def R(self, layer=0): """Rotate the right face. layer=0 is the outermost slice.""" # Rotate the R face self.state['R'] = np.rot90(self.state['R'], k=-1) # Cycle the adjacent faces (U, F, D, B) for the given layer # ... implementation ... self._verify_invariants() def _verify_invariants(self): # 1. All pieces have exactly one sticker of each color? No — central pieces. # Instead, check that total permutation parity is even. # Simplified: count each color; should equal n*n for each face's primary color. for face, color in zip(['U','D','F','B','L','R'], ['U','D','F','B','L','R']): count = np.sum(self.state[face] == color) assert count == self.n * self.n, f"Invariant failed: Face {face} has {count} of {color}" For full verification, implement reduction and test each phase:
from nxnxn import Cube c = Cube(4) # 4x4 c.move("R U R' U'") # Sextet assert c.is_verified() # Checks all cubies are valid nxnxn rubik 39scube algorithm github python verified
Introduction: Beyond the 3x3 For decades, the 3x3 Rubik's Cube has been the poster child for combinatorial puzzles. However, for serious programmers, speedcubing theorists, and puzzle enthusiasts, the ultimate challenge is the NxNxN Rubik's Cube —a cube of any size, from the humble 2x2 to the monstrous 33x33 (the largest ever manufactured). def R(self, layer=0): """Rotate the right face