day1/Problems.tex
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\documentclass[12pt]{article}
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\title{Python Workshop\\Problems and Exercises}
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\author{Asokan Pichai\\Prabhu Ramachandran}
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\begin{document}
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\maketitle
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\section{Python}
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\subsection{Getting started}
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   \begin{verbatim}
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>>> print 'Hello Python' 
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>>> print 3124 * 126789
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>>> 1786 % 12
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>>> 3124 * 126789
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>>> a = 3124 * 126789
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>>> big = 12345678901234567890 ** 3
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>>> verybig = big * big * big * big 
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>>> 12345**6, 12345**67, 12345**678
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>>> s = 'Hello '
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>>> p = 'World'
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>>> s + p 
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>>> s * 12 
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>>> s * s
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>>> s + p * 12, (s + p)* 12
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>>> s * 12 + p * 12
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>>> 12 * s 
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\end{verbatim}
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\newpage
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\begin{verbatim}
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>>> 17/2
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>>> 17/2.0
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>>> 17.0/2
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>>> 17.0/8.5
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>>> int(17/2.0)
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>>> float(17/2)
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>>> str(17/2.0)
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>>> round( 7.5 )
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\end{verbatim}
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\subsection{Mini exercises}
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\begin{itemize}
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  \item Round a float to the nearest integer, using \texttt{int()}?
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  \item What does this do?  \\\texttt{round(amount * 10) /10.0 }
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  \item How to round a number to the nearest  5 paise?
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    \begin{description}
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      \item[Remember] 17.23 $\rightarrow$ 17.25,\\ while 17.22 $\rightarrow$ 17.20
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    \end{description}
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  \item How to round a number to the nearest 20 paise?
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\end{itemize}
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\begin{verbatim}
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    amount = 12.68
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    denom = 0.05
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    nCoins = round(amount/denom)
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    rAmount = nCoins * denom
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\end{verbatim}
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\subsection{Dynamic typing}
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\begin{verbatim}
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a = 1
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a = 1.1
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a = "Now I am a string!"
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\end{verbatim}
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\subsection{Comments}
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\begin{verbatim}
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a = 1  # In-line comments
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# Comment in a line to itself.
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a = "# This is not a comment!"
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  \end{verbatim}
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\section{Data types}
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\subsection{Numbers}
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  \begin{verbatim}
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>>> a = 1 # Int.
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>>> l = 1000000L # Long
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>>> e = 1.01325e5 # float
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>>> f = 3.14159 # float
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>>> c = 1+1j # Complex!
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>>> print f*c/a
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(3.14159+3.14159j)
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>>> print c.real, c.imag
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1.0 1.0
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>>> abs(c)
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1.4142135623730951
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>>> abs( 8 - 9.5 )
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1.5
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  \end{verbatim}
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\subsection{Boolean}
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  \begin{verbatim}
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>>> t = True
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>>> f = not t
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False
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>>> f or t
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True
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>>> f and t
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False
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>>>  NOT True
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\ldots ???
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>>>  not TRUE
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\ldots ???
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\end{verbatim}
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\subsection{Relational and logical operators}
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  \begin{verbatim}
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>>> a, b, c = -1, 0, 1
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>>> a == b
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False
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>>> a <= b 
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True
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>>> a + b != c
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True
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>>> a < b < c
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True
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>>> c >= a + b
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True
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  \end{verbatim}
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\subsection{Strings}
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  \begin{verbatim}
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s = 'this is a string'
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s = 'This one has "quotes" inside!'
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s = "I have 'single-quotes' inside!"
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l = "A string spanning many lines\
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one more line\
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yet another"
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t = """A triple quoted string does
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not need to be escaped at the end and 
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"can have nested quotes" etc."""
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  \end{verbatim}
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  \begin{verbatim}
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>>> w = "hello"    
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>>> print w[0] + w[2] + w[-1]
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hlo
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>>> len(w) # guess what
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5
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>>> s = u'Unicode strings!'
