Hi Callum and All,
A few years ago I've written an algorithm to solve the minefield game as
an expert player wold do ...
For this I've implemented 2 (3) Algorythms:
* Deductive: (Is the same that is already used for the hint)
It slides all the cells and searches for each:
(1) If the number of cells covered around to it is equal to its value,
then these cells are signed with a flag.
(2) If the number of mines marked (with the flag) corresponds to the
value of the cell, then the cells around not marked are free.
* Estimation:
At first executes the deductive algorithm until it doesn't return any
solution.
For each cell near the covered ones it creates the various configuration
(variants) that the mines could assume.
Then it creates all the possible puzzles with the variants created
before.
Next it compares all puzzles cells that are in the same position, if
for all puzzles the specified position is a mine (or a free space) it's in
the reality too.
<pre>
Here an example to clarify: Analyzing the following situation ...
%%%%%%
%3222%
%2001%
%1111%
%%%%%%
... there are only 3 possible configurations ...
?%??%% %%??%% %??%?%
?3222? ?3222? ?3222?
%2001% ?2001% %2001%
?1111% %1111% ?1111%
%%%?%% %%%?%% %%%?%%
... if we now superpose (compare) the 3 configurations ...
%%M%%F
M3222M
%2001F
%1111F
FFFMFF
... it is 100% sure that M is a mine and F a free cell !!!
</pre>
The attached file estimation_debug.txt gives 2 more examples.
* Percentage:
With the estimation algorithm is also assigned the probability for
a cell to be a mine.
This algorithm returns the cell that has the minor probability to be
a mine, if it is minor than 50%.
I've written a patch (attached file solver_patch.gz) for gnomine part of
gnome-games-2.8.1 (apply it in gnomine directory -- patch < solver_patch)
I hope nothing has changed in gnomine in the newest version ...
I give this code following the terms of the GNU GENERAL PUBLIC LICENSE.
The main menu will then contain 2 times Hint ... the upper one is the "one
step" and the second the "solve all".
(I don't have very good knowledge in GTK+ ... I've only learned Xlib and
Motif).
A radiobutton menu has to be written to choose the resolution algorithm (now
it is fix to Estimation).
Is it possible to have all this corrected and implemented "officially" ?
Greetings,
Curzio Della Santa
DEBUG ESTIMATION STRUCTURE
Field situation:
%%%%%%%%%%%100000001*%%%%%%%%%
%%%%%%%%%%%2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%%%%%%%%432%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
BEGIN PATH 1
number of sol = 21
PUZZLE 1
%%%%%%%%%%?100000001*?%%%%%%%%
%%%%%%%%%%%2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%?%?%%?%?432?%%%%%%%%
%%%%%%%%%%%%%%%%%??%?%%%%%%%%%
PUZZLE 2
%%%%%%%%%%?100000001*?%%%%%%%%
%%%%%%%%%%%2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%?%?%%?%?432?%%%%%%%%
%%%%%%%%%%%%%%%%%%??%%%%%%%%%%
PUZZLE 3
%%%%%%%%%%?100000001*?%%%%%%%%
%%%%%%%%%%%2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%??%%?%?432?%%%%%%%%
%%%%%%%%%%%%%%%%%??%?%%%%%%%%%
PUZZLE 4
%%%%%%%%%%?100000001*?%%%%%%%%
%%%%%%%%%%%2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%??%%?%?432?%%%%%%%%
