Soduku Solver

Before solving this problem, it is recommended that you go through “valid sudoku” problem.

Check if the given board is valid Sudoku or not explanation with solution in CPP

This is a classic problem of backtracking with DFS.

The solution is very simple.

We have a DFS helper function, to check if the “num” from 1 to 9 which will not conflict with already present numbers. If it is valid, then again call the helper function recursively.

To check if the number that is placed is valid or not, we use “is_valid” function.

Once all the numbers are placed, we return “true”, else of there is no solution return “false”.

Solution in C++

/*
* File     : sudoku_solver.cpp
*/

#include<iostream>
#include<vector>

using namespace std;

bool isValid(vector<vector<char>>& board, int row, int col, int num)
{
   // check row
    for(int i=0; i<9; i++){
        if(board[i][col] == num+'0')
            return false;
    }

  // check row
    for(int j=0; j<9; j++)
    {
        if(board[row][j] == num+'0')
            return false;
    }
    
  // check block
    for(int i=(row/3)*3; i<(row/3)*3+3; i++)
    {
        for(int j=(col/3)*3; j<(col/3)*3+3; j++){
            if(board[i][j] == num+'0')
                return false;
        }
    }
    return true;
}


bool help(vector<vector<char>>& board, int row, int col)

{
    if(row == 9)
        return true;

    if(col == 9)
        return help(board, row+1, 0);

    if(board[row][col] != '.')
        return help(board, row, col+1);

    for(int num = 1; num<=9; num++)
    {
        if(isValid(board, row, col, num))
        {
            board[row][col] = num+'0';
            if(help(board, row, col+1))
                return true;
            board[row][col] = '.';
        }
    }
    return false;
}


void solveSudoku(vector<vector<char>>& board) 
{
    help(board, 0, 0);
}

int main() 
{ 
   vector<vector<char> > 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' } }; 
    solveSudoku(board);

    for (int i = 0; i < board.size(); i++)
    {
        for (int j = 0; j < board[0].size(); j++)
        {
            cout<< board[i][j]<<" ";
        }
        cout<<endl;
    }


    return 0; 
} 

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