Sudoku Problem using BackTracking in C++

This C++ Program demonstrates the Sudoku Problem using Backtracking.

Here is source code of the C++ Program to solve the Sudoku Problem using BackTracking. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

```
/*
```

 * C++ Program to Solve Sudoku Problem using BackTracking

```
 */
```
```
#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] = {{3, 0, 6, 5, 0, 8, 4, 0, 0},

                      {5, 2, 0, 0, 0, 0, 0, 0, 0},

                      {0, 8, 7, 0, 0, 0, 0, 3, 1},

                      {0, 0, 3, 0, 1, 0, 0, 8, 0},

                      {9, 0, 0, 8, 6, 3, 0, 0, 5},

                      {0, 5, 0, 0, 9, 0, 6, 0, 0},

                      {1, 3, 0, 0, 0, 0, 2, 5, 0},

                      {0, 0, 0, 0, 0, 0, 0, 7, 4},

                      {0, 0, 5, 2, 0, 6, 3, 0, 0}};

```
    if (SolveSudoku(grid) == true)
```
```
          printGrid(grid);
```
```
    else
```

        cout<<"No solution exists"<<endl;

```
    return 0;
```
```
}
```

$ g++ sudoku.cpp
$ a.out
 
3  1  6  5  7  8  4  9  2
5  2  9  1  3  4  7  6  8
4  8  7  6  2  9  5  3  1
2  6  3  4  1  5  9  8  7
9  7  4  8  6  3  1  2  5
8  5  1  7  9  2  6  4  3
1  3  8  9  4  7  2  5  6
6  9  2  3  5  1  8  7  4
7  4  5  2  8  6  3  1  9
 
------------------
(program exited with code: 1)
Press return to continue

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