N-Queen.cpp

/* C++ program to solve N Queen Problem using
backtracking */
#include<bits/stdc++.h>
using namespace std;
#define N 4
/* ld is an array where its indices indicate row-col+N-1
(N-1) is for shifting the difference to store negative
indices */
int ld[30] = { 0 };
/* rd is an array where its indices indicate row+col
and used to check whether a queen can be placed on
right diagonal or not*/
int rd[30] = { 0 };
/*column array where its indices indicates column and
used to check whether a queen can be placed in that
	row or not*/
int cl[30] = { 0 };
/* A utility function to print solution */
void printSolution(int board[N][N])
{
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < N; j++)
			cout<<" "<< board[i][j]<<" ";
		cout<<endl;
	}
}

/* A recursive utility function to solve N
Queen problem */
bool solveNQUtil(int board[N][N], int col)
{
	/* base case: If all queens are placed
	then return true */
	if (col >= N)
		return true;

	/* Consider this column and try placing
	this queen in all rows one by one */
	for (int i = 0; i < N; i++) {
		/* Check if the queen can be placed on
		board[i][col] */
		/* A check if a queen can be placed on
		board[row][col].We just need to check
		ld[row-col+n-1] and rd[row+coln] where
		ld and rd are for left and right
		diagonal respectively*/
		if ((ld[i - col + N - 1] != 1 && rd[i + col] != 1) && cl[i] != 1) {
			/* Place this queen in board[i][col] */
			board[i][col] = 1;
			ld[i - col + N - 1] = rd[i + col] = cl[i] = 1;

			/* recur to place rest of the queens */
			if (solveNQUtil(board, col + 1))
				return true;

			/* If placing queen in board[i][col]
			doesn't lead to a solution, then
			remove queen from board[i][col] */
			board[i][col] = 0; // BACKTRACK
			ld[i - col + N - 1] = rd[i + col] = cl[i] = 0;
		}
	}

	/* If the queen cannot be placed in any row in
		this column col then return false */
	return false;
}
/* This function solves the N Queen problem using
Backtracking. It mainly uses solveNQUtil() to
solve the problem. It returns false if queens
cannot be placed, otherwise, return true and
prints placement of queens in the form of 1s.
Please note that there may be more than one
solutions, this function prints one of the
feasible solutions.*/
bool solveNQ()
{
	int board[N][N] = { { 0, 0, 0, 0 },
						{ 0, 0, 0, 0 },
						{ 0, 0, 0, 0 },
						{ 0, 0, 0, 0 } };

	if (solveNQUtil(board, 0) == false) {
		cout<<"Solution does not exist";
		return false;
	}

	printSolution(board);
	return true;
}

// driver program to test above function
int main()
{
	solveNQ();
	return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)