midterm ii solution

8/12/2019 Midterm II Solution

1/28

Midterm II

Solution

Prof. Mohamed Batouche

Department of Computer Science

CCIS

King Saud UniversitySaudi Arabia


2/28

Question 1

Solve the 8-puzzle problem using

IDA* with h1() heuristic:

Operators: slide-blank-up, slide-

blank-down, slide-blank-right, slide-

blank-left. Operators should beapplied in this order.

57

461

382

567

48

321


3/28

57

461

382

0+5=5Cutoff = 5

Use DFS


4/28

57

461

382

57

46

1

382

0+5=5

1+5=6

Cutoff = 5

up


5/28

57

461

382

57

46

1

382

57

461

382

0+5=5

1+5=6

Cutoff = 5

1+4=5

up right


6/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

0+5=5

1+5=6

Cutoff = 5

1+4=5

2+3=5

up

up

right


7/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

57

4

6

1

3

8

2

0+5=5

1+5=6

Cutoff = 5

1+4=5

2+3=5

3+3=6

up

up

up

right


8/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

57

4

6

1

382

57

4

6

1

3

8

2

0+5=5

1+5=6

Cutoff = 5

1+4=5

2+3=5

3+3=6 3+4=7

up

up

up

right

right


9/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

57

4

6

1

382

57

4

6

1

3

8

2

57

4

6

1

382

0+5=5

1+5=6

Cutoff = 5

1+4=5

2+3=5

3+3=6 3+3=63+4=7

up

up

up

right

right left


10/28

57

461

382

57

46

1

382

57

461

382

57

461

382

57

4

6

1

382

57

4

6

1

382

57

4

6

1

3

8

2

57

4

6

1

382

0+5=5

1+5=6

Cutoff = 5

1+4=5

2+3=5 2+5=7

3+3=6 3+3=63+4=7

up

up

up

right

right

right left


11/28

57

461

382

57

46

1

382

57

461

382

57

461

382

57

4

6

1

382

57

4

6

1

382

57

4

6

1

3

8

2

57

4

6

1

382

0+5=5

1+5=6

Cutoff = 5

1+4=5

2+3=5 2+5=7

3+3=6 3+3=63+4=7

Failure: Change cutoff min(f(leaves)) = 6

up

up

up

right

right

right left


12/28

57

461

382

0+5=5Cutoff = 6

Use DFS


13/28

57

461

382

57

46

1

382

0+5=5

1+5=6

Cutoff = 6

up


14/28

57

461

382

57

46

1

382

0+5=5

1+5=6

Cutoff = 6

up

57

46

1

38

2

2+5=7

up


15/28

57

461

382

57

46

1

382

0+5=5

1+5=6

Cutoff = 6

up

57

46

1

38

2

57

46

1

382

2+5=7 2+5=7

upright


16/28

57

461

382

57

46

1

382

57

461

382

0+5=5

1+5=6

Cutoff = 6

1+4=5

up right

57

46

1

38

2

57

46

1

382

2+5=7 2+5=7

upright


17/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

0+5=5

1+5=6

Cutoff = 6

1+4=5

2+3=5

up

up

right

57

46

1

38

2

57

46

1

382

2+5=7 2+5=7

upright


18/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

57

4

6

1

3

8

2

0+5=5

1+5=6

Cutoff = 6

1+4=5

2+3=5

3+3=6

up

up

up

right

57

46

1

38

2

57

46

1

382

2+5=7 2+5=7

upright


19/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

57

4

6

1

3

8

2

0+5=5

1+5=6

Cutoff = 6

1+4=5

2+3=5

3+3=6

up

up

up

right

57

46

1

38

2

57

46

1

382

2+5=7 2+5=7

upright

57

4

6

1

3

8

2

right

4+4=8


20/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

57

4

6

1

3

8

2

0+5=5

1+5=6

Cutoff = 6

1+4=5

2+3=5

3+3=6

up

up

up

right

57

46

1

38

2

57

46

1

382

2+5=7 2+5=7

upright

57

4

6

1

3

8

2

57

4

6

1

3

8

2

right

left4+4=8

4+2=6


21/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

57

4

6

1

3

8

2

0+5=5

1+5=6

Cutoff = 6

1+4=5

2+3=5

3+3=6

up

up

up

right

57

46

1

38

2

57

46

1

382

2+5=7 2+5=7

upright

57

4

6

1

3

8

2

57

4

6

1

3

8

2

right

left

57

4

6

1 3

8

2

down

4+4=8

4+2=6

5+1=6


22/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

57

4

6

1

3

8

2

0+5=5

1+5=6

Cutoff = 6

1+4=5

2+3=5

3+3=6

up

up

up

right

57

46

1

38

2

57

46

1

382

2+5=7 2+5=7

upright

57

4

6

1

3

8

2

57

4

6

1

3

8

2

right

left

57

4

6

1 3

8

2

down

5

7 4

6

1 3

8

2

down

4+4=8

4+2=6

5+1=6

6+2=8


23/28

57

461

382

57

46

1

382

57

461

382

57

4

6

1

382

57

4

6

1

3

8

2

0+5=5

1+5=6

Cutoff = 6

1+4=5

2+3=5

3+3=6

up

up

up

right

57

46

1

38

2

57

46

1

382

2+5=7 2+5=7

upright

57

4

6

1

3

8

2

57

4

6

1

3

8

2

right

left

57

4

6

1 3

8

2

down

5

7 4

6

1 3

8

2

down right

567

48

321

4+4=8

4+2=6

5+1=6

6+2=8

Goal !!


24/28

Question 2

Explain the way to use hillclimbing for map coloring:

How to start: Start with random solution: assign

randomly colors to regions

How to improve current solution Select the best solution (minconflicts)

in the neighborhood obtained bymodifying region color.

When to stop: Stop when the next solution is not

better than current solution (localminimum)


25/28

Question 3

Consider the following map. The task is to color

the map using the four colors blue, green, red,

and yellowsuch that no two adjacent regions take

the same color.

Color the map using Backtracking Search with

MCV. Show the steps. The values should be

selected according to alphabetical order: (blue,green, red, yellow)

1

4

2

3 6

5


26/28

Question 3

Solution

1

4

2

3 6

5

Order of variable selection using MCV (select first

the variable with most constraints on remaining

variables):

2, 1, 3, 5, 4, 6


27/28

Question 4

Consider the problem of Sudoku where:

No value appears twice in the same row.

No value appears twice in the same column.

No value appears twice in the same block(22 block).

v1 3 V

2 1

v3 1 V4 4

3 4 1 2

v5 V6 4 V7

Solve this problem using Backtracking with Arc

Consistency


28/28

Question 4

Solutionv1

v7v

6v

5

v4v

3

v2

{2}{4}

{2}

{1}

{2}

{3}

{3}

4 3 2 1

2 1 3 4

3 4 1 2

midterm ii solution

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