192 lines
6.0 KiB
Python
192 lines
6.0 KiB
Python
# Copyright 2010-2018 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Solves the Hidato problem with the CP-SAT solver."""
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from __future__ import print_function
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from ortools.sat.python import visualization
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from ortools.sat.python import cp_model
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def build_pairs(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 [
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(x * cols + y, (x + dx) * cols + (y + dy)) for x in range(rows)
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for y in range(cols) for dx in (-1, 0, 1)
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for dy in (-1, 0, 1)
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if (x + dx >= 0 and x + dx < rows and y + dy >= 0 and y + dy < cols and
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(dx != 0 or dy != 0))
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]
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def print_solution(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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print_matrix(board)
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def print_matrix(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 build_puzzle(problem):
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"""Build the problem from its index."""
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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], [0, 2, 8], [1, 0, 0]]
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elif problem == 2:
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puzzle = [[0, 44, 41, 0, 0, 0, 0], [0, 43, 0, 28, 29, 0, 0],
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[0, 1, 0, 0, 0, 33, 0], [0, 2, 25, 4, 34, 0, 36],
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[49, 16, 0, 23, 0, 0, 0], [0, 19, 0, 0, 12, 7,
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0], [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], [0, 0, 0, 16, 18], [22, 0, 15, 0, 0],
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[23, 0, 1, 14, 11], [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], [0, 18, 12, 0, 0], [0, 0, 17, 4, 5],
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[0, 0, 7, 0, 0], [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], [0, 0, 27, 0, 0, 19],
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[31, 23, 0, 0, 14, 0], [0, 33, 8, 0, 15, 1],
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[0, 0, 0, 5, 0, 0], [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], [1, 63, 0, 59, 15, 57, 53, 0],
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[0, 4, 0, 14, 0, 0, 0, 0], [3, 0, 11, 0, 20, 19, 0,
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50], [0, 0, 0, 0, 22, 0, 48, 40],
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[9, 0, 0, 32, 23, 0, 0, 41], [27, 0, 0, 0, 36, 0, 46,
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0], [28, 30, 0, 35, 0, 0, 0, 0]]
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return puzzle
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def solve_hidato(puzzle, index):
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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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if not visualization.RunFromIPython():
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print('')
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print('----- Solving problem %i -----' % index)
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print('')
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print(('Initial game (%i x %i)' % (r, c)))
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print_matrix(puzzle)
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#
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# declare variables
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#
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positions = [
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model.NewIntVar(0, r * c - 1, 'p[%i]' % i) for i in range(r * c)
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]
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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 = build_pairs(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]],
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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.OPTIMAL:
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if visualization.RunFromIPython():
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output = visualization.SvgWrapper(10, r, 40.0)
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for i, var in enumerate(positions):
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val = solver.Value(var)
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x = val % c
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y = val // c
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color = 'white' if puzzle[y][x] == 0 else 'lightgreen'
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output.AddRectangle(x, r - y - 1, 1, 1, color, 'black',
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str(i + 1))
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output.AddTitle('Puzzle %i solved in %f s' % (index,
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solver.WallTime()))
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output.Display()
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else:
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print_solution(
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[solver.Value(x) for x in positions],
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r,
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c,
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)
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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 s' % solver.WallTime())
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for pb in range(1, 7):
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solve_hidato(build_puzzle(pb), pb)
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