8 Queens algorithm using Backtracking technique.

 Algorithm NQueens(k, n)

{

 for i := 1 to n do

 {

 if Place(k, i) then

 {

 x[k]:=i;

 if (k = n) then write (x[l : n]);

 else NQueens(k + 1 , n) ;

 }

 }

}

Algorithm Place(k, i)

{

 for j := 1 to k — 1 do

 if ((x[j] =i)

 or (Abs (x[j] — i) = Abs(j — k)))

 then return false;

 return true;

}


Source Code:

def nqueens(k, n, x):

 for i in range(1, n+1):

 if place(k, i, x):

 x[k] = i

 if k == n:

 print_board(x)

 else:

 nqueens(k+1, n, x)

def place(k, i, x):

 for j in range(1, k):

 if x[j] == i or abs(x[j] - i) == abs(j - k):

 return False

 return True

def print_board(x):

 n = len(x)

 for i in range(n):

 row = ['Q' if x[i] == j+1 else '.' for j in range(n)]

 print(' '.join(row))

n = 8

x = [0] * (n+1)

nqueens(1, n, x)


output

1

5

8

6

3

7

2

4

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