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Problem

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Solution

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25

Difficulty: MEDIUM

Avg. time to solve

40 min

Success Rate

60%

Problem Statement

Suggest Edit

```
1. Each of the digits 1-9 must occur exactly once in each row.
2. Each of the digits 1-9 must occur exactly once in each column.
3. Each of the digits 1-9 must occur exactly once in each of the 9, 3x3 sub-matrices of the matrix.
```

```
1. There will always be a cell in the matrix which is empty.
2. The given initial matrix will always be consistent according to the rules mentioned in the problem statement.
```

```
The first line contains a single integer t - the number of test cases. The next 9t lines contains the description of each test case.
There will be 9 lines for each test case with each line containing 9 space separated digits, (0, if the cell is empty, digit(1-9) otherwise.
```

```
Print “yes”(without quotes), if there is way or “no” (without quotes) otherwise. Note the lowercase format of the output.
```

```
You do not need to print anything, it has already been taken care of. Just implement the given function.
```

```
1 <= T <= 5
N=9
0 <= Matrix[i][j] <= 9
Time Limit: 1sec
```

```
1
9 0 0 0 2 0 7 5 0
6 0 0 0 5 0 0 4 0
0 2 0 4 0 0 0 1 0
2 0 8 0 0 0 0 0 0
0 7 0 5 0 9 0 6 0
0 0 0 0 0 0 4 0 1
0 1 0 0 0 5 0 8 0
0 9 0 0 7 0 0 0 4
0 8 2 0 4 0 0 0 6
```

```
yes
```

```
One of the possible solutions is:
9 4 1 3 2 6 7 5 8
6 3 7 1 5 8 2 4 9
8 2 5 4 9 7 6 1 3
2 6 8 7 1 4 3 9 5
1 7 4 5 3 9 8 6 2
3 5 9 6 8 2 4 7 1
4 1 3 2 6 5 9 8 7
5 9 6 8 7 3 1 2 4
7 8 2 9 4 1 5 3 6
```

```
1
1 5 9 0 0 6 0 3 2
2 7 4 0 0 0 0 0 0
3 8 6 2 0 0 0 0 5
4 9 2 5 0 1 0 8 0
6 3 7 0 4 0 0 0 0
5 1 0 8 2 0 0 0 0
8 2 1 0 0 0 0 0 0
7 6 0 1 0 0 4 2 0
9 4 3 0 7 0 0 6 1
```

```
no
```

```
In the third column from the left, there are two empty cells out of which one has to be filled with ‘8’, but we can’t put 8 in any of those two cells.
```

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