1. CSCI5240 Combinatorial Search and Optimization with Constraints
Tutorial Notes 4

2. CSCI5240 Tutorial 4
Assignment 2

3. Question 1 Give simple and valid examples A CSP (𝑍,𝐷,𝐶) consists of:
Set of variables (𝑍)
Set of domains (𝐷)
Set of constraints (𝐶)

4. Question 2 Variables: 𝑦 1 ,…, 𝑦 𝑛 Domains: 1, …, 𝑛 Constraints:
𝑑𝑖𝑠𝑡𝑖𝑛𝑐𝑡 𝑦 1 ,…, 𝑦 𝑛 ,
|𝑦 𝑖 − 𝑦 𝑗 |≠|𝑖−𝑗| for 𝑖≠𝑗 and 𝑖,𝑗∈ 1, …, 𝑛 1 2 3 4 1 2 3 4

5. There are no queens on a particular row.
Question 2
Variables: 𝑦 1−𝑛 ,…, 𝑦 𝑛−1
Domains:
𝑖 +1, 𝑖 +3,…,2𝑛− 𝑖 −1 ∪{0}
for 𝑖∈[1−𝑛,…,𝑛−1]
There are no queens on a particular row.

6. Question 2 Variables: 𝑦 1−𝑛 ,…, 𝑦 𝑛−1 Domains:
𝑖 +1, 𝑖 +3,…,2𝑛− 𝑖 −1 ∪{0}
for 𝑖∈[1−𝑛,…,𝑛−1]
Constraints:

7. Question 2 Variables: 𝑦 1−𝑛 ,…, 𝑦 𝑛−1 Domains:
𝑖 +1, 𝑖 +3,…,2𝑛− 𝑖 −1 ∪{0}
for 𝑖∈[1−𝑛,…,𝑛−1]
Constraints:

8. Question 2 Variables: 𝑦 1−𝑛 ,…, 𝑦 𝑛−1 Domains:
𝑖 +1, 𝑖 +3,…,2𝑛− 𝑖 −1 ∪{0}
for 𝑖∈[1−𝑛,…,𝑛−1]
Constraints:

9. Question 2 Variables: 𝑦 1−𝑛 ,…, 𝑦 𝑛−1 Domains:
𝑖 +1, 𝑖 +3,…,2𝑛− 𝑖 −1 ∪{0}
for 𝑖∈[1−𝑛,…,𝑛−1]
Constraints:

10. Question 2 Variables: 𝑦 1−𝑛 ,…, 𝑦 𝑛−1 Domains:
𝑖 +1, 𝑖 +3,…,2𝑛− 𝑖 −1 ∪{−𝑛}
for 𝑖∈[1−𝑛,…,𝑛−1]
Constraints:

11. Question 2 Implement the third constraint using following 3 ways:
Arithmetic constraint
Tuple sets
DFA (show the DFA graph)
Usage:
queens -model mod 𝑛
E.g. queens –model 1 5 (arithmetic constraint)
Do not hardcode!
How to get 𝑛?

12. SizeOptions
Accepts an unsigned integer as the last value on the commandline.
The value can be retrieved or set by member functions size().
A virtual print function that accepts a standard output stream as argument.

13. SizeOptions Options -> SizeOptions
class SendMoreMoney : public Script {
protected:
IntVarArray l;
const Options& opt;
public:
enum {
MODEL_ONE,
MODEL_TWO };
SendMoreMoney(const Options& _opt) : opt(_opt), l(*this,8,0,9) { …
switch (opt.model()) {
case MODEL_ONE:
break;
case MODEL_TWO: }
// search support
// print solution
A virtual print function that accepts a standard output stream as argument.
Options -> SizeOptions

14. SizeOptions Options -> SizeOptions
int main(int argc, char* argv[]) {
// commandline options
Options opt(“SEND + MORE = MONEY”);
opt.model(SendMoreMoney::MODEL_ONE, “one”, “use the first model”);
opt.model(SendMoreMoney::MODEL_TWO, “two”, “use the second model”);
opt.model(SendMoreMoney::MODEL_ONE);// default model
opt.solutions(0);// print all solutions
opt.size(4);// default value
opt.parse(argc,argv);
// run script
Script::run<SendMoreMoney, DFS, Options>(opt);
return 0; }
Options -> SizeOptions

15. Question 3 Extend your program in Assignment 1 Usage:
Generalized to have a grid of 𝑛×𝑛 letters
Add extra version 3 for model in 3(a)
Add extra version 4 for model in 3(b)
Usage:
abc_path -model mod 𝑛
E.g. Using model in Asg2 3(a) and 𝑛=4
abc_path –model 3 4
Note that only letter A is initially put on the top left corner cell!

16. Question 4 Hint 1 Hint 2 Hint 3
“Hidden variable transformation” or “Hidden transformation”
Hint 2
“Dual graph transformation”
Hint 3
“On the Conversion between Non-Binary and Binary Constraint Satisfaction Problems”
Pages , AAAI 1998

17. Question 4 Compare the size of the new and old CSPs
Number of variables
Domain size of each variables
Number of constraints

18. Written part Submit your softcopy (PDF file) to me
Write a few statements comparing the performance
Question 1
You need to write down the examples.
Question 2
You need to give the DFA graph and write down the comparisons.
Question 3
You need to write down the constraints and objective function in Part(a) and the comparisons in Part(b).
Question 4
You need to write down the problem transformation techniques and the comparisons.

19. Program Submission Instructions
Programming Part:
Follow the format of the commands used to run your program
Add proper comments to source files
Show sample outputs/your answers enclosed as comments at the end of the source files
Attach 2 cpp files and 1 pdf file and send to with the subject:
CSC5240 Asg2 [studentID] e.g. CSC5240 Asg
Write down your name and student ID in each of your file!

20. Assignment 2 deadline
11 November :59pm

21. END