# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.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@bonetmail.com)
Also see my other Google CP Solver models:
http://www.hakank.org/google_cp_solver/
"""
from ortools.constraint_solver import pywrapcp
def main(unused_argv):
# Create the solver.
solver = pywrapcp.Solver("Least diff")
#
# declare variables
#
digits = 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]
x = solver.IntVar(range(0, 99999), "x")
y = solver.IntVar(range(0, 99999), "y")
diff = solver.IntVar(range(0, 99999), "y")
#
# constraints
#
solver.Add(x == 10000 * a + 1000 * b + 100 * c + 10 * d + e)
solver.Add(y == 10000 * f + 1000 * g + 100 * h + 10 * i + j)
solver.Add(diff == x - y)
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 + [x, y, diff],
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
if __name__ == "__main__":
main("cp sample")