%%%%%%%%%%%%%%%%%%??%%%%%%%%%%
PUZZLE 5
%%%%%%%%%%?100000001*%%%%%%%%%
%%%%%%%%%%%2110001122?%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%?%?%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%??%??%%%%%%%%
PUZZLE 6
%%%%%%%%%%?100000001*%%%%%%%%%
%%%%%%%%%%%2110001122?%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%?%?%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%?%??%%%%%%%%%
PUZZLE 7
%%%%%%%%%%?100000001*%%%%%%%%%
%%%%%%%%%%%2110001122?%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%?%?%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%%??%?%%%%%%%%
PUZZLE 8
%%%%%%%%%%?100000001*%%%%%%%%%
%%%%%%%%%%%2110001122?%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%??%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%??%??%%%%%%%%
PUZZLE 9
%%%%%%%%%%?100000001*%%%%%%%%%
%%%%%%%%%%%2110001122?%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%??%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%?%??%%%%%%%%%
PUZZLE 10
%%%%%%%%%%?100000001*%%%%%%%%%
%%%%%%%%%%%2110001122?%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%??%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%%??%?%%%%%%%%
PUZZLE 11
%%%%%%%%%%?100000001*%%%%%%%%%
%%%%%%%%%%%2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11?%%%%%%%%
%%%%%%%%%%?%?%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%??%?%%%%%%%%%
PUZZLE 12
%%%%%%%%%%?100000001*%%%%%%%%%
%%%%%%%%%%%2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11?%%%%%%%%
%%%%%%%%%%?%?%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%%??%%%%%%%%%%
PUZZLE 13
%%%%%%%%%%?100000001*%%%%%%%%%
%%%%%%%%%%%2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11?%%%%%%%%
%%%%%%%%%%%??%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%??%?%%%%%%%%%
PUZZLE 14
%%%%%%%%%%?100000001*%%%%%%%%%
%%%%%%%%%%%2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11?%%%%%%%%
%%%%%%%%%%%??%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%%??%%%%%%%%%%
PUZZLE 15
%%%%%%%%%%%100000001*?%%%%%%%%
%%%%%%%%%%?2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%%?%%?%?432?%%%%%%%%
%%%%%%%%%%%%%%%%%??%?%%%%%%%%%
PUZZLE 16
%%%%%%%%%%%100000001*?%%%%%%%%
%%%%%%%%%%?2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%%?%%?%?432?%%%%%%%%
%%%%%%%%%%%%%%%%%%??%%%%%%%%%%
PUZZLE 17
%%%%%%%%%%%100000001*%%%%%%%%%
%%%%%%%%%%?2110001122?%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%%?%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%??%??%%%%%%%%
PUZZLE 18
%%%%%%%%%%%100000001*%%%%%%%%%
%%%%%%%%%%?2110001122?%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%%?%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%?%??%%%%%%%%%
PUZZLE 19
%%%%%%%%%%%100000001*%%%%%%%%%
%%%%%%%%%%?2110001122?%%%%%%%%
%%%%%%%%%%%3*21122*11%%%%%%%%%
%%%%%%%%%%%%?%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%%??%?%%%%%%%%
PUZZLE 20
%%%%%%%%%%%100000001*%%%%%%%%%
%%%%%%%%%%?2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11?%%%%%%%%
%%%%%%%%%%%%?%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%??%?%%%%%%%%%
PUZZLE 21
%%%%%%%%%%%100000001*%%%%%%%%%
%%%%%%%%%%?2110001122%%%%%%%%%
%%%%%%%%%%%3*21122*11?%%%%%%%%
%%%%%%%%%%%%?%%?%?432%%%%%%%%%
