175 lines
4.3 KiB
Python
175 lines
4.3 KiB
Python
from ortools.sat.python import cp_model
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def BuildPairs(rows, cols):
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"""Build closeness pairs for consecutive numbers.
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Build set of allowed pairs such that two consecutive numbers touch
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each other in the grid.
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Returns:
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A list of pairs for allowed consecutive position of numbers.
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Args:
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rows: the number of rows in the grid
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cols: the number of columns in the grid
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"""
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return [(x * cols + y, (x + dx) * cols + (y + dy))
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for x in range(rows) for y in range(cols)
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for dx in (-1, 0, 1) for dy in (-1, 0, 1)
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if (x + dx >= 0 and x + dx < rows and
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y + dy >= 0 and y + dy < cols and (dx != 0 or dy != 0))]
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def PrintSolution(positions, rows, cols):
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"""Print a current solution."""
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# Create empty board.
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board = []
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for _ in range(rows):
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board.append([0] * cols)
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# Fill board with solution value.
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for k in range(rows * cols):
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position = positions[k]
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board[position // cols][position % cols] = k + 1
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# Print the board.
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print('Solution')
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PrintMatrix(board)
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def PrintMatrix(game):
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"""Pretty print of a matrix."""
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rows = len(game)
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cols = len(game[0])
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for i in range(rows):
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line = ''
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for j in range(cols):
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if game[i][j] == 0:
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line += ' .'
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else:
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line += '% 3s' % game[i][j]
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print(line)
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def BuildPuzzle(problem):
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#
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# models, a 0 indicates an open cell which number is not yet known.
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#
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#
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puzzle = None
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if problem == 1:
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# Simple problem
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puzzle = [[6, 0, 9],
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[0, 2, 8],
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[1, 0, 0]]
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elif problem == 2:
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puzzle = [[0, 44, 41, 0, 0, 0, 0],
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[0, 43, 0, 28, 29, 0, 0],
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[0, 1, 0, 0, 0, 33, 0],
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[0, 2, 25, 4, 34, 0, 36],
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[49, 16, 0, 23, 0, 0, 0],
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[0, 19, 0, 0, 12, 7, 0],
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[0, 0, 0, 14, 0, 0, 0]]
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elif problem == 3:
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# Problems from the book:
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# Gyora Bededek: "Hidato: 2000 Pure Logic Puzzles"
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# Problem 1 (Practice)
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puzzle = [[0, 0, 20, 0, 0],
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[0, 0, 0, 16, 18],
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[22, 0, 15, 0, 0],
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[23, 0, 1, 14, 11],
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[0, 25, 0, 0, 12]]
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elif problem == 4:
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# problem 2 (Practice)
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puzzle = [[0, 0, 0, 0, 14],
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[0, 18, 12, 0, 0],
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[0, 0, 17, 4, 5],
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[0, 0, 7, 0, 0],
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[9, 8, 25, 1, 0]]
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elif problem == 5:
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# problem 3 (Beginner)
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puzzle = [[0, 26, 0, 0, 0, 18],
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[0, 0, 27, 0, 0, 19],
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[31, 23, 0, 0, 14, 0],
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[0, 33, 8, 0, 15, 1],
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[0, 0, 0, 5, 0, 0],
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[35, 36, 0, 10, 0, 0]]
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elif problem == 6:
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# Problem 15 (Intermediate)
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puzzle = [[64, 0, 0, 0, 0, 0, 0, 0],
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[1, 63, 0, 59, 15, 57, 53, 0],
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[0, 4, 0, 14, 0, 0, 0, 0],
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[3, 0, 11, 0, 20, 19, 0, 50],
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[0, 0, 0, 0, 22, 0, 48, 40],
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[9, 0, 0, 32, 23, 0, 0, 41],
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[27, 0, 0, 0, 36, 0, 46, 0],
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[28, 30, 0, 35, 0, 0, 0, 0]]
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return puzzle
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def SolveHidato(puzzle):
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"""Solve the given hidato table."""
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# Create the model.
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model = cp_model.CpModel()
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r = len(puzzle)
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c = len(puzzle[0])
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print(('Initial game (%i x %i)' % (r, c)))
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PrintMatrix(puzzle)
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#
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# declare variables
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#
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positions = [model.NewIntVar(0, r * c - 1, 'p[%i]' % i)
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for i in range(r * c)]
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#
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# constraints
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#
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model.AddAllDifferent(positions)
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#
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# Fill in the clues
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#
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for i in range(r):
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for j in range(c):
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if puzzle[i][j] > 0:
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model.Add(positions[puzzle[i][j] - 1] == i * c + j)
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# Consecutive numbers much touch each other in the grid.
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# We use an allowed assignment constraint to model it.
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close_tuples = BuildPairs(r, c)
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for k in range(0, r * c - 1):
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model.AddAllowedAssignments([positions[k], positions[k + 1]], close_tuples)
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#
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# solution and search
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#
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solver = cp_model.CpSolver()
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status = solver.Solve(model)
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if status == cp_model.MODEL_SAT:
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PrintSolution([solver.Value(x) for x in positions], r, c,)
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print('Statistics')
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print(' - conflicts : %i' % solver.NumConflicts())
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print(' - branches : %i' % solver.NumBranches())
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print(' - wall time : %f ms' % solver.WallTime())
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def main():
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for i in range(1, 7):
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print('')
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print('----- Solving problem %i -----' % i)
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print('')
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SolveHidato(BuildPuzzle(i))
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if __name__ == '__main__':
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main()
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