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>>> # Raw strings (note the leading 'r')
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... r_s = r'A string $\alpha \nu$'
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  \end{verbatim}
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  \begin{verbatim}
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>>> w[0] = 'H' # Can't do that!
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Traceback (most recent call last):
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  File "<stdin>", line 1, in ?
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TypeError: object does not support item assignment
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  \end{verbatim}
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  \subsection{IPython}
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  \begin{verbatim}
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In [1]: a = 'hello world'
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In [2]: a.startswith('hell')
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Out[2]: True
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In [3]: a.endswith('ld')
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Out[3]: True
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In [4]: a.upper()
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Out[4]: 'HELLO WORLD'
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In [5]: a.upper().lower()
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Out[5]: 'hello world'
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In [6]: a.split()
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Out[6]: ['hello', 'world']
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In [7]: ''.join(['a', 'b', 'c'])
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Out[7]: 'abc'
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In [8] 'd' in ''.join( 'a', 'b', 'c')
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Out[8]: False
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a.split( 'o' )}
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???
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'x'.join( a.split( 'o' ) )
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???
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In [11]: x, y = 1, 1.2
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In [12]: 'x is %s, y is %s' %(x, y)
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Out[12]: 'x is 1, y is 1.234'
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'x is \%d, y is \%f' \%(x, y)
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???
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'x is \%3d, y is \%4.2f' \%(x, y)
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??? 
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  \end{verbatim}
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\subsection{A classic problem}
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    How to interchange values of two variables? Please note that the type of either variable is unknown and it is not necessary that both be of the same type even!
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\subsection{Basic conditional flow}
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  \begin{verbatim}
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In [21]: a = 7
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In [22]: b = 8
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In [23]: if a > b:
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   ....:    print 'Hello'
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   ....: else:
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   ....:     print 'World'
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   ....:
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   ....:
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World
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  \end{verbatim}
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\subsection{\texttt{If...elif...else} example}
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\begin{verbatim}
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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{verbatim}
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\subsection{Basic looping}
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  \begin{verbatim}
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# Fibonacci series:
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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{verbatim}
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\section{Problem set 1}
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All the problems can be solved using \texttt{if} and \texttt{while} 
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\begin{description}
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  \item[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 $abc = a^3 + b^3 + c^3$\\
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These are called $Armstrong$ numbers.
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\item[1.2 Collatz sequence]
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\begin{enumerate}
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  \item Start with an arbitrary (positive) integer. 
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  \item If the number is even, divide by 2; if the number is odd multiply by 3 and add 1.
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  \item Repeat the procedure with the new number.
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  \item There is a cycle of 4, 2, 1 at which the procedure loops.
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\end{enumerate}
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    Write a program that accepts the starting value and prints out the Collatz sequence.
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  \item[1.3 Kaprekar's constant]
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  \begin{enumerate}
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    \item Take a four digit number--with at least two digits different.
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    \item Arrange the digits in ascending and descending order, giving A and D respectively.
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    \item Leave leading zeros in A!
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    \item Subtract A from D.
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    \item With the result, repeat from step 2.
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  \end{enumerate}
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  Write a program to accept a 4-digit number and display the progression to Kaprekar's constant.
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\item[1.4]
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  Write a program that prints the following pyramid on the screen. 
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  \begin{verbatim}
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1
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2  2
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3  3  3
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   256
4  4  4  4
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  \end{verbatim}
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The number of lines must be obtained from the user as input.\\
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When can your code fail?
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\end{description}
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\subsection{Functions: examples}
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  \begin{verbatim}
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def signum( r ):
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    """returns 0 if r is zero
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    -1 if r is negative
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    +1 if r is positive"""
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    if r < 0:
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        return -1
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    elif r > 0:
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        return 1
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    else:
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        return 0
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def pad( n, size ): 
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    """pads integer n with spaces
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    into a string of length size
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    """
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    SPACE = ' '
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    s = str( n )
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    padSize = size - len( s )
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    return padSize * SPACE + s
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  \end{verbatim}
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What about \%3d?