%%%%%%%%%%%%%%%%%%??%%%%%%%%%%
END PATH 1
BEGIN PATH 1
number of sol = 21
PIECE 1 STATISTICS: POS: {11, 0} REF_VALUES: -1 | -1 | -1 | 14 | -1 | -1 | 7 | -1 | -1 |
PIECE 2 STATISTICS: POS: {11, 1} REF_VALUES: 14 | -1 | -1 | 7 | -1 | -1 | 0 | -1 | -1 |
PIECE 3 STATISTICS: POS: {20, 1} REF_VALUES: -1 | -1 | 6 | -1 | -1 | 9 | -1 | -1 | 6 |
PIECE 4 STATISTICS: POS: {11, 2} REF_VALUES: 7 | -1 | -1 | 0 | -1 | -1 | 7 | 7 | 21 |
PIECE 5 STATISTICS: POS: {13, 2} REF_VALUES: -1 | -1 | -1 | -1 | -1 | -1 | 21 | 0 | 0 |
PIECE 6 STATISTICS: POS: {14, 2} REF_VALUES: -1 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 21 |
PIECE 7 STATISTICS: POS: {15, 2} REF_VALUES: -1 | -1 | -1 | -1 | -1 | -1 | 0 | 21 | 0 |
PIECE 8 STATISTICS: POS: {16, 2} REF_VALUES: -1 | -1 | -1 | -1 | -1 | -1 | 21 | 0 | 21 |
PIECE 9 STATISTICS: POS: {17, 2} REF_VALUES: -1 | -1 | -1 | -1 | -1 | -1 | 0 | 21 | -1 |
PIECE 10 STATISTICS: POS: {20, 2} REF_VALUES: -1 | -1 | 9 | -1 | -1 | 6 | -1 | -1 | 6 |
PIECE 11 STATISTICS: POS: {18, 3} REF_VALUES: -1 | -1 | -1 | 21 | -1 | -1 | 12 | 18 | 12 |
PIECE 12 STATISTICS: POS: {19, 3} REF_VALUES: -1 | -1 | -1 | -1 | -1 | -1 | 18 | 12 | 12 |
PIECE 13 STATISTICS: POS: {20, 3} REF_VALUES: -1 | -1 | 6 | -1 | -1 | 6 | 12 | 12 | 6 |
END PATH 1
SOLUTION : { 10 , 2 }
FLAG : { 12 , 3 }
SOLUTION : { 13 , 3 }
SOLUTION : { 14 , 3 }
FLAG : { 15 , 3 }
SOLUTION : { 16 , 3 }
FLAG : { 17 , 3 }
/*****************************************************************************************************/
DEBUG ESTIMATION STRUCTURE
Field situation:
0000001*2*2100000001*1001%%%%%
0011101122*21100011222113%%%%%
002*20000113*21122*11*22**4%%%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
PATH STATISTICS:
PATH 1 : number of sol = 1
PATH 2 : number of sol = 3
PATH 3 : number of sol = 2
PATH 4 : number of sol = 6
BEGIN PATH 1
number of sol = 1
PUZZLE 1
0000001*2*2100000001*1001%%%%%
0011101122*21100011222113%%%%%
002*20000113*21122*11*22**4%%%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
?%?45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
END PATH 1
BEGIN PATH 2
number of sol = 3
PUZZLE 1
0000001*2*2100000001*1001%%%%%
0011101122*21100011222113%%%%%
002*20000113*21122*11*22**4%%%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%?4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%?*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
PUZZLE 2
0000001*2*2100000001*1001%%%%%
0011101122*21100011222113%%%%%
002*20000113*21122*11*22**4%%%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%?%3312*221222123422233*210
%%%%%?*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
PUZZLE 3
0000001*2*2100000001*1001%%%%%
0011101122*21100011222113%%%%%
002*20000113*21122*11*22**4%%%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%?3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
END PATH 2
BEGIN PATH 3
number of sol = 2
PUZZLE 1
0000001*2*2100000001*1001%%%%%
0011101122*21100011222113%%%%%
002*20000113*21122*11*22**4%%%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%?**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%?3101*221112211122211*111
%%%%%?*1012*1000000001**11111*
PUZZLE 2
0000001*2*2100000001*1001%%%%%
