Grading Guide for Assignment 3


The correct answer for the pile depth is: 3.4218

*************************************************************************
 Points |   C	|	S
________ _______ _____________
  5	|  0-3	|      0-1	
________ _______ _____________
  4	|  4-8	|      2-3	
________ _______ _____________
  3	|  9-14	|      4-5	
________ _______ _____________
  2	|  15-20|      6-7	
________ _______ _____________
  1	|  20-30|      7-8	
________ _______ _____________
  0	|  more |      more	

*************************************************************************
UNIVERSAL STYLE/CORRECTESS POINTS (same for all problems)
X represents problem # (i.e. 1,2,4...)

   cXa: doesn't compile, or no submitted file, or discussion is not in a text file
   // c1a counts as 4 correctness points, ie. c1a = 4
   // similarly, c2a = 5, c3a = 9, c4a = 10, c5a = 8

   cXb: compilation warning

   sXa: redundant code;
   sXb: bad formatting for code style;
   sXc: no comments;
   sXd: no header;
   sXx: bad file name;
   sXy: bad formatting for output;
   sXz:	using break in the loop; if they do it for every loops, treat it as one mistake

*************************************************************************
1. guessmethod
   c1c: code syntax: if ... else ... end
   c1d: test case1 input = 3 
        output: bad guessing! equation produces value -33.06 of depth 3.00
   c1e: test case2 input = 3.4218
        output: good guessing! equation produces value -0.00 of depth 3.42     
   c1f: user input error handling 
        input = -1 -> some error message

*************************************************************************
2. manualmethod
test
   c2c: [0, 10]	
   c2d: [3, 4.5], look at the plot, there should be a root
error handling
   c2e: low = -1
   c2f: low = 3; high = 2;
prompt for retesting
   c2g: if user says no, program should terminate
   c2h: if user says yes, program should correctly execute another time
style
   s2e: xlabel, ylabel,
   s2f: title, 
   s2g: tick mark labels

*************************************************************************
3. lhsrhsmethod
code syntax / algorithm correctness
   c3c: correct condition in loop
        while ( abs(eqn-target) > eps && iterations <= max_iterations)
   c3d: increase the iteration counter
   c3e: if sign changes, need to refine the increment --- divide it by 10;
   c3f: if d becomes smaller than 0, need to change direction
   c3l: need to change direction, when the sign changes.
test
   c3g: [1, pos] -> 3.4218, iterations is about 260
   c3h: [4, pos] -> "takes too long", see if terminated
   c3i: [1, neg] -> 3.4218, 
   see if reverse direction when hitting 0, not neccessarily to print out
user input error handling
   c3j: [-1, ..]
   c3k: [3, yes]		
style
   s2e: print out # of iterations
   s2f: prints solution
   s2g: prints value of the equation at solution
(Note: DO NOT take off if program doesn't prompt for retesting)	

*************************************************************************
4. bisection
code syntax / algorithm correctness
   c4c: correct condition in loop
        while ( abs(eqn-target) > eps && iterations <= max_iterations)
   c4d: increase the iteration counter
   c4e: compute the mid point and its equation value correctly
   c4f: update the interval correctly
test
   c4g: [1, 4] -> 3.4218, iterations is about 13
   c4h: [4, 10] -> "takes too long", see if terminated
   c4i: [1, 1000000] -> 3.4218, iterations is around 31
user input error handling
   c4j: [-1, ..]
   c4k: [10, 5]
   c4l: it needs to prompt for another interval if solution isn't found.
style
   s4e: print out # of iterations
   s4f: prints solution
   s4g: prints value of the equation at solution

*************************************************************************
5. newtonsmethod
code syntax / algorithm correctness
   c5c: correct condition in loop
        while ( abs(eqn-target) > eps && iterations <= max_iterations)
   c5d: increase the iteration counter
   c5e: compute the derivative correctly;
   c5f: compute the new value correctly;
test
   c5g: input = 1 -> -0.0705, iterations = 3;
                     or they can ask for a new guessing..
   c5h: input = 4 -> 3.4219, iterations = 3;
   c5i: input = 1e+10 -> 3.4219, iterations = 79;		
user input error handling
   c5j: input = -5
(Note: DO NOT take off points for returning negative root for input 
value near 0. This is technically wrong, but our p-code solution also 
had this wrong, so we can't penalize students for this)



*************************************************************************
6. Discussion
c6c: newtonsmethod is the best, 
c6d: bisection is good, similar to binary search
c6e: lhsrhsmethod is slow, similar to linear search


*************************************************************************
The bonus question is either right or wrong. 

DON'T PUT THE BONUS POINTS IN ASSIGNMENT 3,
PUT THEM IN THE "BONUS POINTS"	--- a separate assignment.

If they used symbolic toolbox and did it right: 10 points 
If they didn't use symbolic toolbox, but also return the right solution: 2 points 

*************************************************************************

 Points |   C	|	S
________ _______ _____________
  5	|  0-3	|      0-1	
________ _______ _____________
  4	|  4-8	|      2-3	
________ _______ _____________
  3	|  9-14	|      4-5	
________ _______ _____________
  2	|  15-20|      6-7	
________ _______ _____________
  1	|  20-30|      7-8	
________ _______ _____________
  0	|  more |      more