CSE 109   Program #0   Due 9:00 PM Thursday 7 February 2008
   (Late collections: 9:00 PM  9, 10 2008)

In this assignment I ask you to develop a class whose objects are meant
to implement the concept of a Path.  At the bottom of the page I describe
the properties of a Path.

In /proj/csc109/p0 I have stored the file p0.cc, which is a driver for
testing the class Path.  The file p0.cc also has the declarations and
code for the class Point that I developed. I have stored in the file
/proj/csc109/p0/p0.out the output that appeared on the screen when I
ran the compiled version of p0.cc with my implementation of class
Path. Further, I have stored the file 'Makefile' in /proj/csc109/p0.
You should copy the files  /proj/csc109/p0/p0.cc and
/proj/csc109/p0/Makefile into your directory cse109.081/p0 (a directory
you should create).  You should do all your work in the directory
cse109.081/p0.  I will collect your work from there.

You should add to p0.cc your declaration of class Path, as well as
the definitions (code), BUT DO NOT CHANGE THE *CODE* THAT I WROTE IN p0.cc
AT ALL (BUT IT IS VERY IMPORTANT THAT YOU DO ADD DOCUMENTATION). I REPEAT,
DO NOT CHANGE THE CODE THAT I WROTE IN ANY WAY, but ADD DOCUMENTATION (name,
assignment, program purpose, etc.,) AND YOUR OWN CODE FOR THE CLASS
Path. OTHERWISE YOU WILL LOSE AT LEAST 20 PTS. I will test your class
Path  by using the command "make clean" to discard your executable
file. Then I will compile and run your p0.cc (by executng the command
'make').

When you are ready to submit your work, create the file "DONE" by executing
the command "touch DONE".

Notes: 1. Both your file p0.cc and your makefile, should have good
         documentation.  Each file should have identifying information at the
         top, e.g., your name, the course, the assignment number.
         Your class should be documented with comments at the top
         which explain the class and its purpose.  The role of each data
         member should be explained.  Each member function should be explained
         (e.g., by stating pre- and post-conditions and by stating the overall
         algorithm).  Hard to to understand sections of the code (definitions)
         should be explained.
       2. I found the class Point useful in my implementation of
         Path. If you do not use the class Point, delete the
         declaration and definitions from p0.cc.
       3. For neatly displaying doubles, see p528 of the text (Savitch).

IN THE SYLLABUS READ THE STATEMENT ABOUT UNFAIR COLLABORATION AND AVOID
UNFAIR COLLABORATION

A Path is a sequence of points. In my description of a Path I indicate in
parentheses the method or operator that the class Path uses to implement
the given property.  Examine the code in p0.cc and the expected output to
clarify how the methods and operators should function. Note that the
expected output is listed in a comment at the bottom of p0.cc and in p0.out.
We should be able to add points to a path (+=).  We should be able to
determine how many points are in the path (length()).  We should be able to
determine how long the path is (distance()).  We should be able to splice
two paths together (+).  We should be able to set a variable equal to a
path (=).  We should be able to ask whether two paths are identical (==, !=).
We should be able to access individual points in the path ([]).  We should
be able to display the points in the path (<<). We should determine whether
a path is a loop, i.e., whether the last point and the first point in the
path are the same (isLoop()).

Note:  4. To compute the distance(), you need to use the square root
          function ( double sqrt(double b) ). In p0.cc I have included
          <cmath>, a library that has the sqrt() function.  The distance
          for a path is the sum of the distances between consecutive points
          in the path.  The distance between points (a,b) and (c,d) is
          the square root of (a-c)*(a-c)+(b-d)*(b-d).