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Backtracking
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Backtracking
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#include <iostream.h>
//Number of queens
int N;
//chessboard
int board[100][100];
//function to check if the cell is attacked or not
int is_attack(int i,int j)
{
int k,l;
//checking if there is a queen in row or column
for(k=0;k<N;k++)
{
if((board[i][k] == 1) || (board[k][j] == 1))
return 1;
}
//checking for diagonals
for(k=0;k<N;k++)
{
for(l=0;l<N;l++)
{
if(((k+l) == (i+j)) || ((k-l) == (i-j)))
{
if(board[k][l] == 1)
return 1;
}
}
}
return 0;
}
int N_queen(int n)
{
int i,j;
//if n is 0, solution found
if(n==0)
return 1;
for(i=0;i<N;i++)
{
for(j=0;j<N;j++)
{
//checking if we can place a queen here or not
//queen will not be placed if the place is being attacked
//or already occupied
if((!is_attack(i,j)) && (board[i][j]!=1))
{
board[i][j] = 1;
//recursion
//wether we can put the next queen with this arrangment or not
if(N_queen(n-1)==1)
{
return 1;
}
board[i][j] = 0;
}
}
}
return 0;
}
int main()
{
//taking the value of N
cout<<"Enter the value of N for NxN chessboard\n";
cin>>N;
int i,j;
//setting all elements to 0
for(i=0;i<N;i++)
{
for(j=0;j<N;j++)
{
board[i][j]=0;
}
}
//calling the function
N_queen(N);
//printing the matix
for(i=0;i<N;i++)
{
for(j=0;j<N;j++)
cout<<board[i][j]<<" ";
cout<<"\n";
}
}