![]() 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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