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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.
"""

  Decomposition of the circuit constraint in Google CP Solver.


  Cf Global constraint catalog:
  http://www.emn.fr/x-info/sdemasse/gccat/Ccircuit.html

  Solution of n=4:
  x: [2, 0, 3, 1]
  x: [3, 0, 1, 2]
  x: [1, 3, 0, 2]
  x: [3, 2, 0, 1]
  x: [1, 2, 3, 0]
  x: [2, 3, 1, 0]

  The 'orbit' method that is used here is based on some
  observations on permutation orbits.

  Compare with the following models:
  * MiniZinc: http://www.hakank.org/minizinc/circuit_test.mzn
  * Gecode: http://www.hakank.org/gecode/circuit_orbit.mzn


  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

#
# circuit(x)
# constraints x to be an circuit
#
# Note: This assumes that x is has the domain 0..len(x)-1,
#       i.e. 0-based.
#


def circuit(solver, x):
  n = len(x)
  z = [solver.IntVar(0, n - 1, "z%i" % i) for i in range(n)]

  solver.Add(solver.AllDifferent(x))
  solver.Add(solver.AllDifferent(z))

  # put the orbit of x[0] in in z[0..n-1]
  solver.Add(z[0] == x[0])
  for i in range(1, n - 1):
    # The following constraint give the error
    # "TypeError: list indices must be integers, not IntVar"
    # solver.Add(z[i] == x[z[i-1]])

    # solution: use Element instead
    solver.Add(z[i] == solver.Element(x, z[i - 1]))

  #
  # Note: At least one of the following two constraint must be set.
  #
  # may not be 0 for i < n-1
  for i in range(1, n - 1):
    solver.Add(z[i] != 0)

  # when i = n-1 it must be 0
  solver.Add(z[n - 1] == 0)



# Create the solver.
solver = pywrapcp.Solver("Send most money")

# data
print("n:", n)

# declare variables
# Note: domain should be 0..n-1
x = [solver.IntVar(0, n - 1, "x%i" % i) for i in range(n)]

#
# constraints
#
circuit(solver, x)

#
# 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()

n = 5