ortools-clone/examples/python/set_partition.py

# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com
#
# 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.
"""

  Set partition problem in Google CP Solver.

  Problem formulation from
  http://www.koalog.com/resources/samples/PartitionProblem.java.html
  '''
   This is a partition problem.
   Given the set S = {1, 2, ..., n},
   it consists in finding two sets A and B such that:

     A U B = S,
     |A| = |B|,
     sum(A) = sum(B),
     sum_squares(A) = sum_squares(B)

  '''

  This model uses a binary matrix to represent the sets.


  Also, compare with other models which uses var sets:
  * MiniZinc: http://www.hakank.org/minizinc/set_partition.mzn
  * Gecode/R: http://www.hakank.org/gecode_r/set_partition.rb
  * Comet: http://hakank.org/comet/set_partition.co
  * Gecode: http://hakank.org/gecode/set_partition.cpp
  * ECLiPSe: http://hakank.org/eclipse/set_partition.ecl
  * SICStus: http://hakank.org/sicstus/set_partition.pl

  This model was created by Hakan Kjellerstrand (hakank@gmail.com)
  Also see my other Google CP Solver models:
  http://www.hakank.org/google_or_tools/
"""
from __future__ import print_function
import sys

from ortools.constraint_solver import pywrapcp


#
# Partition the sets (binary matrix representation).
#
def partition_sets(x, num_sets, n):
  solver = list(x.values())[0].solver()

  for i in range(num_sets):
    for j in range(num_sets):
      if i != j:
        b = solver.Sum([x[i, k] * x[j, k] for k in range(n)])
        solver.Add(b == 0)

  # ensure that all integers is in
  # (exactly) one partition
  b = [x[i, j] for i in range(num_sets) for j in range(n)]
  solver.Add(solver.Sum(b) == n)


def main(n=16, num_sets=2):

  # Create the solver.
  solver = pywrapcp.Solver("Set partition")

  #
  # data
  #
  print("n:", n)
  print("num_sets:", num_sets)
  print()

  # Check sizes
  assert n % num_sets == 0, "Equal sets is not possible."

  #
  # variables
  #

  # the set
  a = {}
  for i in range(num_sets):
    for j in range(n):
      a[i, j] = solver.IntVar(0, 1, "a[%i,%i]" % (i, j))

  a_flat = [a[i, j] for i in range(num_sets) for j in range(n)]

  #
  # constraints
  #

  # partition set
  partition_sets(a, num_sets, n)

  for i in range(num_sets):
    for j in range(i, num_sets):

      # same cardinality
      solver.Add(
          solver.Sum([a[i, k] for k in range(n)]) == solver.Sum(
              [a[j, k] for k in range(n)]))

      # same sum
      solver.Add(
          solver.Sum([k * a[i, k] for k in range(n)]) == solver.Sum(
              [k * a[j, k] for k in range(n)]))

      # same sum squared
      solver.Add(
          solver.Sum([(k * a[i, k]) * (k * a[i, k]) for k in range(n)]) ==
          solver.Sum([(k * a[j, k]) * (k * a[j, k]) for k in range(n)]))

  # symmetry breaking for num_sets == 2
  if num_sets == 2:
    solver.Add(a[0, 0] == 1)

  #
  # search and result
  #
  db = solver.Phase(a_flat, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)

  solver.NewSearch(db)

  num_solutions = 0
  while solver.NextSolution():
    a_val = {}
    for i in range(num_sets):
      for j in range(n):
        a_val[i, j] = a[i, j].Value()

    sq = sum([(j + 1) * a_val[0, j] for j in range(n)])
    print("sums:", sq)
    sq2 = sum([((j + 1) * a_val[0, j])**2 for j in range(n)])
    print("sums squared:", sq2)

    for i in range(num_sets):
      if sum([a_val[i, j] for j in range(n)]):
        print(i + 1, ":", end=" ")
        for j in range(n):
          if a_val[i, j] == 1:
            print(j + 1, end=" ")
        print()

    print()
    num_solutions += 1

  solver.EndSearch()

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


n = 16
num_sets = 2
if __name__ == "__main__":
  if len(sys.argv) > 1:
    n = int(sys.argv[1])
  if len(sys.argv) > 2:
    num_sets = int(sys.argv[2])

  main(n, num_sets)