51-n-queens

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Description

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

Solution(Python)

class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        res = []
        for solution in self.queens(n, 0, [], [], []):
            board = [
                "".join("Q" if i == j else "." for i in range(len(solution)))
                for j in solution
            ]
            res.append(board)
        return res

    def queens(self, n, i, a, b, c):
        if i < n:
            for j in range(n):
                if j not in a and i + j not in b and i - j not in c:
                    yield from self.queens(n, i + 1, a + [j], b + [i + j], c + [i - j])
        else:
            yield a