123/Nqueen.java at main · after-the-end/123 · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
import java.util.*;

import com.microsoft.z3.*;

class Nqueen {
    public static void main(String[] args) {
        try {
            HashMap<String, String> cfg = new HashMap<String, String>();
            cfg.put("model", "true");
            Context ctx = new Context(cfg);
            Scanner scan = new Scanner(System.in);
            int n = 0;
            n = scan.nextInt();
            IntExpr[][] X = new IntExpr[n][];
            for (int i = 0; i < n; ++i) {
                X[i] = new IntExpr[n];
                for (int j = 0; j < n; ++j)
                    X[i][j] = (IntExpr) ctx.mkConst(
                            ctx.mkSymbol("x_" + (i + 1) + "_" + (j + 1)),
                            ctx.getIntSort());
            }

            Solver solver = ctx.mkSolver();

            int num = 0;
            BoolExpr[] loc_c = new BoolExpr[n];
            while (scan.hasNextInt()) {
                int coord_x = scan.nextInt(), coord_y = scan.nextInt();
                loc_c[num] = ctx.mkEq(X[coord_x - 1][coord_y - 1], ctx.mkInt(1));
                solver.add(loc_c[num]);
                ++num;
            }

            BoolExpr[][] cells_c = new BoolExpr[n][];
            for (int i = 0; i < n; ++i) {
                cells_c[i] = new BoolExpr[n];
                for (int j = 0; j < n; ++j) {
                    cells_c[i][j] = ctx.mkAnd(ctx.mkLe(ctx.mkInt(0), X[i][j]), ctx.mkLe(X[i][j], ctx.mkInt(1)));
                }
            }
            for (BoolExpr[] t : cells_c)
                solver.add(t);

            BoolExpr[] row_c = new BoolExpr[n];
            ArithExpr[] row_sum = new ArithExpr[n];
            for (int i = 0; i < n; ++i) {
                row_sum[i] = ctx.mkInt(0);
                for (int j = 0; j < n; ++j) {
                    row_sum[i] = ctx.mkAdd(row_sum[i], X[i][j]);
                }
                row_c[i] = ctx.mkEq(row_sum[i], ctx.mkInt(1));
            }
            solver.add(row_c);

            BoolExpr[] col_c = new BoolExpr[n];
            ArithExpr[] col_sum = new ArithExpr[n];
            for (int j = 0; j < n; ++j) {
                col_sum[j] = ctx.mkInt(0);
                for (int i = 0; i < n; ++i) {
                    col_sum[j] = ctx.mkAdd(col_sum[j], X[i][j]);
                }
                col_c[j] = ctx.mkEq(col_sum[j], ctx.mkInt(1));
            }
            solver.add(col_c);

            BoolExpr[] dia_r_c = new BoolExpr[2 * n - 1];
            ArithExpr[] dia_r_sum = new ArithExpr[2 * n - 1];
            for (int i = 0; i < 2 * n - 1; ++i) {
                dia_r_sum[i] = ctx.mkInt(0);
                if (i < n) {
                    int coord_x = 0, coord_y = i;
                    for (int j = 0; coord_y + j < n; ++j) {
                        dia_r_sum[i] = ctx.mkAdd(dia_r_sum[i], X[coord_x + j][coord_y + j]);
                    }
                } else {
                    int coord_x = i - n + 1, coord_y = 0;
                    for (int j = 0; coord_x + j < n; ++j) {
                        dia_r_sum[i] = ctx.mkAdd(dia_r_sum[i], X[coord_x + j][coord_y + j]);
                    }
                }
                dia_r_c[i] = ctx.mkLe(dia_r_sum[i], ctx.mkInt(1));
            }
            solver.add(dia_r_c);

            BoolExpr[] dia_l_c = new BoolExpr[2 * n - 1];
            ArithExpr[] dia_l_sum = new ArithExpr[2 * n - 1];
            for (int i = 0; i < 2 * n - 1; ++i) {
                dia_l_sum[i] = ctx.mkInt(0);
                if (i < n) {
                    int coord_x = 0, coord_y = i;
                    for (int j = 0; coord_y + j < n; ++j) {
                        dia_l_sum[i] = ctx.mkAdd(dia_l_sum[i], X[coord_x + j][coord_y + j]);
                    }
                } else {
                    int coord_x = i - n + 1, coord_y = 0;
                    for (int j = 0; coord_x + j < n; ++j) {
                        dia_l_sum[i] = ctx.mkAdd(dia_l_sum[i], X[coord_x + j][coord_y + j]);
                    }
                }
                dia_l_c[i] = ctx.mkLe(dia_l_sum[i], ctx.mkInt(1));
            }
            solver.add(dia_l_c);
            int ans = 0;
            if (solver.check() == Status.SATISFIABLE) {
                ++ans;
                Model m = solver.getModel();
                Expr[][] R = new Expr[n][n];
                for (int i = 0; i < n; ++i) {
                    for (int j = 0; j < n; ++j) {
                        R[i][j] = m.evaluate(X[i][j], false);
                    }
                }
                BoolExpr past_ans = ctx.mkTrue();
                for (int i = 0; i < n; ++i) {
                    for (int j = 0; j < n; ++j) {
                        past_ans = ctx.mkAnd(past_ans, ctx.mkEq(R[i][j], X[i][j]));
                    }
                }
                past_ans = ctx.mkNot(past_ans);
                solver.add(past_ans);
                while (solver.check() == Status.SATISFIABLE) {
                    ++ans;
                    m = solver.getModel();
                    R = new Expr[n][n];
                    for (int i = 0; i < n; ++i) {
                        for (int j = 0; j < n; ++j) {
                            R[i][j] = m.evaluate(X[i][j], false);
                        }
                    }
                    past_ans = ctx.mkTrue();
                    for (int i = 0; i < n; ++i) {
                        for (int j = 0; j < n; ++j) {
                            past_ans = ctx.mkAnd(past_ans, ctx.mkEq(R[i][j], X[i][j]));
                        }
                    }
                    past_ans = ctx.mkNot(past_ans);
                    solver.add(past_ans);
                }
                System.out.println("The number of solutions is: " + ans);
                System.out.println("N queen solution:");
                for (int i = 0; i < n; ++i) {
                    for (int j = 0; j < n; ++j) {
                        System.out.print(" " + R[i][j]);
                    }
                    System.out.println();
                }
            } else {
                System.out.println("No solution");
            }
            String str1 = scan.nextLine();
            ctx.close();
        } catch (Z3Exception e) {
            e.printStackTrace();
        }
    }
}