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dekker.one
1/**** , [ MatrixGame.cpp ],
2Copyright (c) 2007 Universite d'Orleans - Arnaud Lallouet
3
4Permission is hereby granted, free of charge, to any person obtaining a copy
5of this software and associated documentation files (the "Software"), to deal
6in the Software without restriction, including without limitation the rights
7to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
8copies of the Software, and to permit persons to whom the Software is
9furnished to do so, subject to the following conditions:
10
11The above copyright notice and this permission notice shall be included in
12all copies or substantial portions of the Software.
13
14THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
15IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
16FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
17AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
18LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
19OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
20THE SOFTWARE.
21 *************************************************************************/
22
23#include <cstdlib> /* for srand, rand et RAND_MAX */
24#include <ctime> /* for time */
25#include <math.h> /* for pow */
26
27#include <iostream>
28
29#include <gecode/minimodel.hh>
30#include <gecode/int/element.hh>
31
32#include "qsolver_qcsp.hh"
33#include "QCOPPlus.hh"
34
35#define UNIVERSAL true
36#define EXISTENTIAL false
37
38// The Matrix game consists in a square boolean matrix of size 2^depth. First player cuts it vertically in two parts and removes one half,
39// while secodn player do the same, but cutting the matrix horizontally. The game ends when there are only one cell left in the matrix.
40// If this last cell has value 1, the first player wins. If it has value 0, the second player wins.
41
42// The present model of this game is pure QBF, that QeCode can handle (though not as fast as QBF solvers...)
43
44using namespace MiniModel;
45
46int main (int argc, char * const argv[]) {
47
48 int depth = 5; // Size of the matrix is 2^depth. Larger values may take long to solve...
49 int nbDecisionVar = 2*depth;
50 int nbScope = nbDecisionVar+1;
51 bool* qtScopes = new bool[nbScope];
52 for (int i=0;i<nbScope;i++) {
53 qtScopes[i] = ((i%2) != 0);
54// cout << (((i%2) != 0)?"true":"false")<<endl;
55 }
56 int boardSize = (int)pow((double)2,(double)depth);
57
58 std::srand(std::time(NULL));
59
60 IntArgs board(boardSize*boardSize);
61 for (int i=0; i<boardSize; i++)
62 for (int j=0; j<boardSize; j++)
63 board[j*boardSize+i] = (int)( (double)rand() / ((double)RAND_MAX + 1) * 50 ) < 25 ? 0:1;
64
65 IntArgs access(nbDecisionVar);
66 access[nbDecisionVar-1]=1;
67 access[nbDecisionVar-2]=boardSize;
68 for (int i=nbDecisionVar-3; i>=0; i--)
69 access[i]=access[i+2]*2;
70
71 // debug
72 for (int i=0; i<boardSize; i++)
73 {
74 for (int j=0; j<boardSize; j++)
75 cout << board[j*boardSize+i] << " ";
76 cout << endl;
77 }
78 cout << endl;
79 // for (int i=0; i<nbDecisionVar; i++)
80// cout << access[i] << " ";
81// cout << endl;
82 // end debug
83
84 int * scopesSize = new int[nbScope];
85 for (int i=0; i<nbScope-1; i++)
86 scopesSize[i]=1;
87 scopesSize[nbScope-1]=2;
88
89 Qcop p(nbScope, qtScopes, scopesSize);
90
91 // Defining the variable of the n first scopes ...
92 for (int i=0; i<nbDecisionVar; i++)
93 {
94 p.QIntVar(i, 0, 1);
95 IntVarArgs b(i+1);
96 for (int plop=0;plop<(i+1);plop++)
97 b[plop] = p.var(plop);
98 branch(*(p.space()),b,INT_VAR_SIZE_MIN(),INT_VAL_MIN());
99 p.nextScope();
100 }
101
102 // Declaring last scope variables ...
103
104 p.QIntVar(nbDecisionVar, 0, 1);
105 p.QIntVar(nbDecisionVar+1, 0, boardSize*boardSize);
106 IntVarArgs b(nbDecisionVar+2);
107 for (int plop=0;plop<(nbDecisionVar+2);plop++)
108 b[plop] = p.var(plop);
109 branch(*(p.space()),b,INT_VAR_SIZE_MIN(),INT_VAL_MIN());
110
111 p.nextScope();
112 // Body
113
114 rel(*(p.space()), p.var(nbDecisionVar) == 1);
115
116 IntVarArgs X(nbDecisionVar);
117 for (int i=0; i<nbDecisionVar; i++)
118 X[i]=p.var(i);
119
120 linear(*(p.space()), access, X, IRT_EQ, p.var(nbDecisionVar+1));
121 // MiniModel::LinRel R(E, IRT_EQ, MiniModel::LinExpr(p.var(nbDecisionVar+1)));
122 element(*(p.space()), board, p.var(nbDecisionVar+1), p.var(nbDecisionVar));
123
124 // Note : declaring a brancher for the goal is not mandatory, as the goal will be tested only when all variables are assigned.
125
126 // When every variables and constraints have been declared, the makeStructure method
127 // must be called in order to lead the problem ready for solving.
128 p.makeStructure();
129
130 // So, we build a quantified solver for our problem p, using the heuristic we just created.
131 QCSP_Solver solver(&p);
132
133 unsigned long int nodes=0;
134
135 // then we solve the problem. Nodes and Steps will contain the number of nodes encountered and
136 // of propagation steps achieved during the solving.
137 Strategy outcome = solver.solve(nodes);
138
139 cout << " outcome: " << ( outcome.isFalse()? "FALSE" : "TRUE") << endl;
140 cout << " nodes visited: " << nodes << endl;
141
142}