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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.
"""

  Least diff problem in Google CP Solver.

  This model solves the following problem:

  What is the smallest difference between two numbers X - Y
  if you must use all the digits (0..9) exactly once.

  Compare with the following models:
  * Choco   : http://www.hakank.org/choco/LeastDiff2.java
  * ECLiPSE : http://www.hakank.org/eclipse/least_diff2.ecl
  * Comet   : http://www.hakank.org/comet/least_diff.co
  * Tailor/Essence': http://www.hakank.org/tailor/leastDiff.eprime
  * Gecode  : http://www.hakank.org/gecode/least_diff.cpp
  * Gecode/R: http://www.hakank.org/gecode_r/least_diff.rb
  * JaCoP   : http://www.hakank.org/JaCoP/LeastDiff.java
  * MiniZinc: http://www.hakank.org/minizinc/least_diff.mzn
  * SICStus : http://www.hakank.org/sicstus/least_diff.pl
  * Zinc    : http://hakank.org/minizinc/least_diff.zinc

  This model was created by Hakan Kjellerstrand (hakank@gmail.com)
  Also see my other Google CP Solver models:
  http://www.hakank.org/google_cp_solver/
"""
from __future__ import print_function
from ortools.constraint_solver import pywrapcp


# Create the solver.
solver = pywrapcp.Solver("Least diff")

#
# declare variables
#
digits = list(range(0, 10))
a = solver.IntVar(digits, "a")
b = solver.IntVar(digits, "b")
c = solver.IntVar(digits, "c")
d = solver.IntVar(digits, "d")
e = solver.IntVar(digits, "e")

f = solver.IntVar(digits, "f")
g = solver.IntVar(digits, "g")
h = solver.IntVar(digits, "h")
i = solver.IntVar(digits, "i")
j = solver.IntVar(digits, "j")

letters = [a, b, c, d, e, f, g, h, i, j]

digit_vector = [10000, 1000, 100, 10, 1]
x = solver.ScalProd(letters[0:5], digit_vector)
y = solver.ScalProd(letters[5:], digit_vector)
diff = x - y

#
# constraints
#
solver.Add(diff > 0)
solver.Add(solver.AllDifferent(letters))

# objective
objective = solver.Minimize(diff, 1)

#
# solution
#
solution = solver.Assignment()
solution.Add(letters)
solution.Add(x)
solution.Add(y)
solution.Add(diff)

# last solution since it's a minimization problem
collector = solver.LastSolutionCollector(solution)
search_log = solver.SearchLog(100, diff)
# Note: I'm not sure what CHOOSE_PATH do, but it is fast:
#       find the solution in just 4 steps
solver.Solve(
    solver.Phase(letters, solver.CHOOSE_PATH, solver.ASSIGN_MIN_VALUE),
    [objective, search_log, collector])

# get the first (and only) solution

xval = collector.Value(0, x)
yval = collector.Value(0, y)
diffval = collector.Value(0, diff)
print("x:", xval)
print("y:", yval)
print("diff:", diffval)
print(xval, "-", yval, "=", diffval)
print([("abcdefghij" [i], collector.Value(0, letters[i])) for i in range(10)])
print()
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
print()