The main principle of this program is to demonstrate the concepts of recursive function, inherently recursive problem and backtracking. The program, in fact, implements a simple backtracking algorithm DFS to search for a solution starting from the current disposition of the pieces on the board. One of the spaces in the triangle is left empty, and the object is to jump pegs, removing each peg jumped, until you are left with only one. The game consists of 14 pegs set in a triangle shape with 15 holes like bowling pins, but with one more row. This program allows you play Solitaire puzzle also known as Peg Solitaire Puzzle. The puzzle gained in popularity when the restaurant put one on every table to amuse patrons waiting for their food.
#PEG SOLITAIRE SOLUTIONS CRACKER#
It is also known as peg solitaire or the Cracker Barrel puzzle. Smith patented a triangular version of the game in 1891. CodeĪ basic Ilog Solver program to solve central Solitaire can be found here.The 15-hole triangle peg board game is a modern version of a game that has been played in Europe since the end of the 17 th century. The problem is then to maximise the occurrences of ‘DeadEnd’ in moves. This move is only applicable when no other move is possible. This can be modelled by adding a special ‘DeadEnd’ move to the domain of each variable in moves. Fool’s SolitaireĪn optimisation variant of peg Solitaire is to attempt to reach a position where no further moves are possible in the shortest sequence of moves. Other modelsĪs described in a PDDL model suitable for use with AI planning systems can easily be created, as can an integer programming model. These symmetries can be broken by identifying the symmetric paths and adding constraints to allow only one representative from each equivalence class, but the identification process itself is expensive. On some occasions this is due to independent moves, but on others disjoint sets of moves can lead to the same position. There are also symmetric paths to the same board state. Independent(moves, moves) -> moves <= moves
Symmetries of larger groups of independent moves are more expensive to break. Symmetries of pairs of independent moves can be broken by imposing an ordering on moves as follows. There are also symmetries of independent moves: that is, entries in moves that can be exchanged without affecting the solution. Depending on the shape of the board, rotation and reflection symmetries will usually apply. Peg Solitaire contains a lot of symmetry. This array is used also to specify the three pre-conditions (two pegs and a hole) and three post-conditions (two holes and a peg) of each possible move. The number of possibilities will vary according to the board shape, but the English board has 76 such possible moves.Ī second array, bState of 01 variables (where i, j specify a board position and t is the time-step), is used to keep track of the state of the board before and after each move. all ways of removing a peg from the board. The domain of each element of this array is the set of possible moves, i.e. A CP model found to be successful in employs a 1-dimensional array of variables, moves, which records the move made at time-step t. We are helped by the fact that we know exactly how many moves are necessary: (the number of pegs in the initial configuration - the number of pegs in the goal configuration).
Peg Solitaire is essentially a planning problem: the goal is to find a sequence of actions that transform the initial state into the goal state.
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