% Student number:

%% ----------------------------------------------------------
%%    Answers to Questions 7-12, Assignment 1

%% Instructions: 

%% Please edit this file in the following way to answer the text
%% questions of Assignment 1. 

%% - Please replace any occurence of '[yes/no]' with either 'yes' or
%% 'no' to answer the respective question.

%% - Replace any occurence of '[explain N words]' or '[if yes (resp.
%%   no), explain N words]' with an explanation containing no more
%%   than N words if the condition (yes/no) applies to your previous
%%   answer.

%% - Do not remove any other lines, in particular do not remove the
%%   task-tags (<tasknumber>)

%% - Any line starting with a '%' will be ignored.

%% - Submit this file electronically.

%% ----------------------------------------------------------


% 7. What is the cost function for this problem? Which part 
%    of the problem description specifed it?

[explain 100 words]


%% /* ------------------------------------------------------ */


%% 8. Which of the four heuristics are admissible?

%%  - hfn_null
<8.1>
[yes/no]
[if no explain 100]

%%  - hfn_misplaced
<8.2>
[yes/no]
[if no explain 100]

%%  - hfn_manhattan
<8.3>
[yes/no]
[if no explain 100]

%%  - hfn_inversions
<8.4>
[yes/no]
[if no explain 100]




%% /* ------------------------------------------------------ */

% 9. Suppose we would change the cost for sliding a tile 
% downwards to 2 and leave the cost of all the other movements
% at 1. Does this affect the admissibility of the four 
% heuristics? Which of the heuristics are admissible now? 
% For any which is not, why not?

%%  - hfn_null
<9.1>
[yes/no]
[if no explain 100]

%%  - hfn_misplaced
<9.2>
[yes/no]
[if no explain 100]

%%  - hfn_manhattan
<9.3>
[yes/no]
[if no explain 100]

%%  - hfn_inversions
<9.4>
[yes/no]
[if no explain 100]




%% /* ------------------------------------------------------ */

% 10. Now suppose for sliding a tile to the left we would 
% change the cost from 1 to 0.5 and leave all the other moves 
% at cost 1.

% a). Does this affect the admissibility of the heuristics? 
% Again, which of them are admissible now? For any which
% is not, why not?
<10.1>


%%  - hfn_null
<10.1.1>
[yes/no]
[if no explain 100]


%%  - hfn_misplaced
<10.1.2>
[yes/no]
[if no explain 100]


%%  - hfn_manhattan
<10.1.3>
[yes/no]
[if no explain 100]


%%  - hfn_inversions
<10.1.4>
[yes/no]
[if no explain 100]


% b). Pick one of the heuristics which are admissible 
% in the original problem, but are no longer admissible. How
% would you modify it so that it becomes admissible?
<10.2>
[explain 200]

%% /* ------------------------------------------------------ */

% 11. In the last modification (sliding to the left costs 0.5), 
% can you say for sure which heuristic will be the fastest 
% (expand the least number of states) in finding a (not 
% necessary optimal) solution? Explain.

[explain 300 words]


%% /* ------------------------------------------------------ */

% 12. Imagine a variant of the problem where, in addition to 
% sliding the tiles, you were allowed to swap any two tiles. 
% The "swap" move would cost 1, just as any other move, but 
% you are allowed to use it at most three times for each 
% problem.

% a). How would you minimally represent the states for 
% this problem?

<12.1>
[explain 100 words]

% b). What changes to the successors predicate would you 
% have to make? (Do not write any code for this question,
% just brie?y explain in English)

<12.2>
[explain 200 words]