1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2007 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | /// \ingroup demos |
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20 | /// \file |
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21 | /// \brief Solver for SAT problems. |
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22 | /// |
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23 | /// This demo progam solves the SAT problem, i.e. the boolean |
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24 | /// satisfiability problem. The problem in general case is |
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25 | /// NP-complete. |
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26 | /// |
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27 | /// The program uses an integer linear program solver. A <tt>{0, |
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28 | /// 1}</tt> variable is assigned to each boolean variable. The |
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29 | /// disjunctions are converted to linear inequalities as each negation |
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30 | /// is replaced with a substraction from one and each disjunction is |
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31 | /// converted to addition. The generated linear expression should be |
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32 | /// at least one. |
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33 | /// |
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34 | /// \include sat.cc |
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35 | |
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36 | #include <iostream> |
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37 | #include <fstream> |
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38 | #include <sstream> |
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39 | #include <string> |
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40 | |
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41 | #include <lemon/lp.h> |
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42 | |
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43 | using namespace std; |
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44 | using namespace lemon; |
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45 | |
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46 | |
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47 | int main(int argc, const char *argv[]) { |
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48 | if (argc != 2) { |
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49 | std::cerr << "The SAT solver demo" << std::endl << std::endl; |
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50 | std::cerr << "The parameter should be a filename" << std::endl; |
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51 | std::cerr << "Each line of the file should contain a bool expression:" |
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52 | << std::endl; |
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53 | std::cerr << " [not] <variable> [or [not] <variable>]..." << std::endl; |
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54 | std::cerr << "The program prints a feasible solution if it exists" |
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55 | << std::endl; |
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56 | return -1; |
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57 | } |
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58 | ifstream is(argv[1]); |
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59 | |
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60 | Mip mip; |
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61 | mip.max(); |
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62 | mip.obj(0); |
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63 | |
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64 | string line; |
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65 | while (getline(is, line)) { |
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66 | istringstream ls(line); |
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67 | |
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68 | Mip::Expr expr; |
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69 | |
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70 | |
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71 | string op; |
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72 | do { |
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73 | string var; |
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74 | bool neg = false; |
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75 | |
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76 | ls >> var; |
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77 | if (var == "not") { |
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78 | neg = true; |
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79 | ls >> var; |
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80 | } |
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81 | |
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82 | Mip::Col col = mip.colByName(var); |
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83 | |
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84 | if (col == INVALID) { |
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85 | col = mip.addCol(); |
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86 | mip.colName(col, var); |
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87 | mip.colLowerBound(col, 0); |
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88 | mip.colUpperBound(col, 1); |
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89 | mip.integer(col, true); |
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90 | } |
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91 | |
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92 | expr += (neg ? 1 - col : col); |
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93 | |
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94 | } while (ls >> op && op == "or"); |
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95 | if (ls) { |
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96 | std::cerr << "Wrong bool expression" << std::endl; |
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97 | return -1; |
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98 | } |
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99 | mip.addRow(expr >= 1); |
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100 | } |
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101 | |
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102 | mip.solve(); |
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103 | |
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104 | if (mip.mipStatus() == Mip::OPTIMAL) { |
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105 | for (Mip::ColIt it(mip); it != INVALID; ++it) { |
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106 | std::cout << mip.colName(it) << " = " |
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107 | << (mip.primal(it) == 1 ? "true" : "false") |
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108 | << std::endl; |
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109 | } |
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110 | } else { |
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111 | std::cout << "There is no feasible solution." << std::endl; |
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112 | } |
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113 | |
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114 | return 0; |
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115 | } |
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