The objective is to depict the complete set of optimal solutions for a given state in the 15 puzzle game using a layered graph structure.
For a solution to be considered optimal, it must be achieved through the shortest possible sequence of moves. Therefore, all solutions have the same length in terms of moves.
In this representation, each node corresponds to a distinct puzzle configuration, and the edges between nodes illustrate the specific moves taken to transition from one state to another.
Since each node represents a unique state, the solutions will tend to separate at the beginning and then progressively reunite, until arriving at a single final state.
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