051 N-Queens.py

'''
The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.



Given an integer n, return all distinct solutions to the n-queens puzzle.

Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space respectively.

For example,
There exist two distinct solutions to the 4-queens puzzle:

[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]
'''

class Solution(object):
    def solveNQueens(self, n):
        """
        :type n: int
        :rtype: List[List[str]]
        """
        self.col = [False] * n
        self.diag = [False] * (2 * n)
        self.anti_diag = [False] * (2 * n)
        self.result = []
        self.recursive(0, n, [])
        return self.result

    def recursive(self, row, n, column):
        if row == n:
            self.result.append(list(map(lambda x: '.' * x + 'Q' + '.' * (n - 1 - x), column)))
        else:
            for i in range(n):
                if not self.col[i] and not self.diag[row + i] and not self.anti_diag[n - i + row]:
                    self.col[i] = self.diag[row + i] = self.anti_diag[n - i + row] = True
                    self.recursive(row + 1, n, column + [i])
                    self.col[i] = self.diag[row + i] = self.anti_diag[n - i + row] = False


if __name__ == "__main__":
    print(Solution().solveNQueens(5))