1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | /// \ingroup demos |
---|
20 | /// \file |
---|
21 | /// \brief Solver for SAT problems. |
---|
22 | /// |
---|
23 | /// This demo progam solves the SAT problem, i.e. the boolean |
---|
24 | /// satisfiability problem. The problem in general case is |
---|
25 | /// NP-complete. |
---|
26 | /// |
---|
27 | /// The program uses an integer linear program solver. A <tt>{0, |
---|
28 | /// 1}</tt> variable is assigned to each boolean variable. The |
---|
29 | /// disjunctions are converted to linear inequalities as each negation |
---|
30 | /// is replaced with a substraction from one and each disjunction is |
---|
31 | /// converted to addition. The generated linear expression should be |
---|
32 | /// at least one. |
---|
33 | /// |
---|
34 | /// \include sat.cc |
---|
35 | |
---|
36 | #include <iostream> |
---|
37 | #include <fstream> |
---|
38 | #include <sstream> |
---|
39 | #include <string> |
---|
40 | |
---|
41 | #include <lemon/lp.h> |
---|
42 | |
---|
43 | using namespace std; |
---|
44 | using namespace lemon; |
---|
45 | |
---|
46 | |
---|
47 | int main(int argc, const char *argv[]) { |
---|
48 | if (argc != 2) { |
---|
49 | std::cerr << "The SAT solver demo" << std::endl << std::endl; |
---|
50 | std::cerr << "The parameter should be a filename" << std::endl; |
---|
51 | std::cerr << "Each line of the file should contain a bool expression:" |
---|
52 | << std::endl; |
---|
53 | std::cerr << " [not] <variable> [or [not] <variable>]..." << std::endl; |
---|
54 | std::cerr << "The program prints a feasible solution if it exists" |
---|
55 | << std::endl; |
---|
56 | return -1; |
---|
57 | } |
---|
58 | ifstream is(argv[1]); |
---|
59 | |
---|
60 | Mip mip; |
---|
61 | mip.max(); |
---|
62 | mip.obj(0); |
---|
63 | |
---|
64 | string line; |
---|
65 | while (getline(is, line)) { |
---|
66 | istringstream ls(line); |
---|
67 | |
---|
68 | Mip::Expr expr; |
---|
69 | |
---|
70 | |
---|
71 | string op; |
---|
72 | do { |
---|
73 | string var; |
---|
74 | bool neg = false; |
---|
75 | |
---|
76 | ls >> var; |
---|
77 | if (var == "not") { |
---|
78 | neg = true; |
---|
79 | ls >> var; |
---|
80 | } |
---|
81 | |
---|
82 | Mip::Col col = mip.colByName(var); |
---|
83 | |
---|
84 | if (col == INVALID) { |
---|
85 | col = mip.addCol(); |
---|
86 | mip.colName(col, var); |
---|
87 | mip.colLowerBound(col, 0); |
---|
88 | mip.colUpperBound(col, 1); |
---|
89 | mip.integer(col, true); |
---|
90 | } |
---|
91 | |
---|
92 | expr += (neg ? 1 - col : col); |
---|
93 | |
---|
94 | } while (ls >> op && op == "or"); |
---|
95 | if (ls) { |
---|
96 | std::cerr << "Wrong bool expression" << std::endl; |
---|
97 | return -1; |
---|
98 | } |
---|
99 | mip.addRow(expr >= 1); |
---|
100 | } |
---|
101 | |
---|
102 | mip.solve(); |
---|
103 | |
---|
104 | if (mip.mipStatus() == Mip::OPTIMAL) { |
---|
105 | for (Mip::ColIt it(mip); it != INVALID; ++it) { |
---|
106 | std::cout << mip.colName(it) << " = " |
---|
107 | << (mip.primal(it) == 1 ? "true" : "false") |
---|
108 | << std::endl; |
---|
109 | } |
---|
110 | } else { |
---|
111 | std::cout << "There is no feasible solution." << std::endl; |
---|
112 | } |
---|
113 | |
---|
114 | return 0; |
---|
115 | } |
---|