n queens Algorithm
The eight queens puzzle is an example of the more general N queens problem of put 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.The eight queens puzzle is the problem of put eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution necessitates that no two queens share the same row, column, or diagonal. Chess composer Max Bezzel published the eight queens puzzle in 1848.Nauck also extended the puzzle to the N queens problem, with N queens on a chessboard of n×n squares. In 1874, S. Gunther proposed a method use determinants to find solutions.
#include <iostream>
#define N 4
using namespace std;
void printSolution(int board[N][N])
{
cout << "\n";
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
cout << "" << board[i][j];
cout << "\n";
}
}
bool isSafe(int board[N][N], int row, int col)
{
int i, j;
/* Check this row on left side */
for (i = 0; i < col; i++)
if (board[row][i])
return false;
/* Check upper diagonal on left side */
for (i = row, j = col; i >= 0 && j >= 0; i--, j--)
if (board[i][j])
return false;
/* Check lower diagonal on left side */
for (i = row, j = col; j >= 0 && i < N; i++, j--)
if (board[i][j])
return false;
return true;
}
void solveNQ(int board[N][N], int col)
{
if (col >= N)
{
printSolution(board);
return;
}
/* Consider this column and try placing
this queen in all rows one by one */
for (int i = 0; i < N; i++)
{
/* Check if queen can be placed on
board[i][col] */
if (isSafe(board, i, col))
{
/* Place this queen in board[i][col] */
// cout<<"\n"<<col<<"can place"<<i;
board[i][col] = 1;
/* recur to place rest of the queens */
solveNQ(board, col + 1);
board[i][col] = 0; // BACKTRACK
}
}
}
int main()
{
int board[N][N] = {{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0}};
solveNQ(board, 0);
return 0;
}
