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
Python3
class Solution:
def totalNQueens(self, n: int) -> int:
cols, diag1, diag2 = set(), set(), set()
def go(row):
if row == n: return 1
res = 0
for col in range(n):
if col not in cols and row - col not in diag1 and row + col not in diag2:
cols.add(col)
diag1.add(row - col)
diag2.add(row + col)
res += go(row + 1)
cols.remove(col)
diag1.remove(row - col)
diag2.remove(row + col)
return res
return go(0)