51. N-Queens

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

Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.

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

Example 1:

Input: n = 4
Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above

Example 2:

Input: n = 1
Output: [["Q"]]

Constraints:

1 <= n <= 9

Solutions (Python)

1. Solution

class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        ret = []

        for ys in itertools.permutations(range(n)):
            board = [['.'] * n for _ in range(n)]
            for x, y in zip(range(n), ys):
                if any(board[x - i][y - i] == 'Q' for i in range(1, min(x, y) + 1)) or \
                        any(board[x - i][y + i] == 'Q' for i in range(1, min(x, n - y - 1) + 1)):
                    break
                board[x][y] = 'Q'
            else:
                ret.append([''.join(row) for row in board])

        return ret

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