Check Valid N-Queens Solution in Python

Suppose we have a n x n matrix represents a chess board. There are some 1s and 0s, where 1 represents a queen and 0 represents an empty cell. We have to check whether the board is valid solution to the N-Queen puzzle or not. As we know a board is a solution of valid N-queen solution where no two queens are attacking each other.

So, if the input is like

then the output will be True

To solve this, we will follow these steps:

• n := row count of matrix
• rows := a new set, cols := a new set, diags := a new set, rev_diags := a new set
• for i in range 0 to n, do
  • for j in range 0 to n, do
    • if matrix[i, j] is 1, then
      • insert i into rows
      • insert j into cols
      • insert (i - j) into diags
      • insert (i + j) into rev_diags
• return true when size of rows, size of cols, size of diags, size of rev_diags is same as n, otherwise false

Let us see the following implementation to get better understanding:

Example

Live Demo

class Solution:
   def solve(self, matrix):
      n = len(matrix)

      rows = set()
      cols = set()
      diags = set()
      rev_diags = set()

      for i in range(n):
         for j in range(n):
            if matrix[i][j]:
               rows.add(i)
               cols.add(j)
               diags.add(i - j)
               rev_diags.add(i + j)

      return len(rows) == len(cols) == len(diags) == len(rev_diags) == n

ob = Solution()
matrix = [
   [0, 0, 0, 1, 0],
   [0, 1, 0, 0, 0],
   [0, 0, 0, 0, 1],
   [0, 0, 1, 0, 0],
   [1, 0, 0, 0, 0]
]
print(ob.solve(matrix))

Input

matrix = [    
   [0, 0, 0, 1, 0],    
   [0, 1, 0, 0, 0],    
   [0, 0, 0, 0, 1],    
   [0, 0, 1, 0, 0],    
   [1, 0, 0, 0, 0]
]

Output

True