1 // Copyright 2010-2021 Google LLC
2 // Licensed under the Apache License, Version 2.0 (the "License");
3 // you may not use this file except in compliance with the License.
4 // You may obtain a copy of the License at
5 //
6 // http://www.apache.org/licenses/LICENSE-2.0
7 //
8 // Unless required by applicable law or agreed to in writing, software
9 // distributed under the License is distributed on an "AS IS" BASIS,
10 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
11 // See the License for the specific language governing permissions and
12 // limitations under the License.
13
14 // Use CP-SAT to solve a simple cryptarithmetic problem: SEND+MORE=MONEY.
15
16 #include "ortools/sat/cp_model.h"
17
18 namespace operations_research {
19 namespace sat {
20
SendMoreMoney()21 void SendMoreMoney() {
22 CpModelBuilder cp_model;
23
24 // Possible domains for variables.
25 Domain all_digits(0, 9);
26 Domain non_zero_digits(1, 9);
27 // Create variables.
28 // Since s is a leading digit, it can't be 0.
29 const IntVar s = cp_model.NewIntVar(non_zero_digits);
30 const IntVar e = cp_model.NewIntVar(all_digits);
31 const IntVar n = cp_model.NewIntVar(all_digits);
32 const IntVar d = cp_model.NewIntVar(all_digits);
33 // Since m is a leading digit, it can't be 0.
34 const IntVar m = cp_model.NewIntVar(non_zero_digits);
35 const IntVar o = cp_model.NewIntVar(all_digits);
36 const IntVar r = cp_model.NewIntVar(all_digits);
37 const IntVar y = cp_model.NewIntVar(all_digits);
38
39 // Create carry variables. c0 is true if the first column of addends carries
40 // a 1, c2 is true if the second column carries a 1, and so on.
41 const BoolVar c0 = cp_model.NewBoolVar();
42 const BoolVar c1 = cp_model.NewBoolVar();
43 const BoolVar c2 = cp_model.NewBoolVar();
44 const BoolVar c3 = cp_model.NewBoolVar();
45
46 // Force all letters to take on different values.
47 cp_model.AddAllDifferent({s, e, n, d, m, o, r, y});
48
49 // Column 0:
50 cp_model.AddEquality(c0, m);
51
52 // Column 1:
53 cp_model.AddEquality(c1 + s + m + o, 10 * c0);
54
55 // Column 2:
56 cp_model.AddEquality(c2 + e + o, n + 10 * c1);
57
58 // Column 3:
59 cp_model.AddEquality(c3 + n + r, e + 10 * c2);
60
61 // Column 4:
62 cp_model.AddEquality(d + e, y + 10 * c3);
63
64 // Declare the model, solve it, and display the results.
65 const CpSolverResponse response = Solve(cp_model.Build());
66 LOG(INFO) << CpSolverResponseStats(response);
67 LOG(INFO) << "s: " << SolutionIntegerValue(response, s);
68 LOG(INFO) << "e: " << SolutionIntegerValue(response, e);
69 LOG(INFO) << "n: " << SolutionIntegerValue(response, n);
70 LOG(INFO) << "d: " << SolutionIntegerValue(response, d);
71 LOG(INFO) << "m: " << SolutionIntegerValue(response, m);
72 LOG(INFO) << "o: " << SolutionIntegerValue(response, o);
73 LOG(INFO) << "r: " << SolutionIntegerValue(response, r);
74 LOG(INFO) << "y: " << SolutionIntegerValue(response, y);
75 }
76
77 } // namespace sat
78 } // namespace operations_research
79
main()80 int main() {
81 operations_research::sat::SendMoreMoney();
82 return EXIT_SUCCESS;
83 }
84