# Valid Sudoku

Moderate
0/80
Average time to solve is 40m
Contributed by

## Problem statement

You have been given a 9 X 9 2D matrix 'MATRIX' with some cells filled with digits(1 - 9), and some empty cells (denoted by 0).

You need to find whether there exists a way to fill all the empty cells with some digit(1 - 9) such that the final matrix is a valid Sudoku solution.

A Sudoku solution must satisfy all the following conditions-

``````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, 3 x 3 sub-matrices of the matrix.
``````
Note
``````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.
``````
Detailed explanation ( Input/output format, Notes, Images )
Constraints:
``````1 <= 'T' <= 5
N = 9
0 <= MATRIX[i][j] <= 9

Where 'N' denotes the size of the given square matrix.

Time Limit: 1sec
``````
##### Sample Input 1:
``````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
``````
##### Sample Output 1:
``````yes
``````
##### Explanation of the Sample Input1:
``````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
``````
##### Sample Input 2:
``````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
``````
##### Sample Output 2:
``````no
``````
##### Explanation of the Sample Input2:
``````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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