52-n-queens-ii

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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 the number of distinct solutions to the n-queens puzzle.

 

Example 1:

Input: n = 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown.

Example 2:

Input: n = 1
Output: 1

 

Constraints:

• 1 <= n <= 9

Solution(Python)

class Solution:
    def totalNQueens(self, n: int) -> int:
        cnt = 0
        for sol in self.nqueens(n, 0, [], [], []):
            cnt += 1
        return cnt

    def nqueens(self, n, i, collkup, ldlkup, rdlkup):
        if i < n:
            for j in range(n):
                if j not in collkup and i + j not in ldlkup and i - j not in rdlkup:
                    yield from self.nqueens(
                        n, i + 1, collkup + [j], ldlkup +
                        [i + j], rdlkup + [i - j]
                    )

        else:
            yield collkup