Solve 8 queenss problem in Python

Fellow coders, in this tutorial we are going to learn about 8 queens problem and write a python program to solve it with the help of backtracking.

What is the 8 queens problem?

The 8 queens problem is a problem in swhich we figure out a way to put 8 queens on an 8×8 chessboard in such a way that no queen should attack the other. For basic info about the queen in a chess game, you should know that a queen can move in any direction ( vertically, horizontally, and diagonally) and to any number of places. In the figure below you can see how to place 4 queens on a 4×4 chessboard.

Similarly, we have to place 8 queens on an 8×8 chessboard. We will use backtracking to solve this interesting problem(puzzle).

What is Backtracking?

Backtracking the solution of the problem depends on the previous steps taken. We take a step and then analyze it that whether it will give the correct answer or not? and if not, then we move back and change the previous step.

How to solve 8 queens problem in Python

# Taking number of queens as input from user
print ("Enter the number of queens")
N = int(input())

# here we create a chessboard
# NxN matrix with all elements set to 0
board = [[0]*N for _ in range(N)]

def attack(i, j):
    #checking vertically and horizontally
    for k in range(0,N):
        if board[i][k]==1 or board[k][j]==1:
            return True
    #checking diagonally
    for k in range(0,N):
        for l in range(0,N):
            if (k+l==i+j) or (k-l==i-j):
                if board[k][l]==1:
                    return True
    return False

def N_queens(n):
    if n==0:
        return True
    for i in range(0,N):
        for j in range(0,N):
            if (not(attack(i,j))) and (board[i][j]!=1):
                board[i][j] = 1
                if N_queens(n-1)==True:
                    return True
                board[i][j] = 0

    return False

N_queens(N)
for i in board:
    print (i)

Result:

Enter the number of queens
8

Output:

[1, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 1, 0, 0]
[0, 0, 1, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 1, 0]
[0, 1, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 1, 0, 0, 0, 0]

Also read: Using Stacks to solve Desert Crossing Problem in Python