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   286
\subsection  {What does this function do?}
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  \begin{verbatim}
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def what( n ):
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    if n < 0: n = -n
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    while n > 0:
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   291
        if n % 2 == 1:
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            return False
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        n /= 10
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    return True
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  \end{verbatim}
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   296
\newpage
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   298
\subsection{What does this function do?}
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\begin{verbatim}
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def what( n ):
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    i = 1    
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    while i * i < n:
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        i += 1
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    return i * i == n, i
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  \end{verbatim}
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   307
\subsection{What does this function do?}
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   308
  \begin{verbatim}
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def what( n, x ):
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    z = 1.0
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   311
    if n < 0:
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        x = 1.0 / x
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        n = -n
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   314
    while n > 0:
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   315
        if n % 2 == 1:
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            z *= x
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   317
        n /= 2
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        x *= x
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   319
    return z
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   320
  \end{verbatim}
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   321
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   322
\section{Problem set 2}
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   323
  The focus is on writing functions and calling them.
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   324
\begin{description}
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   325
  \item[2.1] Write a function to return the gcd of two numbers.
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   326
  \item[2.2 Primitive Pythagorean Triads] 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 should not be displayed by our program. \\
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   327
Write a program to print primitive pythagorean triads. The program should generate all triads with a, b values in the range 0---100
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   328
\item[2.3] Write a program that generates a list of all four digit numbers that have all their digits even and are perfect squares.\\For example, the output should include 6400 but not 8100 (one digit is odd) or 4248 (not a perfect square).
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   329
\item[2.4 Aliquot] The aliquot of a number is defined as: the sum of the \emph{proper} divisors of the number. For example, the aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.\\
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   330
  Write a function that returns the aliquot number of a given number. 
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   331
\item[2.5 Amicable pairs] A pair of numbers (a, b) is said to be \emph{amicable} if the aliquot number of a is b and the aliquot number of b is a.\\
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   332
  Example: \texttt{220, 284}\\
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   333
  Write a program that prints all five digit amicable pairs.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   334
\end{description}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   335
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   336
\section{Lists}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   337
\subsection{List creation and indexing}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   338
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   339
>>> a = [] # An empty list.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   340
>>> a = [1, 2, 3, 4] # More useful.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   341
>>> len(a) 
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   342
4
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   343
>>> a[0] + a[1] + a[2] + a[-1]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   344
10
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   345
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   346
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   347
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   348
>>> a[1:3] # A slice.
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   349
[2, 3]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   350
>>> a[1:-1]
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   351
[2, 3, 4]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   352
>>> a[1:] == a[1:-1]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   353
False  
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   354
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   355
Explain last result
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   356
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   357
\newpage
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   358
\subsection{List: more slices}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   359
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   360
>>> a[0:-1:2] # Notice the step!
