What is N Queen Problem ?

1) Start from the leftmost column
2) If all queens are placed
    return true
3) Try all rows in the current column.  Do following for every tried row.
    a) If the queen can be placed safely in this row then mark this [row, 
        column] as part of the solution and recursively check if placing queen here leads to a solution.
    b) If placing the queen in [row, column] leads to a solution then return 
        true.
    c) If placing queen does not lead to a solution then umark this [row, 
        column] (Backtrack) and go to step (a) to try other rows.
4) If all rows have been tried and nothing worked, return false to trigger 
    backtracking.

/* C/C++ program to solve N Queen Problem using 
backtracking */
#define N 4 
#include<stdio.h> 
#include<stdbool.h> 

/* 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++) 
			printf(" %d ", board[i][j]); 
		printf("\n"); 
	} 
} 

/* A utility function to check if a queen can be placed on board[row][col]. 
Note that this function is called when "col" queens are already placed in columns
 from 0 to col -1. So we need to check only left side for attacking queens */
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; 
} 

/* 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] */
		if ( isSafe(board, i, col) ) 
		{ 
			/* Place this queen in board[i][col] */
			board[i][col] = 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 
		} 
	} 

	/* If the queen cannot be placed in any row in 
		this colum 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 ) 
	{ 
	printf("Solution does not exist"); 
	return false; 
	} 

	printSolution(board); 
	return true; 
} 

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

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