## Sudoku Solver

Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

- Each of the digits
`1-9`

must occur exactly once in each row. - Each of the digits
`1-9`

must occur exactly once in each column. - Each of the digits
`1-9`

must occur exactly once in each of the 9`3x3`

sub-boxes of the grid.

The `'.'`

character indicates empty cells.

Example 1:

Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]] Output: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]] Explanation: The input board is shown above and the only valid solution is shown below:

Constraints:

`board.length == 9`

`board[i].length == 9`

`board[i][j]`

is a digit or`'.'`

.- It is guaranteed that the input board has only one solution.

### Solution To the Above Question

class Solution {

public:

//For checking if the input is Valid or not

bool isValid(vector<vector<char>>& board, int row, int col, char c){

int RowNum=(row/3)*3;

int ColNum=(col/3)*3;

for(int i=0; i<9; i++){

if((board[i][col]==c) || (board[row][i]==c) || (board[RowNum+i/3][ColNum+i%3]==c)) {

return false;

}

}

return true;

}

// For Solving the Sudoku

bool solve(vector<vector<char>>& board){

for(int i=0; i<9; i++){

for(int j=0; j<9; j++){

if(board[i][j]=='.'){

for(char c='1'; c<='9'; c++){

if(isValid(board, i, j, c)){

board[i][j]=c;

if(solve(board)){

return true;

}

else {

board[i][j]='.';

}

}

}

return false;

}

}

}

return true;

}

//Main Function

void solveSudoku(vector<vector<char>>& board) {

solve(board);

}

};

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