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alldifferent_except_0

examples/notebook/contrib/alldifferent_except_0.ipynb

2016-064.1 KB
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alldifferent_except_0

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/alldifferent_except_0.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/examples/contrib/alldifferent_except_0.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python
%pip install ortools

All different except 0 Google CP Solver.

Decomposition of global constraint alldifferent_except_0.

From Global constraint catalogue: http://www.emn.fr/x-info/sdemasse/gccat/Calldifferent_except_0.html ''' Enforce all variables of the collection VARIABLES to take distinct values, except those variables that are assigned to 0.

Example (<5, 0, 1, 9, 0, 3>)

The alldifferent_except_0 constraint holds since all the values (that are different from 0) 5, 1, 9 and 3 are distinct. '''

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
from ortools.constraint_solver import pywrapcp

#
# Decomposition of alldifferent_except_0
# Thanks to Laurent Perron (Google) for
# suggestions of improvements.
#


def alldifferent_except_0(solver, a):
  n = len(a)
  for i in range(n):
    for j in range(i):
      solver.Add((a[i] != 0) * (a[j] != 0) <= (a[i] != a[j]))


# more compact version:


def alldifferent_except_0_b(solver, a):
  n = len(a)
  [
      solver.Add((a[i] != 0) * (a[j] != 0) <= (a[i] != a[j]))
      for i in range(n)
      for j in range(i)
  ]


def main(unused_argv):
  # Create the solver.
  solver = pywrapcp.Solver("Alldifferent except 0")

  # data
  n = 7

  # declare variables
  x = [solver.IntVar(0, n - 1, "x%i" % i) for i in range(n)]
  # Number of zeros.
  z = solver.Sum([x[i] == 0 for i in range(n)]).VarWithName("z")

  #
  # constraints
  #
  alldifferent_except_0(solver, x)

  # we require 2 0's
  solver.Add(z == 2)

  #
  # solution and search
  #
  solution = solver.Assignment()
  solution.Add([x[i] for i in range(n)])
  solution.Add(z)

  collector = solver.AllSolutionCollector(solution)
  solver.Solve(
      solver.Phase([x[i] for i in range(n)], 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(n)])
    print("z:", collector.Value(s, z))
    print()

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


main("cp sample")