hidato_sat.py

# Copyright 2010-2018 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Solves the Hidato problem with the CP-SAT solver."""

from __future__ import print_function

from ortools.sat.python import visualization
from ortools.sat.python import cp_model


def build_pairs(rows, cols):
    """Build closeness pairs for consecutive numbers.

  Build set of allowed pairs such that two consecutive numbers touch
  each other in the grid.

  Returns:
    A list of pairs for allowed consecutive position of numbers.

  Args:
    rows: the number of rows in the grid
    cols: the number of columns in the grid
  """
    return [
        (x * cols + y, (x + dx) * cols + (y + dy)) for x in range(rows)
        for y in range(cols) for dx in (-1, 0, 1)
        for dy in (-1, 0, 1)
        if (x + dx >= 0 and x + dx < rows and y + dy >= 0 and y + dy < cols and
            (dx != 0 or dy != 0))
    ]


def print_solution(positions, rows, cols):
    """Print a current solution."""
    # Create empty board.
    board = []
    for _ in range(rows):
        board.append([0] * cols)
    # Fill board with solution value.
    for k in range(rows * cols):
        position = positions[k]
        board[position // cols][position % cols] = k + 1
    # Print the board.
    print('Solution')
    print_matrix(board)


def print_matrix(game):
    """Pretty print of a matrix."""
    rows = len(game)
    cols = len(game[0])
    for i in range(rows):
        line = ''
        for j in range(cols):
            if game[i][j] == 0:
                line += '  .'
            else:
                line += '% 3s' % game[i][j]
        print(line)


def build_puzzle(problem):
    """Build the problem from its index."""
    #
    # models, a 0 indicates an open cell which number is not yet known.
    #
    #
    puzzle = None
    if problem == 1:
        # Simple problem
        puzzle = [[6, 0, 9], [0, 2, 8], [1, 0, 0]]

    elif problem == 2:
        puzzle = [[0, 44, 41, 0, 0, 0, 0], [0, 43, 0, 28, 29, 0, 0],
                  [0, 1, 0, 0, 0, 33, 0], [0, 2, 25, 4, 34, 0, 36],
                  [49, 16, 0, 23, 0, 0, 0], [0, 19, 0, 0, 12, 7,
                                             0], [0, 0, 0, 14, 0, 0, 0]]

    elif problem == 3:
        # Problems from the book:
        # Gyora Bededek: "Hidato: 2000 Pure Logic Puzzles"
        # Problem 1 (Practice)
        puzzle = [[0, 0, 20, 0, 0], [0, 0, 0, 16, 18], [22, 0, 15, 0, 0],
                  [23, 0, 1, 14, 11], [0, 25, 0, 0, 12]]

    elif problem == 4:
        # problem 2 (Practice)
        puzzle = [[0, 0, 0, 0, 14], [0, 18, 12, 0, 0], [0, 0, 17, 4, 5],
                  [0, 0, 7, 0, 0], [9, 8, 25, 1, 0]]

    elif problem == 5:
        # problem 3 (Beginner)
        puzzle = [[0, 26, 0, 0, 0, 18], [0, 0, 27, 0, 0, 19],
                  [31, 23, 0, 0, 14, 0], [0, 33, 8, 0, 15, 1],
                  [0, 0, 0, 5, 0, 0], [35, 36, 0, 10, 0, 0]]
    elif problem == 6:
        # Problem 15 (Intermediate)
        puzzle = [[64, 0, 0, 0, 0, 0, 0, 0], [1, 63, 0, 59, 15, 57, 53, 0],
                  [0, 4, 0, 14, 0, 0, 0, 0], [3, 0, 11, 0, 20, 19, 0,
                                              50], [0, 0, 0, 0, 22, 0, 48, 40],
                  [9, 0, 0, 32, 23, 0, 0, 41], [27, 0, 0, 0, 36, 0, 46,
                                                0], [28, 30, 0, 35, 0, 0, 0, 0]]
    return puzzle


def solve_hidato(puzzle, index):
    """Solve the given hidato table."""
    # Create the model.
    model = cp_model.CpModel()

    r = len(puzzle)
    c = len(puzzle[0])
    if not visualization.RunFromIPython():
        print('')
        print('----- Solving problem %i -----' % index)
        print('')
        print(('Initial game (%i x %i)' % (r, c)))
        print_matrix(puzzle)

    #
    # declare variables
    #
    positions = [
        model.NewIntVar(0, r * c - 1, 'p[%i]' % i) for i in range(r * c)
    ]

    #
    # constraints
    #
    model.AddAllDifferent(positions)

    #
    # Fill in the clues
    #
    for i in range(r):
        for j in range(c):
            if puzzle[i][j] > 0:
                model.Add(positions[puzzle[i][j] - 1] == i * c + j)

    # Consecutive numbers much touch each other in the grid.
    # We use an allowed assignment constraint to model it.
    close_tuples = build_pairs(r, c)
    for k in range(0, r * c - 1):
        model.AddAllowedAssignments([positions[k], positions[k + 1]],
                                    close_tuples)

    #
    # solution and search
    #

    solver = cp_model.CpSolver()
    status = solver.Solve(model)

    if status == cp_model.OPTIMAL:
        if visualization.RunFromIPython():
            output = visualization.SvgWrapper(10, r, 40.0)
            for i, var in enumerate(positions):
                val = solver.Value(var)
                x = val % c
                y = val // c
                color = 'white' if puzzle[y][x] == 0 else 'lightgreen'
                output.AddRectangle(x, r - y - 1, 1, 1, color, 'black',
                                    str(i + 1))

            output.AddTitle('Puzzle %i solved in %f s' % (index,
                                                          solver.WallTime()))
            output.Display()
        else:
            print_solution(
                [solver.Value(x) for x in positions],
                r,
                c,
            )
            print('Statistics')
            print('  - conflicts : %i' % solver.NumConflicts())
            print('  - branches  : %i' % solver.NumBranches())
            print('  - wall time : %f s' % solver.WallTime())


for pb in range(1, 7):
    solve_hidato(build_puzzle(pb), pb)