Minesweeper Solving Tool Simulator in JavaFX
Strives to maximize the solving rate by deterministic algorithms and compares the quality of various guessing heuristics.
Requires javafx-jdk 15.0.1 or higher.
Commonly known as the 1-1 or 1-2 rules.
Let x be a sqaure on the board which is revealed and has hidden unflagged neighboring squares. x provides the following clue:
cx = ({x1, .. , xn}, bx) with n being the number of hidden unflagged neighbors and b the number of unflagged bombs in neighboring squares.
Let cy = ({y1, .. , ym}, by) be another clue and cz a non-empty intersection of {x1, .. , xn} and {y1, .. , ym} with bc = 0 for now.
cz has a minimum number of bombs that have be contained and a maximum number of bombs that may be contained within the squares. Those are determined as follows:
minBombs = max( bx - (|cx| - |cz|), by - (|cy| - |cz|) )
E.g. if cx has 4 squares, contains 3 bombs and cz has 2 squares,
a maximum of 2 bombs may be contained in the remaining 2 non-intersecting squares of cx and at least 1 bomb has to be in the intersection cz.
The same applies to cy and the maximum of the two potential values is the minimum number of bombs in the intersection.
maxBombs = min( bx, by, |cz| )
The maximum number of bombs possible in the intersection cz is the mandatory minimum number of bombs in cx, cy or naturally the size of the intersection itself.
If minBombs equals maxBombs, the number of bombs in the intersection has to be just that. As a consequence, the clues cx, cy can be split into cx', cy' and cz
where cx' is cx minus the squares in cz and minus the bombs in cz. The same applies to cy'.
In case of cx == cz, cx may be deleted since all its information is now in cz. The same applies to cy.
After intersecting enough clues it may happen that cx' contains 0 bombs, in which case every square in cx' may be safely revealed
or that cx' contains as many bombs as it has squares, in which case every square may be flagged as bomb.
This chaining and unravelling of clues gradually reveals the entire board in the best case, which currently occurs about 9.8% of the time on the standard hard board. Flagging is not strictly necessary for this rule, because it reveals no new information, but it helps with performance.
- extending the subset rule to cover 1-3-1 corners
- bottom-up solving algorithm based on remaining bombs
- extensively multithreading the simulations
- determining the optimal starting square
- all of the guessing heuristics
- proper UI with fancy animations and all
- proper documentation with report of findings