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# 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.
"""

  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:
  * Comet: http://hakank.org/comet/alldifferent_except_0.co
  * ECLiPSe: http://hakank.org/eclipse/alldifferent_except_0.ecl
  * Tailor/Essence': http://hakank.org/tailor/alldifferent_except_0.eprime
  * Gecode: http://hakank.org/gecode/alldifferent_except_0.cpp
  * Gecode/R: http://hakank.org/gecode_r/all_different_except_0.rb
  * MiniZinc: http://hakank.org/minizinc/alldifferent_except_0.mzn
  * SICStus_ http://hakank.org/sicstus/alldifferent_except_0.pl
  * Choco: http://hakank.org/choco/AllDifferentExcept0_test.java
  * JaCoP: http://hakank.org/JaCoP/AllDifferentExcept0_test.java
  * Zinc: http://hakank.org/minizinc/alldifferent_except_0.zinc

  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

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)
  ]


# 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())