![]() ![]() Even after 23 hours, the algorithm didn't find any solution. If you enjoyed this article, please consider following me on twitter. I am trying to solve Peg Solitaire with a depth-first search algorithm it should be possible to solve the game since 'modern computers can easily examine all game positions in a reasonable time'. ("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() Jumps are always in either a vertical direction or a horizontal direction where one peg jumps over. The following is 52 lines of code according to IntelliJ LoC metric. One attempts to remove all pegs by moving pegs via jumps. 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. Unlimited Puzzles: Our advanced algorithm generates an endless stream of distinctive peg solitaire challenges, ensuring you never run out of new puzzles to. ![]() 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. Let's start with the board representation.English Peg Solitaire Solution Implementation Before we can implement the algorithm, we have to write some game logic first. You're not allowed to jump over multiple pegs or multiple empty cells.įor the implementation we'll use Kotlin, but of course you can use any other language. ![]() The game is won when there's 1 peg left in the center of the board and it's lost when you cannot jump anymore or the last peg is not in the center. The rules are simple: each turn you can pick one peg, jump over a neighboring one (horizontal or vertical) and remove the one you just jumped over. What is Peg Solitaire? Peg Solitaire is a single player board game where the player has to move pegs (pins) and remove them on a board in order to win. There's also an example repository on GitHub.īut first things first. So in this post we'll solve Peg Solitaire with the help of backtracking. ![]() (if we get here step 4 produced a undesired board state) undo the move made in step 4 and recall step 4 with the next possible move that peg. Find the first possible peg that can move in 1 or more directions call solve () for that peg and it's direction. I really liked the idea and was curious to solve this puzzle. Check if there is a still a peg that can be moved, if there isn't one exit the function. If you read the comments, you'll notice that backtracking is the most common answer given. That algorithm can be problem-specific, a (graph/tree) search algorithm The program presented in the following, that finds a solution for peg solitaire, fits this scheme but there are other problems that dont. This post was originally published on my blog.Ī few days ago I saw a post on Reddit where someone asked what an algorithm for solving Peg Solitaire might look like. Apply an algorithm that applies transformations until the desired state has been reached. ![]()
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