N Queens Chess Problem Solution using C++

The N Queens Problem is the problem of placing N chess queens on an N×N chessboard so that no two queens threaten each other. Thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the N queens problem of placing N non-attacking queens on an N×N chessboard, for which solutions exist for all natural numbers N with the exception of N=2 and N=3.

In the code, backtracking method is used to solve the problem. A queen is placed in a column that is known not to cause conflict. If a column is not found the program returns to the last good state and then tries a different column by increments or decrements the column index.

//A C++ code to Solve N-Queen Chess problem

#include <iostream>

#include <cstdio>

#include <cstdlib>

#include <conio.h>

const unsigned int N = 8;

using namespace std;

// Print N Queen chess problem solution

void PrintNQSolution(bool board[N][N])

{

     for (int i = 0; i < N; i++)

     {

           for (int j = 0; j < N; j++)

                cout << board[i][j] << "  ";

           cout << endl;

     }

}

/* check if a queen can be placed on the board[row][col]*/

bool CheckSafe(bool board[N][N], int row, int col)

{

     int i, j;

     for (i = 0; i < col; i++)

     {

           if (board[row][i])

                return false;

     }

     for (i = row, j = col; i >= 0 && j >= 0; i--, j--)

     {

           if (board[i][j])

                return false;

     }

     for (i = row, j = col; j >= 0 && i < N; i++, j--)

     {

           if (board[i][j])

                return false;

     }

     return true;

}

/*solve N Queen problem */

bool SolveNQ(bool board[N][N], int col)

{

     if (col >= N)

           return true;

     for (int i = 0; i < N; i++)

     {

           if (CheckSafe(board, i, col))

           {

                board[i][col] = true;

                if (SolveNQ(board, col + 1) == true)

                     return true;

                board[i][col] = false;

           }

     }

     return false;

}

/* solves the N Queen problem using Backtracking and print the solution.*/

bool SolveAndPrintNQ()

{

     bool board[N][N] = { 0 };

     if (SolveNQ(board, 0) == false)

     {

           cout << "Solution does not exist" << endl;

           return false;

     }

     PrintNQSolution(board);

     return true;

}

int main()

{

     cout << "**** " << N << " Queens Problem Solution *****\n\n";

     SolveAndPrintNQ();

     _getch();

     return 0;

}

Output:

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 &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: