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langford

examples/notebook/contrib/langford.ipynb

2016-063.6 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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langford

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

First, you must install ortools package in this colab.

python
%pip install ortools

Langford's number problem in Google CP Solver.

Langford's number problem (CSP lib problem 24) http://www.csplib.org/prob/prob024/ ''' Arrange 2 sets of positive integers 1..k to a sequence, such that, following the first occurence of an integer i, each subsequent occurrence of i, appears i+1 indices later than the last. For example, for k=4, a solution would be 41312432 '''

Also, see 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(k=8, num_sol=0):

  # Create the solver.
  solver = pywrapcp.Solver("Langford")

  #
  # data
  #
  print("k:", k)
  p = list(range(2 * k))

  #
  # declare variables
  #
  position = [solver.IntVar(0, 2 * k - 1, "position[%i]" % i) for i in p]
  solution = [solver.IntVar(1, k, "position[%i]" % i) for i in p]

  #
  # constraints
  #
  solver.Add(solver.AllDifferent(position))

  for i in range(1, k + 1):
    solver.Add(position[i + k - 1] == position[i - 1] + i + 1)
    solver.Add(solver.Element(solution, position[i - 1]) == i)
    solver.Add(solver.Element(solution, position[k + i - 1]) == i)

  # symmetry breaking
  solver.Add(solution[0] < solution[2 * k - 1])

  #
  # search and result
  #
  db = solver.Phase(position, solver.CHOOSE_FIRST_UNBOUND,
                    solver.ASSIGN_MIN_VALUE)

  solver.NewSearch(db)
  num_solutions = 0
  while solver.NextSolution():
    print("solution:", ",".join([str(solution[i].Value()) for i in p]))
    num_solutions += 1
    if num_sol > 0 and num_solutions >= num_sol:
      break

  solver.EndSearch()

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


k = 8
num_sol = 0
if len(sys.argv) > 1:
  k = int(sys.argv[1])
if len(sys.argv) > 2:
  num_sol = int(sys.argv[2])

main(k, num_sol)