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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.
"""

  Costas array in Google CP Solver.

  From http://mathworld.wolfram.com/CostasArray.html:
  '''
  An order-n Costas array is a permutation on {1,...,n} such
  that the distances in each row of the triangular difference
  table are distinct. For example, the permutation {1,3,4,2,5}
  has triangular difference table {2,1,-2,3}, {3,-1,1}, {1,2},
  and {4}. Since each row contains no duplications, the permutation
  is therefore a Costas array.
  '''

  Also see
  http://en.wikipedia.org/wiki/Costas_array

  About this model:
  This model is based on Barry O'Sullivan's model:
  http://www.g12.cs.mu.oz.au/mzn/costas_array/CostasArray.mzn

  and my small changes in
  http://hakank.org/minizinc/costas_array.mzn

  Since there is no symmetry breaking of the order of the Costas
  array it gives all the solutions for a specific length of
  the array, e.g. those listed in
  http://mathworld.wolfram.com/CostasArray.html

  1     1       (1)
  2     2       (1, 2), (2,1)
  3     4       (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2)
  4     12      (1, 2, 4, 3), (1, 3, 4, 2), (1, 4, 2, 3), (2, 1, 3, 4),
                (2, 3, 1, 4), (2, 4, 3, 1), (3, 1, 2, 4), (3, 2, 4, 1),
                (3, 4, 2, 1), (4, 1, 3, 2), (4, 2, 1, 3), (4, 3, 1, 2)
  ....

  See http://www.research.att.com/~njas/sequences/A008404
  for the number of solutions for n=1..
  1, 2, 4, 12, 40, 116, 200, 444, 760, 2160, 4368, 7852, 12828,
  17252, 19612, 21104, 18276, 15096, 10240, 6464, 3536, 2052,
  872, 200, 88, 56, 204,...


  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



# Create the solver.
solver = pywrapcp.Solver("Costas array")

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

#
# declare variables
#
costas = [solver.IntVar(1, n, "costas[%i]" % i) for i in range(n)]
differences = {}
for i in range(n):
  for j in range(n):
    differences[(i, j)] = solver.IntVar(-n + 1, n - 1,
                                        "differences[%i,%i]" % (i, j))
differences_flat = [differences[i, j] for i in range(n) for j in range(n)]

#
# constraints
#

# Fix the values in the lower triangle in the
# difference matrix to -n+1. This removes variants
# of the difference matrix for the the same Costas array.
for i in range(n):
  for j in range(i + 1):
    solver.Add(differences[i, j] == -n + 1)

# hakank: All the following constraints are from
# Barry O'Sullivans's original model.
#
solver.Add(solver.AllDifferent(costas))

# "How do the positions in the Costas array relate
#  to the elements of the distance triangle."
for i in range(n):
  for j in range(n):
    if i < j:
      solver.Add(differences[(i, j)] == costas[j] - costas[j - i - 1])

# "All entries in a particular row of the difference
#  triangle must be distint."
for i in range(n - 2):
  solver.Add(
      solver.AllDifferent([differences[i, j] for j in range(n) if j > i]))

#
# "All the following are redundant - only here to speed up search."
#

# "We can never place a 'token' in the same row as any other."
for i in range(n):
  for j in range(n):
    if i < j:
      solver.Add(differences[i, j] != 0)

for k in range(2, n):
  for l in range(2, n):
    if k < l:
      solver.Add(differences[k - 2, l - 1] + differences[k, l] ==
                 differences[k - 1, l - 1] + differences[k - 1, l])

#
# search and result
#
db = solver.Phase(costas + differences_flat, solver.CHOOSE_FIRST_UNBOUND,
                  solver.ASSIGN_MIN_VALUE)

solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
  print("costas:", [costas[i].Value() for i in range(n)])
  print("differences:")
  for i in range(n):
    for j in range(n):
      v = differences[i, j].Value()
      if v == -n + 1:
        print("  ", end=" ")
      else:
        print("%2d" % v, 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 = 6