You may rotate a piece by tapping it, or you may flip it (in 3D) by double-tapping it. When you touch a piece, it will grow to a size that fits the dimensions of the squares on the board. The pieces you may use are initially shown at the bottom of the screen, and you simply touch a piece to drag it onto the board. The sole exception to this is the smallest board which has only a few solutions. Some puzzles may have more than one solution, in fact if you start with an empty board there may be hundreds or even thousands of possible solutions. If you quit PentoMind during a timed game (or if you’re interrupted by a phone call), then the timing for the puzzle will resume the next time you start PentoMind. Then you can replay the same puzzle with a friend to see who can solve it the fastest. Your job is then to place the pieces at teh bottom of the screen so that each white square of the board is covered by some pentomino. Your objective is to cover the board using the pentominoes.Īfter you choose a board size and difficulty level, PentoMind will generate an appropriate new puzzle for you to solve. These pieces represent all the possible ways to arrange five unit squares together so that their edges align. The puzzle consists of a rectangular checkerboard and twelve pieces called pentominoes.
#PEG SOLITAIRE FOR RECTANGLE MIT MAC#
If you enjoyed this article, please consider following me on twitter.Looks and plays well on the iPad and Mac as well as the iPhone! ("Completed in " + (System.currentTimeMillis() - time) + " ms.") start recursively search for the initial board from the goal (reverse direction!) fill in the global moves variable that is used by the solver randomize the order of the moves (this highly influences the resulting runtime)
Private static void printBoard(long board) Private static final long moves = new long Private static final long VALID_BOARD_CELLS = 124141734710812L Private static final long INITIAL_BOARD = 124141717933596L Private static final long GOAL_BOARD = 16777216L Private static final ArrayList solution = new ArrayList() Private static final HashSet seenBoards = new HashSet()
#PEG SOLITAIRE FOR RECTANGLE MIT CODE#
The following is 52 lines of code according to IntelliJ LoC metric. Update: In the following you’ll find the Java version, but the reddit user leonardo_m has also translated the code to C++! which move makes “more sense” for a given board. The branch that the algorithm follows might not include a solution, but it still is searched in its entirety.Īn idea to reduce the fluctuation would be to use heuristics and to rank the moves depending on the board, i.e. The program always checks the moves in the same order when looking at any given boards and sometimes this (initially determined) order is “unlucky”. Interestingly the run time highly fluctuates, depending on the ordering of the possible moves. In general a gigabyte of ram, used to remember the known boards, should be enough to allow for a solution to be found. Not doing so means that my computer is still working on a solution since 24 hours (however it is using almost no ram). Remembering the boards that we have already seen (and not rechecking them unnecessarily) means that a solution is found in a very reasonable time (usually a few seconds). With this particular algorithm it is no different. There is often a tradeoff with algorithms when it comes to memory usage and run time. You can find more details on this in the comment header of the program below. The really interesting part is that the algorithm is optimized by reverting the search direction.
Checking of possible moves and applying them can be done by using simple bit operations. However there are some bits that are not valid and never used, i.e. The first 49 bits (7 x 7) of the long represent the board. The idea is as following: Since there exists 33 slots on the board, it can not be represented by using an integer (32 bits), but we can use a long (64 bits). The implementation is highly optimized and uses bit operators to efficiently find a solution. English Peg Solitaire Solution Implementation
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