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   361
[1, 3]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   362
>>> a[::2]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   363
[1, 3]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   364
>>> a[-1::-1]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   365
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   366
What do you think the last one will do?\\
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   367
\emph{Note: Strings also use same indexing and slicing.}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   368
  \subsection{List: examples}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   369
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   370
>>> a = [1, 2, 3, 4]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   371
>>> a[:2]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   372
[1, 3]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   373
>>> a[0:-1:2]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   374
[1, 3]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   375
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   376
\emph{Lists are mutable (unlike strings)}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   377
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   378
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   379
>>> a[1] = 20
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   380
>>> a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   381
[1, 20, 3, 4]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   382
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   383
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   384
  \subsection{Lists are mutable and heterogenous}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   385
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   386
>>> a = ['spam', 'eggs', 100, 1234]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   387
>>> a[2] = a[2] + 23
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   388
>>> a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   389
['spam', 'eggs', 123, 1234]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   390
>>> a[0:2] = [1, 12] # Replace items
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   391
>>> a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   392
[1, 12, 123, 1234]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   393
>>> a[0:2] = [] # Remove items
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   394
>>> a.append( 12345 )
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   395
>>> a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   396
[123, 1234, 12345]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   397
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   398
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   399
  \subsection{List methods}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   400
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   401
>>> a = ['spam', 'eggs', 1, 12]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   402
>>> a.reverse() # in situ
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   403
>>> a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   404
[12, 1, 'eggs', 'spam']
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   405
>>> a.append(['x', 1]) 
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   406
>>> a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   407
[12, 1, 'eggs', 'spam', ['x', 1]]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   408
>>> a.extend([1,2]) # Extend the list.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   409
>>> a.remove( 'spam' )
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   410
>>> a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   411
[12, 1, 'eggs', ['x', 1], 1, 2]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   412
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   413
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   414
  \subsection{List containership}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   415
  \begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   416
>>> a = ['cat', 'dog', 'rat', 'croc']
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   417
>>> 'dog' in a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   418
True
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   419
>>> 'snake' in a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   420
False
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   421
>>> 'snake' not in a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   422
True
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   423
>>> 'ell' in 'hello world'
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   424
True
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   425
  \end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   426
  \subsection{Tuples: immutable}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   427
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   428
>>> t = (0, 1, 2)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   429
>>> print t[0], t[1], t[2], t[-1] 
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   430
0 1 2 2
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   431
>>> t[0] = 1
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   432
Traceback (most recent call last):
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   433
  File "<stdin>", line 1, in ?
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   434
TypeError: object does not support item assignment
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   435
\end{verbatim}  
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   436
    Multiple return values are actually a tuple.\\
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   437
    Exchange is tuple (un)packing
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   438
  \subsection{\texttt{range()} function}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   439
  \begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   440
>>> range(7)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   441
[0, 1, 2, 3, 4, 5, 6]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   442
>>> range( 3, 9)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   443
[3, 4, 5, 6, 7, 8]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   444
>>> range( 4, 17, 3)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   445
[4, 7, 10, 13, 16]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   446
>>> range( 5, 1, -1)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   447
[5, 4, 3, 2]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   448
>>> range( 8, 12, -1)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   449
[]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   450
  \end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   451
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   452
  \subsection{\texttt{for\ldots range(\ldots)} idiom}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   453
  \begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   454
In [83]: for i in range(5):
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   455
   ....:     print i, i * i
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   456
   ....:     
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   457
   ....:     
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   458
0 0
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   459
1 1
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   460
2 4
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   461
3 9
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   462
4 16
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   463
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   464
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   465
  \subsection{\texttt{for}: the list companion}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   466
  
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   467
  \begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   468
In [84]: a = ['a', 'b', 'c']
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   469
In [85]: for x in a:
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   470
   ....:    print x, chr( ord(x) + 10 )
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   471
   ....:
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   472
a  k
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   473
b  l
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   474
c  m
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   475
  \end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   476
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   477
  \subsection{\texttt{for}: the list companion}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   478
  \begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   479
In [89]: for p, ch in enumerate( a ):
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   480
   ....:     print p, ch
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   481
   ....:     
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   482
   ....:     
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   483
0 a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   484
1 b
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   485
2 c
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   486
  \end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   487
Try: \texttt{print enumerate(a)}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   488
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   489
\section{Problem set 3}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   490
  As you can guess, idea is to use \texttt{for}!
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   491
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   492
\begin{description}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   493
  \item[3.1] Which of the earlier problems is simpler when we use \texttt{for} instead of \texttt{while}? 
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   494
  \item[3.2] Given an empty chessboard and one Bishop placed in any square, say (r, c), generate the list of all squares the Bishop could move to.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   495
  \item[3.3] Given two real numbers \texttt{a, b}, and an integer \texttt{N}, write a
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   496
  function named \texttt{linspace( a, b, N)} that returns an ordered list
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   497
  of \texttt{N} points starting with \texttt{a} and ending in \texttt{b} and
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   498
  equally spaced.\\
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   499
  For example, \texttt{linspace(0, 5, 11)}, should return, \\
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   500
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   501
[ 0.0 ,  0.5,  1.0 ,  1.5,  2.0 ,  2.5,  
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   502
  3.0 ,  3.5,  4.0 ,  4.5,  5.0 ]
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   503
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   504
  \item[3.4a] Use the \texttt{linspace} function and generate a list of N tuples of the form\\
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   505
\texttt{[($x_1$,f($x_1$)),($x_2$,f($x_2$)),\ldots,($x_N$,f($x_N$))]}\\for the following functions,
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   506
\begin{itemize}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   507
  \item \texttt{f(x) = sin(x)}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   508
  \item \texttt{f(x) = sin(x) + sin(10*x)}.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   509
\end{itemize}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   510
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   511
\item[3.4b] Using the tuples generated earlier, determine the intervals where the roots of the functions lie.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   512
\end{description}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   513
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   514
\section{IO}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   515
  \subsection{Simple tokenizing and parsing}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   516
  \begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   517
s = """The quick brown fox jumped
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   518
       over the lazy dog"""
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   519
for word in s.split():
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   520
    print word.capitalize()
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   521
  \end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   522
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   523
  \begin{description}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   524
    \item[4.1] Given a string like, ``1, 3-7, 12, 15, 18-21'', produce the list \texttt{[1,3,4,5,6,7,12,15,18,19,20,21]}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   525
\end{description}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   526
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   527
  \subsection{File handling}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   528
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   529
>>> f = open('/path/to/file_name')
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   530
>>> data = f.read() # Read entire file.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   531
>>> line = f.readline() # Read one line.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   532
>>> f.close() # close the file.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   533
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   534
Writing files
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   535
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   536
>>> f = open('/path/to/file_name', 'w')
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   537
>>> f.write('hello world\n')
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   538
>>> f.close()
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   539
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   540
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   541
    \subsection{File and \texttt{for}}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   542
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   543
>>> f = open('/path/to/file_name')
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   544
>>> for line in f:
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   545
...     print line
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   546
...
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   547
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   548
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   549
  \begin{description}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   550
    \item[4.2] The given file has lakhs of records in the form:
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   551
    \texttt{RGN;ID;NAME;MARK1;\ldots;MARK5;TOTAL;PFW}.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   552
    Some entries may be empty.  Read the data from this file and print the
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   553
    name of the student with the maximum total marks.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   554
  \item[4.3] For the same data file compute the average marks in different
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   555
    subjects, the student with the maximum mark in each subject and also
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   556
    the standard deviation of the marks.  Do this efficiently.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   557
\end{description}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   558
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   559
\section{Modules}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   560
\begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   561
>>> sqrt(2)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   562
Traceback (most recent call last):
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   563
  File "<stdin>", line 1, in <module>
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   564
NameError: name 'sqrt' is not defined
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   565
>>> import math        
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   566
>>> math.sqrt(2)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   567
1.4142135623730951
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   568
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   569
>>> from math import sqrt
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   570
>>> from math import *
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   571
>>> from os.path import exists
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   572
\end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   573
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   574
  \subsection{Modules: example}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   575
  \begin{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   576
# --- arith.py ---
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   577
def gcd(a, b):
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   578
    if a%b == 0: return b
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   579
    return gcd(b, a%b)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   580
def lcm(a, b):
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   581
    return a*b/gcd(a, b)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   582
# ------------------
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   583
>>> import arith
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   584
>>> arith.gcd(26, 65)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   585
13
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   586
>>> arith.lcm(26, 65)
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   587
130
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   588
  \end{verbatim}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   589
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   590
  \begin{description}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   591
    \item[5.1] Put all the functions you have written so far as part of the problems
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   592
  into one module called \texttt{iitb.py} and use this module from IPython.
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   593
\end{description}
9243d75024cc Initial data added.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   594
\end{document}