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CSC 373            Homework Exercise 3 -- Marking Scheme          Fall 2008
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NOTE TO STUDENTS:

You will find below the marking scheme used for your homework, including
the meaning of marking codes and number of marks associated with each one.
This file also contains my instructions to the marker (so you can get an
idea of how the homework was marked) and the marker's comments about each
question.

Please take the time to read this carefully before you ask questions about
the grading of your homework.


NOTE TO MARKER:

Be picky!  On any homework, it is the responsibility of students to show
that they understand how to solve each problem and to write up their
answers carefully.  At the same time, keep in mind that exercises are worth
only 1.5% of the final grade, so your marking should be somewhat coarse.
And remember that marking is not just about evaluating the students's
performances, but also about giving them feedback so that they can learn
from their mistakes.  This is especially important for students who made
numerous or more serious mistakes, as they are likely to need more feedback
in order to understand why their answers were incorrect.

For each question, I list solution elements with an associated code for
writing on student papers (the letter(s) between underscores _) and a
number of marks.  There are also general errors (with associated codes)
given below, with a maximum number of marks to take off for each type of
general error (as a percentage of the value of the question).  You will
likely encounter other common errors, or maybe decide to break down the
marking scheme further.  Simply make note of these changes/additions to
the marking scheme, and introduce new code letters (or short words) to
allow you to quickly give accurate feedback to the students (both in terms
of what they did wrong and how many marks it cost them).


GENERAL ERRORS (marked negatively, in addition to any other errors):

    _N_otation [up to 20%]:  incorrect/ambiguous notation

    _V_agueness [up to 20%]:  incorrect/unjustified/vague claim


1.  [15 marks]

    _S_tructure [3 marks]:  clear attempt to define an array of values
        related to the problem, to give a recurrence relation for the
        array values, to justify the recurrence based on the recursive
        structure of an optimal solution, to give an algorithm to compute
        the array values bottom-up, and to generate an actual solution
        from those values

    _A_rray [2 mark]:  clear and correct definition of the array

    _R_ecurrence [3 marks]:  correct recurrence for the array,
        including appropriate base cases

    _J_ustification [2 marks]:  good justification of correctness for
        the recurrence

    _B_ottom-up algorithm [2 marks]:  correct bottom-up algorithm to
        compute array values -- give marks for correctly computing array
        values following the recurrence, even if recurrence is incorrect

    _C_onstructing solution [3 marks]:  correct algorithm to find an actual
        solution -- working backwards and making correct choices based on
        values in the array -- give marks for correctly finding a solution
        assuming that array values have been computed correctly, even if
        they haven't been

    Marker's Comments:

    Fairly well done.  Major problem: forgetting to check for out-of-bounds
    indices.  Also, some students who tried to start at (n,n) and work
    backwards to (1,1) mixed up their indices and would add 1 instead of
    subtracting it.