Sudoku

出处： http://acm.hnu.cn:8080/online/?action=problem&type=show&id=11203&courseid=0

Sudoku

Time Limit: 1000ms, Special Time Limit:2500ms, Memory Limit:32768KB

Total submit users: 10, Accepted users: 10

Problem 11203 : Special judge

Problem description

A Sudoku puzzle, once solved, is a 9x9 grid of digits organized as a 3x3 grid of smaller 3x3 units. Each of the nine rows must contain every positive digits exactly once, as do each column and also each 3x3 unit. The puzzle is to start from a partially filled 9x9 grid and to fill in the remaining cells using only logic. The puzzle maker usually makes sure that the solution will be unique and that it can be reached using deduction only, without guessing.

This number placing game is gaining popularity in the west, and every second newspaper publishes weekly instances of the puzzle. Somewhere at the head of one such newspaper, someone decided that buying individual instances from a puzzle maker would be too expansive, and instead decided to steal puzzles from other newspapers and also to print randomly generated Sudoku-like grids.

One week later, his assistant gets stuck with the job of printing the solution to the Sudoku puzzles his boss previously published. Unfortunately, his boss doesn’t have those solutions, the randomly generated problems don’t have any solution, and he doesn’t even remember which is which. In despair, the assistant calls for your help.

Input

The first line of the input will contain the number of test cases. Each test case will consist of a 9 by 9 grid of characters, where each character will either be ‘?’ or a digit between 1 and 9 inclusively.

Output

For each test case, you must print back the grid to the standard input, replacing each question mark with an appropriate digit to solve the Sudoku. If a test case does not allow any solution, output ”impossible” instead of a completed grid. If a test case do allow a solution, you can assume that the solution will be unique, and that theoretically it could be reached without guessing.

Test cases are separated by “---” both in the input and in the output.

Sample Input

3
            ??4??9??8
            ?3??5??1?
            7??4??2??
            3??8??1??
            ?5?????9?
            ??6??1??2
            ??8??3??1
            ?2??4??5?
            6??1??7??
            ---
            ??4??9??8
            ?3??5??1?
            7??4??2??
            3??8??1??
            ?5?????9?
            ??6??1??2
            ??8??3??1
            62??4??5?
            6??1??7??
            ---
            3?1????76
            7??9?????
            2?5?3????
            ?????64?1
            ???2?1???
            1?25?????
            ????8?9?3
            ?????9??4
            51????7?8

Sample Output

  1 #include < iostream >
  2
  3 using namespace std;
  4
  5 bool x[ 9 ][ 10 ];
  6 bool y[ 9 ][ 10 ];
  7 bool z[ 9 ][ 10 ];
  8 int   result[ 9 ][ 9 ];
  9 int   num = 0 ;
10
11
12 int GetID( int x, int y )
13 {
14      if ( x < 3 && y < 3 )
15      return 0 ;
16      else if ( x < 3 && y >= 3 && y < 6 )
17      return 1 ;
18      else if ( x < 3 && y >= 6 && y < 9 )
19      return 2 ;
20      else if ( x >= 3 && x < 6 && y < 3 )
21      return 3 ;
22      else if ( x >= 3 && x < 6 && y >= 3 && y < 6 )
23      return 4 ;
24      else if ( x >= 3 && x < 6 && y >= 6 && y < 9 )
25      return 5 ;
26      else if ( x >= 6 && x < 9 && y < 3 )
27      return 6 ;
28      else if ( x >= 6 && x < 9 && y >= 3 && y < 6 )
29      return 7 ;
30      else if ( x >= 6 && x < 9 && y >= 6 && y < 9 )
31      return 8 ;
32 }
33
34
35 void Print()
36 {
37      for ( int i = 0 ; i < 9 ; ++ i )
38      {
39          for ( int j = 0 ; j < 9 ; ++ j )
40              printf( " %d " ,result[i][j] );
41
42          if ( i < 8 ) printf( " \n " );
43     }
44 }
45
46
47 bool GetXY( int & xx, int & yy )
48 {
49      for ( int i = 0 ; i < 9 ; i ++ )
50      {
51          for ( int j = 0 ; j < 9 ; j ++ )
52          if ( result[i][j] == 0 )
53          {
54             xx = i;
55             yy = j;
56
57              return true ;
58         }
59     }
60
61      return false ;
62 }
63
64
65 void Try( int xx, int yy )
66 {
67      for ( int i = 1 ; i <= 9 ; ++ i )
68      {
69          if ( ! x[xx][i] && ! y[yy][i] && ! z[ GetID(xx,yy) ][i] )
70          {
71              int a, b;
72
73             result[xx][yy] = i;
74
75             x[xx][i] = true ;
76             y[yy][i] = true ;
77             z[ GetID(xx,yy) ][i] = true ;
78
79              if ( ! GetXY( a, b ) )
80              {
81                 Print();
82                 num = 1 ;
83                  return ;
84             }
85
86             Try( a, b );
87             result[xx][yy] = 0 ;
88
89             x[xx][i] = false ;
90             y[yy][i] = false ;
91             z[ GetID(xx,yy) ][i] = false ;
92         }
93     }
94 }
95
96
97
98 int main()
99 {
100      int n;
101     scanf( " %d " , & n);
102      char aaa[ 10 ];
103
104      for ( int mm = 0 ; mm < n; mm ++ )
105      {
106          char graph[ 9 ][ 10 ];
107         num = 0 ;
108
109         memset( x, false , sizeof (x) );
110         memset( y, false , sizeof (y) );
111         memset( z, false , sizeof (z) );
112         memset( result, 0 , sizeof ( result ) );
113
114          for ( int i = 0 ; i < 9 ; ++ i )
115              scanf( " %s " , graph[i] );
116
117          for ( int i = 0 ; i < 9 ; ++ i )
118          {
119              for ( int j = 0 ; j < 9 ; ++ j )
120              if ( graph[i][j] != ' ? ' )
121              {
122                  int t = graph[i][j] - ' 0 ' ;
123                 result[i][j] = t;
124
125                 x[i][t] = true ;
126                 y[j][t] = true ;
127                 z[ GetID( i, j ) ][t] = true ;
128             }
129         }
130
131          int x, y;
132
133         GetXY( x, y );
134         Try( x, y );
135
136          if ( mm < n - 1 )
137          {
138              printf( " \n---\n " );
139              scanf( " %s " ,aaa);
140         }
141
142          if ( num == 0 )
143              printf( " impossible " );
144     }
145
146      return 0 ;
147 }
148
149

Sudoku

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