Peg solitaire solution code#

This is due to the special layout, which I will explain in the following. Note that many boundary bit-numbers appear twice in the diagram. Moves are not allowed to end up in any of these bits. The boundary of the board is shown by the squares in above diagram. I designed the following layout for the bit-board representation of the Diamond-41 variant of peg solitaire.Įach number represents the corresponding bit in the bit-board. Additionally, the representation is very memory efficient so that positions can be easily stored in a hash table or other data structures. If the encoding of each individual hole is done in a suitable way, many operations (such as the generation of valid moves for each position, mirroring the board along a certain axis, counting pegs, etc.) can be executed with a minimum amount of CPU cycles. Bit boards have the advantage that the whole board can be processed at once with bitwise operations. This is, as we will see later, important for checking if a move is performed within the allowed boundaries. There are also enough bits left over which can be used to encode the boundary of the board. In this way, only 41 bit are required to encode any board position. For peg solitaire, the usage of bit-boards is especially easy, since each hole can either be empty (binary 0) or filled with a peg (binary 1). One major improvement of a classical algorithm can be achieved when instead of arrays, so called bit-boards are used for representing a position. Without the utilization of some advanced approaches, an algorithm could run for many days until a solution is found. Also for backtracking algorithms the computational effort is enormous in order to solve this problem. Since there are many corners on this board it is rather difficult to find a solution where only one peg is left over in the end. In the beginning, only two moves are possible. As I was told – in contrast to the English variant – the only initial empty hole is not located in the center of the board but has to be placed at a slightly different position in order to be able to solve the game (as I found later, the solver was not able to solve the game for an initially empty hole in the center of the board). Efficiently Solving the Diamond-41 BoardĪs the name suggests, the Diamond-41 board consists of 41 holes. This stirred my interest in the game again and I spent several hours writing a solver using bit boards and some other enhancements for this board, as described in the following section. Recently, I again stumbled across peg solitaire when I saw a different board with the shape of a diamond. The solver gave me the following solution: With a slightly adjusted move ordering the solver apparently needs much more time (several hours). I suppose that I was actually quite lucky with the standard move ordering that I was using. It is not nice nor efficient, but surprisingly finds the solution in less than a second.

Peg solitaire solution code#

The code is attached at the end of this post. Since I could never solve the game myself I decided to write a solver for the problem. When I started programming a few years ago, English peg solitaire was one of my first projects. The solution for the diamond shaped board is even more tricky. Many players need quite a few attempts in order to find the solution for the English peg solitaire. The English variant is shown in the figure below.Įven though the rules of the game are rather simple, finding a solution is not trivial. The English variant, as shown below, has one additional rule: In order to win, it is not sufficient that only one peg is left in the end this peg also has to be located in the center of the board. This is the case when there is no pair of pegs which are orthogonally adjacent or if only one peg is left. Once no move is possible any longer, the game is over. So, in each move, one peg jumps 2 holes further and the peg in-between is removed. The neighboring peg is then removed, leaving an empty hole. In each move the player selects one peg and jumps – either vertically or horizontally, not diagonally – with this peg over a directly neighboring one into an empty hole.

For example, the English variant consists of 33 holes while the typical diamond variant consists of 41 holes.

The number of holes depends on the board variant.

Peg solitaire is a one-player game played on a board with holes and pegs. Many of us might now the board game peg solitaire and might even have one of its many variants at home. Solving Peg Solitaire with efficient Bit-Board Representations