88 lines
3.3 KiB
C++
88 lines
3.3 KiB
C++
// Copyright 2010-2018 Google LLC
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// Use CP-SAT to solve a simple cryptarithmetic problem: SEND+MORE=MONEY.
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#include "ortools/sat/cp_model.h"
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namespace operations_research {
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namespace sat {
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void SendMoreMoney() {
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CpModelBuilder cp_model;
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// Possible domains for variables.
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Domain all_digits(0, 9);
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Domain non_zero_digits(1, 9);
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// Create variables.
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// Since s is a leading digit, it can't be 0.
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const IntVar s = cp_model.NewIntVar(non_zero_digits);
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const IntVar e = cp_model.NewIntVar(all_digits);
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const IntVar n = cp_model.NewIntVar(all_digits);
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const IntVar d = cp_model.NewIntVar(all_digits);
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// Since m is a leading digit, it can't be 0.
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const IntVar m = cp_model.NewIntVar(non_zero_digits);
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const IntVar o = cp_model.NewIntVar(all_digits);
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const IntVar r = cp_model.NewIntVar(all_digits);
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const IntVar y = cp_model.NewIntVar(all_digits);
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// Create carry variables. c0 is true if the first column of addends carries
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// a 1, c2 is true if the second column carries a 1, and so on.
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const BoolVar c0 = cp_model.NewBoolVar();
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const BoolVar c1 = cp_model.NewBoolVar();
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const BoolVar c2 = cp_model.NewBoolVar();
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const BoolVar c3 = cp_model.NewBoolVar();
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// Force all letters to take on different values.
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cp_model.AddAllDifferent({s, e, n, d, m, o, r, y});
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// Column 0: Force c0 == m.
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cp_model.AddEquality(c0, m);
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// Column 1: Force c1 + s + m + o == 10*c0.
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cp_model.AddEquality(LinearExpr::Sum({c1, s, m, o}),
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LinearExpr::ScalProd({c0}, {10}));
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// Column 2: Force c2 + e + o == n + 10*c1.
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cp_model.AddEquality(LinearExpr::Sum({c2, e, o}),
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LinearExpr::ScalProd({n, c1}, {1, 10}));
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// Column 3: Force c3 + n + r == e + 10*c2.
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cp_model.AddEquality(LinearExpr::Sum({c3, n, r}),
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LinearExpr::ScalProd({e, c2}, {1, 10}));
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// Column 4: Force d + e == y + 10*c3.
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cp_model.AddEquality(LinearExpr::Sum({d, e}),
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LinearExpr::ScalProd({y, c3}, {1, 10}));
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// Declare the model, solve it, and display the results.
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const CpSolverResponse response = Solve(cp_model.Build());
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LOG(INFO) << CpSolverResponseStats(response);
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LOG(INFO) << "s: " << SolutionIntegerValue(response, s);
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LOG(INFO) << "e: " << SolutionIntegerValue(response, e);
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LOG(INFO) << "n: " << SolutionIntegerValue(response, n);
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LOG(INFO) << "d: " << SolutionIntegerValue(response, d);
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LOG(INFO) << "m: " << SolutionIntegerValue(response, m);
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LOG(INFO) << "o: " << SolutionIntegerValue(response, o);
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LOG(INFO) << "r: " << SolutionIntegerValue(response, r);
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LOG(INFO) << "y: " << SolutionIntegerValue(response, y);
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}
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} // namespace sat
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} // namespace operations_research
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int main() {
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operations_research::sat::SendMoreMoney();
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return EXIT_SUCCESS;
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}
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