52. N-Queens II

Hard

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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

class Solution:
    def totalNQueens(self, n: int) -> int:
        col = set()
        posDia = set()
        negDia = set()
        board = [["."]*n for _ in range(n)]
        count = 0
        def backtrack(r):
            nonlocal count
            if r == n:
                count += 1
                return
            for c in range(n):
                if c in col or (r+c) in posDia or (r-c) in negDia:
                    continue
                col.add(c)
                posDia.add(r+c)
                negDia.add(r-c)
                backtrack(r+1)
                col.remove(c)
                posDia.remove(r+c)
                negDia.remove(r-c)
        backtrack(0)
        return count