% Kruskal count (2010/12/9, revised 12/11)
% Reference:
% Fulves, C. & Gardner, M.(1975):
% The Kruskal principle. The Pallbearer's review, 10(8), 967-976.  

numb(I):- 
	 length( L, 13), nth1( I, L, _).
suit(S, K):-
	 nth1( K, [c, h, s, d], S).
card(S, K, I):-
	 suit( S, K), numb(I).

:- dynamic c/3.

% initialize and shuffle the deck

init_deck:- 
	 retractall( c(_,_,_)),
	 card(S, _, I),
	 P is random(100000), 
	 assert( c( P, S, I) ),
	 fail; true.

show_all_deck:- 
	 X = c(_,_,_),
	 findall( X, X, O), sort( O, H),
	 member(X, H), nl, write(X), fail; true.

/*

?- init_deck.

?- show_all_deck.

c(1957, s, 11)
c(3756, d, 1)
c(3944, c, 6)
c(4689, d, 10)
c(5418, d, 7)
...

*/


:- dynamic kc/2.

% initialize key numbers data

init_kc:- 
	 retractall( kc(_,_)).


% Key number reference: all face cards are 5.

knum( J, J):- J =< 10.
knum( J, 5):- J > 10.


% The Krascal count procedure

mentally_choosed_number(K):-
	 length(L, 10),
	 nth1(K, L,_).

kcount( M, K):- 
	 mentally_choosed_number( M),
%	 init_deck,
%	 init_kc,
	 X = c(_, _, _),
	 findall( X, X, O),
	 sort( O, H),
	 kcount( M, H, K),
	 assert( kc( M, K) ). 

kcount( M, H, K):-
	 length( L, M),
	 append( L, [Y | R], H),
	 Y = c(_, _, K_next),
	 debugmode(Y),
	 knum( K_next, J),
	 kcount( J, [Y|R], K).

% find the tapped number

kcount( K, H, K):-
	 length( H, U),
	 U =< K.



:- dynamic debug/1.

%debug( on).

debugmode(X) :- 
	clause(debug(on),_), !, nl, write(X).
debugmode(_).


stat_kc:-
	 findall( M -> K, kc(M, K), O),
	 sort(O, H), 
	 member(J -> K, H),
	 findall(1, member(J -> K, O), U), 
	 length(U, D),
	 nl,
	 write( J-> K : [D]),
	 fail; true.



/*

% debug mode on

?- init_deck, init_kc.

?- kcount(M, K).

c(5918, s, 5)
c(11020, h, 3)
c(14855, c, 4)
c(27526, s, 6)
c(46920, h, 2)
c(49051, d, 1)
c(53425, d, 6)
c(79697, c, 1)
c(80642, d, 13)
c(87048, h, 4)
c(95203, h, 11)

M = 1,
K = 5 ;

c(6916, h, 12)
c(13601, c, 12)
c(21014, c, 10)
c(47857, d, 3)
c(57695, s, 7)
c(80642, d, 13)
c(87048, h, 4)
c(95203, h, 11)

M = 2,
K = 5 ;

% debug mode off

 ?- init_all, kcount(M, K), fail; stat_kc.

1->8:[1]
2->8:[1]
3->8:[1]
4->8:[1]
5->8:[1]
6->8:[1]
7->8:[1]
8->8:[1]
9->8:[1]
10->8:[1]


*/



violate_kc:-
	 \+ \+ violate_kc( _, _).

violate_kc( M):-
	 kc( M, K), kc( _, J), K \= J.


run_kcount_for_all_mental_numbers_at_step( _):-
	 init_kc,
 	 mentally_choosed_number(M), 
	 kcount( M, _),
	 fail.
run_kcount_for_all_mental_numbers_at_step( I):-
 	 mentally_choosed_number(M), 
	 rec_kc_failures( M, I),
	 fail ; true.

:- dynamic  kcv/2.

rec_kc_failures( M, I):-
	 violate_kc(M), 
	 assert( kcv( M, I)).


init_kcv:-
	 abolish( kcv/2).

% count of violations

count_kc_violations( M, K):-
	 mentally_choosed_number(M),
	 findall( 1, kcv(M ,_), O),
	 length(O, K).

count_gross_total_kc_violations( K):-
	 findall( 1, kcv(_, _ ), O),
	 length(O, K).

kc_violations(I):-
	 count_gross_total_kc_violations( I).

run_ntimes_kc( N):-
	 init_kcv,
	 length(L, N), member(I, L),
	 init_deck,
	 run_kcount_for_all_mental_numbers_at_step(I),
	 fail
	 ;
	 true.

stat_kcv:-
	 count_kc_violations(M, V),
	 nl,
	 write('mental number': M -> (V-violations)),
	 fail ; nl.

stat_kc_success_prob( N):-
	 count_kc_violations(M, V),
	 A is V / (N * 10),
	 B is (1 - A),
	 nl,
	 write( M-> B),
	 fail.
stat_kc_success_prob( N):-
	 total_kc_success_prob( N, P),
	 nl,
	 write( 'total prob of success': P). 

total_kc_success_prob( N, P):-
	 count_gross_total_kc_violations(I),
	 A is I/( N * 10 * 10),
	 P is (1 - A).


/*

 ?- init_deck, init_kc.

Yes
 ?- run_ntimes_kc( 100), stat_kc.

?- run_ntimes_kc( 100), stat_kc.

1->6:[1]
2->5:[1]
3->6:[1]
4->5:[1]
5->6:[1]
6->6:[1]
7->6:[1]
8->5:[1]
9->6:[1]
10->5:[1]

Yes

?- init_all.
true.

 ?- N=10000, run_ntimes_kc(N), stat_kcv.

mental number:1->13376-violations
mental number:2->13564-violations
mental number:3->13679-violations
mental number:4->13988-violations
mental number:5->14354-violations
mental number:6->14496-violations
mental number:7->14682-violations
mental number:8->14888-violations
mental number:9->15141-violations
mental number:10->15362-violations
N = 10000.

?- stat_kc_success_prob(10000).

1->0.86624
2->0.86436
3->0.86321
4->0.86012
5->0.85646
6->0.85504
7->0.85318
8->0.85112
9->0.84859
10->0.84638
total prob of success:0.85647
true.

% Note that if a recursive condition kcount( J, [Y|R], K)
% in the second rule of kcount/3 is (wrongly:-) replaced with 
% kcount( J, R, K), then the correction rate decreases to about 0.75.


*/

init_all:-
	 init_deck, 
	 init_kc, 
	 init_kcv.

%