Question 2:
===========

You are asked to develop software for
the following new version of the SDG game.
The raw material is a collection of
weighted constraints as in SDG(CSP)
and all constraints are expressed
as linear inequalities of the form:

sum x_i = j
sum x_i >= j
sum x_i <= j

Example of a raw material in this new form:

10  x1 x6 x8 = 1
3   x1 x5 x7 = 2
4   x1 x2 >= 1
200 x1 x2 <= 1
2   x2 = 1

The meaning of the first constraint 
10  x1 x6 x8 = 1
is
x1 + x6 + x8 = 1 with weight 10.
The addition is integer addition but as usual,
the variables only assume values 0 or 1.

How would you manage this software development project?
Develop a brief plan and write it down succinctly like:

1. Class dictionary for new notation.
2. Extend class dictionary to cover new and old notation.
3. Write DemeterF function object ...

Design a class dictionary for inputting the
new kind of raw material.

Find the UNKNOWNs in the following class dictionary:

CSP = ConstraintList.
Constraint = *l UNKNOWN UNKNOWN UNKNOWN UNKNOWN.
Kind : Exact | GreaterThanEqual | LessThanEqual.
Exact = "=".
GreaterThanEqual = ">=".
LessThanEqual = "<=".
Variable = <v> Ident.
Relation = <v> int.
Weight = <v> int.
Constant = <v> int.

ConstraintList : NECL | ECL.
NECL = <first> Constraint <rest> ConstraintList.
ECL = .

VariableList : NEVL | EVL.
NEVL = <first> Variable <rest> VariableList.
EVL = .

How would you leverage the current SDG(CSP) implementation?
You must translate the new input format into
an XML style input format and figure out
a function relNumber(int numberOfvariables, Kind kind, Constant constant)
that determines the relation number.
For example, relNumber("3","=","1") = 22.

Assume that this function is given to you and it currently
is the constant 3000.

Write a program to translate constraints of the new form:

10 x1 x6 x8=1
3 x1 x5 x7=2
4 x1 x2>=1
200 x1 x2<=1
2 x2=1 

to constraints of the old XML style form:

<constraint><weight>10</weight><relation>3000</relation>
  <variables>x1 x6 x8</variables></constraint>
<constraint><weight>3</weight><relation>3000</relation>
  <variables>x1 x5 x7</variables></constraint>
<constraint><weight>4</weight><relation>3000</relation>
  <variables>x1 x2</variables></constraint>
<constraint><weight>200</weight><relation>3000</relation>
  <variables>x1 x2</variables></constraint>
<constraint><weight>2</weight><relation>3000</relation>
  <variables>x2</variables></constraint> done 

Find the UNKNOWNS in the enclosed program:

import edu.neu.ccs.demeterf.*;

class Trans extends IDf{ 
  UNKNOWN
  static CSP trans (Object o)
    {
	return new Traversal(new Trans()). <CSP> UNKNOWN(o);
    }

}