POJ-2676 Sudoku （DFS）

Sudoku is a very simple task. A square table with 9 rows and 9 columns is divided to 9 smaller squares 3x3 as shown on the Figure. In some of the cells are written decimal digits from 1 to 9. The other cells are empty. The goal is to fill the empty cells with decimal digits from 1 to 9, one digit per cell, in such way that in each row, in each column and in each marked 3x3 subsquare, all the digits from 1 to 9 to appear. Write a program to solve a given Sudoku-task.

Input

The input data will start with the number of the test cases. For each test case, 9 lines follow, corresponding to the rows of the table. On each line a string of exactly 9 decimal digits is given, corresponding to the cells in this line. If a cell is empty it is represented by 0.

Output

For each test case your program should print the solution in the same format as the input data. The empty cells have to be filled according to the rules. If solutions is not unique, then the program may print any one of them.

Sample Input

Sample Output

143628579
572139468
986754231
391542786
468917352
725863914
237481695
619275843
854396127



题目分析：数独题。就这道数独题而言仅仅DFS是可以AC的。先建立一棵搜索树，然后就搜！


代码如下：

 1 # include<iostream>
 2 # include<cstdio>
 3 # include<cstring>
 4 # include<algorithm>
 5 using namespace std;
 6 char p[12][12];
 7 int cnt,a[12][12];
 8 struct Position
 9 {
10     int x,y;
11     Position(){}
12     Position(int a,int b):x(a),y(b){}
13     bool operator < (const Position &a) const {
14         if(x==a.x)
15             return y<a.y;
16         return x<a.x;
17     }
18 };
19 bool yy;
20 Position pos[100];
21 bool ok(int x,int y,int m)
22 {
23     for(int k=1;k<=9;++k){
24         if(a[x][k]==m||a[k][y]==m)
25             return false;
26     }
27     int it=x,jt=y;
28     while(it%3!=1)
29         --it;
30     while(jt%3!=1)
31         --jt;
32     for(int i=it;i<=it+2;++i)
33         for(int j=jt;j<=jt+2;++j)
34             if(a[i][j]==m)
35                 return false;
36     return true;
37 }
38 void dfs(int p)
39 {
40     if(yy)
41         return ;
42     if(p==cnt){
43         for(int i=1;i<=9;++i){
44             for(int j=1;j<=9;++j)
45                 printf("%d",a[i][j]);
46             printf("
");
47         }
48         yy=true;
49         return ;
50     }
51     int x=pos[p].x,y=pos[p].y;
52     for(int i=1;i<=9;++i){
53         if(ok(x,y,i)){
54             a[x][y]=i;
55             dfs(p+1);
56             a[x][y]=0;  ///注意要将这个位置重新置为0，否则影响接下来的搜索过程。
57         }
58         if(yy)
59             return ;
60     }
61 }
62 int main()
63 {
64     int T;
65     scanf("%d",&T);
66     while(T--)
67     {
68         cnt=0;
69         for(int i=1;i<=9;++i){
70             scanf("%s",p[i]+1);
71             for(int j=1;j<=9;++j){
72                 a[i][j]=p[i][j]-'0';
73                 if(a[i][j]==0){
74                     pos[cnt++]=Position(i,j);
75                 }
76             }
77         }
78         sort(pos,pos+cnt);
79         yy=false;
80         dfs(0);
81     }
82     return 0;
83 }

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