110 lines
3.5 KiB
C++
110 lines
3.5 KiB
C++
// Copyright 2010 Google
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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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//
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// Cryptoarithmetics problem
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//
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// Solves equation SEND + MORE = MONEY among numbers
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// where each digit is represented by a letter.
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//
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// Solution:
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// S=9; M=1; O=0; E=5; N=6; D=7; R=8; Y=2.
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#include "base/commandlineflags.h"
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#include "base/logging.h"
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#include "base/scoped_ptr.h"
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#include "constraint_solver/constraint_solver.h"
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namespace operations_research {
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void Cryptoarithmetics() {
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scoped_ptr<Solver> solver(new Solver("cryptarithm"));
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// model with carry
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IntVar* s = solver->MakeIntVar(1, 9, "s");
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IntVar* m = solver->MakeIntVar(1, 9, "m");
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IntVar* o = solver->MakeIntVar(0, 9, "o");
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IntVar* e = solver->MakeIntVar(0, 9, "e");
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IntVar* n = solver->MakeIntVar(0, 9, "n");
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IntVar* d = solver->MakeIntVar(0, 9, "d");
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IntVar* r = solver->MakeIntVar(0, 9, "r");
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IntVar* y = solver->MakeIntVar(0, 9, "y");
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vector<IntVar*> letters;
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letters.push_back(s);
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letters.push_back(m);
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letters.push_back(o);
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letters.push_back(e);
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letters.push_back(n);
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letters.push_back(d);
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letters.push_back(r);
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letters.push_back(y);
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solver->AddConstraint(solver->MakeAllDifferent(letters, false));
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// carry variables
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IntVar* c1 = solver->MakeIntVar(0, 1, "c1");
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IntVar* c2 = solver->MakeIntVar(0, 1, "c2");
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IntVar* c3 = solver->MakeIntVar(0, 1, "c3");
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// initial constraint is separated into four small constraints
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IntVar* v1 = solver->MakeSum(e, d)->Var();
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IntVar* v2 = solver->MakeSum(y, solver->MakeProd(c1, 10))->Var();
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solver->AddConstraint(solver->MakeEquality(v1, v2));
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v1 = solver->MakeSum(solver->MakeSum(c1, n), r)->Var();
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v2 = solver->MakeSum(e, solver->MakeProd(c2, 10))->Var();
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solver->AddConstraint(solver->MakeEquality(v1, v2));
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v1 = solver->MakeSum(solver->MakeSum(c2, e), o)->Var();
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v2 = solver->MakeSum(n, solver->MakeProd(c3, 10))->Var();
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solver->AddConstraint(solver->MakeEquality(v1, v2));
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v1 = solver->MakeSum(solver->MakeSum(c3, s), m)->Var();
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v2 = solver->MakeSum(o, solver->MakeProd(m, 10))->Var();
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solver->AddConstraint(solver->MakeEquality(v1, v2));
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DecisionBuilder* const db = solver->MakePhase(letters,
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Solver::CHOOSE_FIRST_UNBOUND,
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Solver::ASSIGN_MIN_VALUE);
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if (solver->Solve(db)) {
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CHECK_EQ(s->Value(), 9);
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CHECK_EQ(m->Value(), 1);
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CHECK_EQ(o->Value(), 0);
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CHECK_EQ(e->Value(), 5);
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CHECK_EQ(n->Value(), 6);
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CHECK_EQ(d->Value(), 7);
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CHECK_EQ(r->Value(), 8);
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CHECK_EQ(y->Value(), 2);
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LG << "S=" << s->Value();
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LG << "M=" << m->Value();
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LG << "O=" << o->Value();
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LG << "E=" << e->Value();
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LG << "N=" << n->Value();
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LG << "D=" << d->Value();
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LG << "R=" << r->Value();
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LG << "Y=" << y->Value();
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} else {
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LG << "Cannot solve problem: number of failures " << solver->failures();
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}
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}
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} // namespace operations_research
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int main(int argc, char **argv) {
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google::ParseCommandLineFlags(&argc, &argv, true);
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operations_research::Cryptoarithmetics();
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return 0;
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}
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