Sunday, 10 September 2017

A Sudoku Problem Solver using C++

This C++ program demonstrates the Sudoku problem solver using Backtracking Method. We basically check that the same number is not present in current row, current column and current 3 x 3 sub grid. 

After checking for safety, we assign the number and recursively check whether this assignment leads to a solution or not. If the assignment does not lead to a solution, then we try next number for current empty cell and if none of number lead to solution we return false.

Source Code:

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
using namespace std;
#define UNASSIGNED 0
#define N 9

bool FindUnassignedLocation(int grid[N][N], int &row, int &col);
bool isSafe(int grid[N][N], int row, int col, int num);

/* assign values to all unassigned locations for Sudoku solution
*/
bool SolveSudoku(int grid[N][N])
{
       int row, col;
       if (!FindUnassignedLocation(grid, row, col))
              return true;
       for (int num = 1; num <= 9; num++)
       {
              if (isSafe(grid, row, col, num))
              {
                     grid[row][col] = num;
                     if (SolveSudoku(grid))
                           return true;
                     grid[row][col] = UNASSIGNED;
              }
       }
       return false;
}

/* Searches the grid to find an entry that is still unassigned. */
bool FindUnassignedLocation(int grid[N][N], int &rowint &col)
{
       for (row = 0; row < Nrow++)
              for (col = 0; col < Ncol++)
                     if (grid[row][col] == UNASSIGNED)
                           return true;
       return false;
}

/* Returns whether any assigned entry n the specified row matches
the given number. */
bool UsedInRow(int grid[N][N], int rowint num)
{
       for (int col = 0; col < N; col++)
              if (grid[row][col] == num)
                     return true;
       return false;
}

/* Returns whether any assigned entry in the specified column matches
the given number. */
bool UsedInCol(int grid[N][N], int colint num)
{
       for (int row = 0; row < N; row++)
              if (grid[row][col] == num)
                     return true;
       return false;
}

/* Returns whether any assigned entry within the specified 3x3 box matches
the given number. */
bool UsedInBox(int grid[N][N], int boxStartRowint boxStartColint num)
{
       for (int row = 0; row < 3; row++)
              for (int col = 0; col < 3; col++)
                     if (grid[row + boxStartRow][col + boxStartCol] == num)
                           return true;
       return false;
}

/* Returns whether it will be legal to assign num to the given row,col location.
*/
bool isSafe(int grid[N][N], int rowint colint num)
{
       return !UsedInRow(gridrownum) && !UsedInCol(gridcolnum) &&
              !UsedInBox(gridrow - row % 3, col - col % 3, num);
}

/* print grid  */
void printGrid(int grid[N][N])
{
       for (int row = 0; row < N; row++)
       {
              for (int col = 0; col < N; col++)
                     cout << grid[row][col] << "  ";
              cout << endl;
       }
}

/* Main */
int main()
{
       int grid[N][N] =
       {
              { 8, 0, 0, 0, 0, 0, 0, 0, 0 },
              { 0, 0, 3, 6, 0, 0, 0, 0, 0 },
              { 0, 7, 0, 0, 9, 0, 2, 0, 0 },
              { 0, 5, 0, 0, 0, 7, 0, 0, 0 },
              { 0, 0, 0, 0, 4, 5, 7, 0, 0 },
              { 0, 0, 0, 1, 0, 0, 0, 3, 0 },
              { 0, 0, 1, 0, 0, 0, 0, 6, 8 },
              { 0, 0, 8, 5, 0, 0, 0, 1, 0 },
              { 0, 9, 0, 0, 0, 0, 4, 0, 0 }
       };

       if (SolveSudoku(grid) == true)
              printGrid(grid);
       else
              cout << "No solution exists" << endl;
       getchar();
       return 0;
}

Output: