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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.
"""

  Magic squares in Google CP Solver.

  Magic square problem.

  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("n-queens")

#
# data
#

#
# declare variables
#
x = {}
for i in range(n):
  for j in range(n):
    x[(i, j)] = solver.IntVar(1, n * n, "x(%i,%i)" % (i, j))
x_flat = [x[(i, j)] for i in range(n) for j in range(n)]

# the sum
# s = ( n * (n*n + 1)) / 2
s = solver.IntVar(1, n * n * n, "s")

#
# constraints
#
# solver.Add(s == ( n * (n*n + 1)) / 2)

solver.Add(solver.AllDifferent(x_flat))

[solver.Add(solver.Sum([x[(i, j)] for j in range(n)]) == s) for i in range(n)]
[solver.Add(solver.Sum([x[(i, j)] for i in range(n)]) == s) for j in range(n)]

solver.Add(solver.Sum([x[(i, i)] for i in range(n)]) == s)  # diag 1
solver.Add(solver.Sum([x[(i, n - i - 1)] for i in range(n)]) == s)  # diag 2

# symmetry breaking
# solver.Add(x[(0,0)] == 1)

#
# solution and search
#
solution = solver.Assignment()
solution.Add(x_flat)
solution.Add(s)

# db: DecisionBuilder
db = solver.Phase(
    x_flat,
    # solver.INT_VAR_DEFAULT,
    solver.CHOOSE_FIRST_UNBOUND,
    # solver.CHOOSE_MIN_SIZE_LOWEST_MAX,

    # solver.ASSIGN_MIN_VALUE
    solver.ASSIGN_CENTER_VALUE)

solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
  print("s:", s.Value())
  for i in range(n):
    for j in range(n):
      print("%2i" % x[(i, j)].Value(), end=" ")
    print()

  print()
  num_solutions += 1
  if num_solutions > limit:
    break
solver.EndSearch()

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

n = 4
limit=100