0011101122*21100011222113%%%%%
002*20000113*21122*11*22**4%%%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%?1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%?*1012*1000000001**11111*
END PATH 3
BEGIN PATH 4
number of sol = 6
PUZZLE 1
0000001*2*2100000001*1001?%%%%
0011101122*21100011222113%??%%
002*20000113*21122*11*22**4%?%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
PUZZLE 2
0000001*2*2100000001*1001?%%%%
0011101122*21100011222113%?%%%
002*20000113*21122*11*22**4?%%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
PUZZLE 3
0000001*2*2100000001*1001?%%%%
0011101122*21100011222113%%?%%
002*20000113*21122*11*22**4?%%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
PUZZLE 4
0000001*2*2100000001*1001%%%%%
0011101122*21100011222113??%%%
002*20000113*21122*11*22**4%?%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
PUZZLE 5
0000001*2*2100000001*1001%%%%%
0011101122*21100011222113?%?%%
002*20000113*21122*11*22**4%?%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
PUZZLE 6
0000001*2*2100000001*1001%%%%%
0011101122*21100011222113?%%%%
002*20000113*21122*11*22**4?%%
003*30000002*21*4*4323*223*22*
003*300111012222***2*432011111
123*3112*3101*2223234**1000011
%%%45*22**1012*10002**4200002*
%%%***32221001232113*4*100002*
%%%%%4*10111001**11*2211011111
%%%%%%3312*221222123422233*210
%%%%%%*4*22*3*20002***4***5*31
%%%%%%**33323*21112*5**4**4*3*
%%%%%%322**12222*3223322222121
%%%%%%1013321*12**11*100011100
%%%%%%3101*221112211122211*111
%%%%%%*1012*1000000001**11111*
END PATH 4
BEGIN PATH 1
number of sol = 1
PIECE 1 STATISTICS: POS: { 0, 5} REF_VALUES: -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 0 |
PIECE 2 STATISTICS: POS: { 1, 5} REF_VALUES: -1 | -1 | -1 | -1 | -1 | -1 | 1 | 0 | 1 |
PIECE 3 STATISTICS: POS: { 2, 5} REF_VALUES: -1 | -1 | -1 | -1 | -1 | -1 | 0 | 1 | -1 |
PIECE 4 STATISTICS: POS: { 3, 6} REF_VALUES: -1 | -1 | -1 | 1 | -1 | -1 | 0 | -1 | -1 |
END PATH 1
BEGIN PATH 2
number of sol = 3
PIECE 1 STATISTICS: POS: { 5, 8} REF_VALUES: -1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 |
PIECE 2 STATISTICS: POS: { 6, 9} REF_VALUES: -1 | -1 | -1 | 1 | -1 | -1 | 2 | -1 | -1 |
END PATH 2
BEGIN PATH 3
number of sol = 2
PIECE 1 STATISTICS: POS: { 6,12} REF_VALUES: 1 | -1 | -1 | 0 | -1 | -1 | 1 | -1 | -1 |
PIECE 2 STATISTICS: POS: { 6,13} REF_VALUES: 0 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 |
PIECE 3 STATISTICS: POS: { 6,14} REF_VALUES: 1 | -1 | -1 | 1 | -1 | -1 | 2 | -1 | -1 |
END PATH 3
BEGIN PATH 4
number of sol = 6
PIECE 1 STATISTICS: POS: {24, 0} REF_VALUES: -1 | -1 | -1 | -1 | -1 | 3 | -1 | -1 | 3 |
PIECE 2 STATISTICS: POS: {24, 1} REF_VALUES: -1 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | -1 |
PIECE 3 STATISTICS: POS: {26, 2} REF_VALUES: 3 | 3 | 3 | -1 | -1 | 3 | -1 | -1 | -1 |
PIECE 4 STATISTICS: POS: {27, 3} REF_VALUES: -1 | 3 | 3 | -1 | -1 | -1 | -1 | -1 | -1 |
PIECE 5 STATISTICS: POS: {28, 3} REF_VALUES: 3 | 3 | 0 | -1 | -1 | -1 | -1 | -1 | -1 |
END PATH 4
FLAG : { 0 , 6 }
SOLUTION : { 1 , 6 }
FLAG : { 2 , 6 }
SOLUTION : { 2 , 7 }
SOLUTION : { 5 , 12 }
FLAG : { 5 , 15 }
SOLUTION : { 29 , 2 }
Attachment:
solver_patch.gz
Description: Unix tar archive