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place_number_puzzle

examples/notebook/contrib/place_number_puzzle.ipynb

2016-063.4 KB
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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

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place_number_puzzle

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/place_number_puzzle.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/examples/contrib/place_number_puzzle.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python
%pip install ortools

Place number puzzle Google CP Solver.

http://ai.uwaterloo.ca/~vanbeek/Courses/Slides/introduction.pdf ''' Place numbers 1 through 8 on nodes

  • each number appears exactly once
  • no connected nodes have consecutive numbers 2 - 5 / | X |
    1 - 3 - 6 - 8 \ | X | / 4 - 7 ""

Compare with the following models:

This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/

python
import sys
from ortools.constraint_solver import pywrapcp


def main():

  # Create the solver.
  solver = pywrapcp.Solver("Place number")

  # data
  m = 32
  n = 8
  # Note: this is 1-based for compatibility (and lazyness)
  graph = [[1, 2], [1, 3], [1, 4], [2, 1], [2, 3], [2, 5], [2, 6], [3, 2],
           [3, 4], [3, 6], [3, 7], [4, 1], [4, 3], [4, 6], [4, 7], [5, 2],
           [5, 3], [5, 6], [5, 8], [6, 2], [6, 3], [6, 4], [6, 5], [6, 7],
           [6, 8], [7, 3], [7, 4], [7, 6], [7, 8], [8, 5], [8, 6], [8, 7]]

  # declare variables
  x = [solver.IntVar(1, n, "x%i" % i) for i in range(n)]

  #
  # constraints
  #
  solver.Add(solver.AllDifferent(x))
  for i in range(m):
    # Note: make 0-based
    solver.Add(abs(x[graph[i][0] - 1] - x[graph[i][1] - 1]) > 1)

  # symmetry breaking
  solver.Add(x[0] < x[n - 1])

  #
  # solution and search
  #
  solution = solver.Assignment()
  solution.Add(x)

  collector = solver.AllSolutionCollector(solution)

  solver.Solve(
      solver.Phase(x, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE),
      [collector])

  num_solutions = collector.SolutionCount()
  for s in range(num_solutions):
    print("x:", [collector.Value(s, x[i]) for i in range(len(x))])

  print()
  print("num_solutions:", num_solutions)
  print("failures:", solver.Failures())
  print("branches:", solver.Branches())
  print("WallTime:", solver.WallTime())
  print()


main()