function}
  \begin{itemize}
      \item Variety of builtin functions are available
      \item \typ{abs, any, all, len, max, min}
      \item \typ{pow, range, sum, type}
      \item Refer here:
          \url{http://docs.python.org/library/functions.html}
  \end{itemize}
  \inctime{10} 
\end{frame}
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\subsection{Exercises}
\begin{frame}{Problem set 2: Problem 2.1}
  Write a function to return the gcd of two numbers.
\end{frame}

\begin{frame}{Problem 2.2}
Write a program to print all primitive pythagorean triads (a, b, c) where a, b are in the range 1---100 \\
A pythagorean triad $(a,b,c)$ has the property $a^2 + b^2 = c^2$.\\By primitive we mean triads that do not `depend' on others. For example, (4,3,5) is a variant of (3,4,5) and hence is not primitive. And (10,24,26) is easily derived from (5,12,13) and is also not primitive.
\end{frame}

\begin{frame}{Problem 2.3}
  Write a program that generates a list of all four digit numbers that have all their digits even and are perfect squares.\newline\\\emph{For example, the output should include 6400 but not 8100 (one digit is odd) or 4248 (not a perfect square).}
\end{frame}

\begin{frame}{Problem 2.4}
  The aliquot of a number is defined as: the sum of the \emph{proper} divisors of the number. For example, aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.\\
  Write a function that returns the aliquot number of a given number. 
\end{frame}

\begin{frame}{Problem 2.5}
  A pair of numbers (a, b) is said to be \alert{amicable} if the aliquot number of a is b and the aliquot number of b is a.\\
  Example: \texttt{220, 284}\\
  Write a program that prints all four digit amicable pairs.
  \inctime{25}
\end{frame}

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% TIME: 25 m, running 55m 
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\section{Lists}

\subsection{Manipulating}
\begin{frame}[fragile]
  \frametitle{List creation and indexing}
\begin{lstlisting}
>>> a = [] # An empty list.
>>> a = [1, 2, 3, 4] # More useful.
>>> len(a) 
4
>>> a[0] + a[1] + a[-1]
7
\end{lstlisting}
  \begin{itemize}
  \item Indices start with ?
  \item Negative indices indicate ?
  \end{itemize}
\end{frame}

\begin{frame}[fragile]
  \frametitle{List: slices}
  \begin{itemize}
  \item Slicing is a basic operation
  \item \typ{list[initial:final:step]}
  \item  The step is optional
  \end{itemize}
\begin{lstlisting}
>>> a[1:3] # A slice.
[2, 3]
>>> a[1:-1]
[2, 3]
>>> a[1:] == a[1:-1]
False  
\end{lstlisting}
Explain last result
\end{frame}

\begin{frame}[fragile]
  \frametitle{List: more slices}
\begin{lstlisting}
>>> a[0:-1:2] # Notice the step!
[1, 3]
>>> a[::2]
[1, 3]
>>> a[-1::-1]
\end{lstlisting}
What do you think the last one will do?
  \emphbar{Strings also use same indexing and slicing.}
\end{frame}

\begin{frame}[fragile]
  \frametitle{List: examples}
\begin{lstlisting}
>>> a = [1, 2, 3, 4]
>>> a[:2]
[1, 2]
>>> a[0:-1:2]
[1, 3]
\end{lstlisting}
\pause
\alert{Lists are mutable (unlike strings)}
\begin{lstlisting}
>>> a[1] = 20
>>> a
[1, 20, 3, 4]
\end{lstlisting}
\end{frame}

\begin{frame}[fragile]
  \frametitle{Lists are mutable and heterogenous}
\begin{lstlisting}
>>> a = ['spam', 'eggs', 100, 1234]
>>> a[2] = a[2] + 23
>>> a
['spam', 'eggs', 123, 1234]
>>> a[0:2] = [1, 12] # Replace items
>>> a
[1, 12, 123, 1234]
>>> a[0:2] = [] # Remove items
>>> a.append( 12345 )
>>> a
[123, 1234, 12345]
\end{lstlisting}
\inctime{10}
\end{frame}

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\subsection{Methods}
\begin{frame}[fragile]
  \frametitle{List methods}
\begin{lstlisting}
>>> a = ['spam', 'eggs', 1, 12]
>>> a.reverse() # in situ
>>> a
[12, 1, 'eggs', 'spam']
>>> a.append(['x', 1])
>>> a
[12, 1, 'eggs', 'spam', ['x', 1]]
>>> a.extend([1,2]) # Extend the list.
>>> a.remove( 'spam' )
>>> a
[12, 1, 'eggs', ['x', 1], 1, 2]
\end{lstlisting}
\end{frame}

\begin{frame}[fragile]
  \frametitle{List containership}
  \begin{lstlisting}
>>> a = ['cat', 'dog', 'rat', 'croc']
>>> 'dog' in a
True
>>> 'snake' in a
False
>>> 'snake' not in a
True
>>> 'ell' in 'hello world'
True
  \end{lstlisting}
  \inctime{5}
\end{frame}

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\section{Tuples}
\begin{frame}[fragile]
  \frametitle{Tuples: immutable}
\begin{lstlisting}
>>> t = (0, 1, 2)
>>> print t[0], t[1], t[2], t[-1] 
0 1 2 2
>>> t[0] = 1
Traceback (most recent call last):
  File "<stdin>", line 1, in ?
TypeError: object does not support
item assignment
\end{lstlisting}  
\begin{itemize}
    \item Multiple return values are actually a tuple.
    \item Exchange is tuple (un)packing
\end{itemize}
\inctime{5}
\end{frame}

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\section{for and range()}
\begin{frame}[fragile]
  \frametitle{\typ{range()} function}
  \begin{lstlisting}
>>> range(7)
[0, 1, 2, 3, 4, 5, 6]
>>> range( 3, 9)
[3, 4, 5, 6, 7, 8]
>>> range( 4, 17, 3)
[4, 7, 10, 13, 16]
>>> range( 5, 1, -1)
[5, 4, 3, 2]
>>> range( 8, 12, -1)
[]
  \end{lstlisting}
\end{frame}

\begin{frame}[fragile]
  \frametitle{\typ{for\ldots range(\ldots)} idiom}
  \begin{lstlisting}
In [83]: for i in range(5):
   ....:     print i, i * i
   ....:     
   ....:     
0 0
1 1
2 4
3 9
4 16
\end{lstlisting}
\end{frame}

\begin{frame}[fragile]
  \frametitle{\typ{for}: the list companion}
  
  \begin{lstlisting}
In [84]: a = ['a', 'b', 'c']
In [85]: for x in a:
   ....:    print x, chr( ord(x) + 10 )
   ....:
a  k
b  l
c  m
  \end{lstlisting}
  Iterating over the list and not the index + reference\\
  what if you want the index?
\end{frame}

\begin{frame}[fragile]
  \frametitle{\typ{for}: the list companion}
  \begin{lstlisting}
In [89]: for p, ch in enumerate( a ):
   ....:     print p, ch
   ....:     
   ....:     
0 a
1 b
2 c
  \end{lstlisting}
Try: \typ{print enumerate(a)}
\inctime{10}
\end{frame}

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% TIME: 10 m, running 85m 
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\begin{frame}
  \frametitle{What did we learn?}
  \begin{itemize}
    \item Control flow in action
    \item Functions
    \item Manipulating Lists 
    \item Tuples
    \item range() function
    \item for loops
    \item for...range() idiom
  \end{itemize}
\end{frame}
\end{document}