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 &row, int &col)
{
for (row =
0; row < N; row++)
for (col =
0; col < N; col++)
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 row, int 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 col, int 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 boxStartRow, int boxStartCol, int 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 row, int col, int num)
{
return !UsedInRow(grid, row, num)
&& !UsedInCol(grid, col, num)
&&
!UsedInBox(grid, row - 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: