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\begin{document}

Name: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Directions: {\bf Work only on this sheet} (on both sides, if needed); do
not turn in any supplementary sheets of paper. There is actually plenty
of room for your answers, as long as you organize yourself BEFORE
starting writing.

{\bf 1.}  In this problem you will enhance the {\bf textfile} class on
p.22.  

First, you will add a member variable {\bf tfiles}, a list of
pointers to all the files for which {\bf textfile} instances currently
exist.

Second, you will add method named {\bf cat()}, which has just a
\underline{single} argument, whose name is {\bf outflname}.  This
function will concatenate all the files in {\bf tfiles}, outputting the
result to a new file whose name is given by {\bf outflname}.  Use the
open-for-writing form of {\tt open()}, which just involves adding 'w' as
a second argument, and {\bf writelines()}, which works as the opposite
of {\bf readlines()} except that now there is an argument, the outfile
name.  You should also use the {\bf close()} method for files.  You can
read examples on p.52 if you wish, but it's not necessary, as all the
information is above.

If for example file {\bf a} consists of

\begin{lstlisting}
abc
de
f
\end{lstlisting}

and file {\bf b} consists of

\begin{lstlisting}
8
168
\end{lstlisting}

then the concatenated file contents are

\begin{lstlisting}
abc
de
f
8
168
\end{lstlisting}

{\bf PLEASE WRITE YOUR SOLUTION AS FOLLOWS:} Simply write the new lines
that must be added; don't copy down the entire existing {\bf textfile}
class code.  So, write something like, ``In between lines 5 and 6,
insert the following code...''

{\bf 2.}  Consider the unit square S in the plane, with lower-left corner
at (0,0) and upper-right corner at (1,1).  We are interested in
distances from points in this square to (1,0).  There also is a smaller
rectangle R, of width 2w and height h, with lower left point (0.5-w,0) to
and upper-right point (0.5+w,h) (sides parallel to the outer square).

We are interested in the minimum travel distance to (1,0) for each point
in S that is not in R, under the constraint that travel is not allowed
within R.  Note (see the function {\bf d()} below) that we are using
``Manhattan street distance,'' which means paths consist only of
vertical and horizontal segments.

Say for instance w = 0.25 and h = 0.50, and we are considering the point
(0.20,0.10).  The shortest path to (1,0) consists first of going to
(0.25,0.50), then along the top of R, and then to (1,0), for a total
distance of 0.05 + 0.40 + 0.50 + 0.50 + 0.25.

We set up an nxn grid of points within S [(0,0) through $(\frac{n-1}{n},
\frac{n-1}{n})$, and for each one wish to compute the length of the
shortest path to (1,0).  For points in R, we define this distance to be
-1.0.  

The function {\bf getdists(w,h,n)} below returns the $n^2$ distances in
a list of lists (i.e. two-dimensional ``array'').  Fill in the details.

\begin{lstlisting}
import math

def d(x,y,x1,y1):
   return abs(x1-x) + abs(y1-y)

# returns the minimum distance
# from (x,y) to (1,0) (or returns -1.0)
def calcdistto10(x,y,w,h):
   # insert 1 or more lines here
   # ...

def getdists(w,h,n):
   # insert 1 or more lines here
   # ...
   return dists
\end{lstlisting}

{\bf IMPORTANT NOTE:} Don't worry whether boundary lines of R
count as part of R or not.  

\onecolumn

{\bf 
Solutions:} 

{\bf 1.}  

\begin{lstlisting}[numbers=left]
class textfile:
   ntfiles = 0  # count of number of textfile objects
   fls = []
   def __init__(self,fname):
      textfile.ntfiles += 1
      textfile.fls.append(self)
      self.name = fname  # name 
      self.fh = open(fname)  # handle for the file
      self.lines = self.fh.readlines()
      self.nlines = len(self.lines)  # number of lines 
      self.nwords = 0  # number of words
      self.wordcount()

   def wordcount(self):
      "finds the number of words in the file"
      self.nwords = \
         reduce(lambda x,y: x+y,map(lambda line: len(line.split()),self.lines))
   def grep(self,target):
      "prints out all lines containing target"
      lines = filter(lambda line: line.find(target) >= 0,self.lines)
      print lines
   def cat(outflname):
      ofl = open(outflname,'w')
      lns = []
      for fl in textfile.fls:
         lns += fl.lines
      ofl.writelines(lns)
      ofl.close()
   cat = staticmethod(cat)
\end{lstlisting}

{\bf 2.}

\begin{lstlisting}
def d(x,y,x1,y1):
   return abs(x1-x) + abs(y1-y)

def calcdistto10(x,y,w,h):
   if x > 0.5 - w and x < 0.5 + w and y < h: return -1.0
   if x < 0.5 - w and y < h: 
      return d(x,y,0.5-w,h) + 2*w + h + (0.5-w)
   return d(x,y,1,0)

def getdists(w,h,n):
   dists = []
   for i in range(n):
      rowofdists = []
      for j in range(n):
         tmp = calcdistto10(float(i)/n,float(j)/n,w,h)
         rowofdists.append(tmp)
      dists.append(rowofdists)
   return dists
\end{lstlisting}

\end{document}