回溯 N-Queens

1. [52]N-Queens II

# 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 
#  
#  Related Topics 回溯 👍 441 👎 0


# leetcode submit region begin(Prohibit modification and deletion)
class Solution:
    def __init__(self):
        self.res = 0
        self.cols = set()
        self.right_down = set()
        self.left_down = set()

    def dfs(self, cur, n):
        if cur >= n:
            self.res += 1
        for i in range(n):
            if i + cur not in self.left_down and i - cur not in self.right_down and i not in self.cols:
                self.left_down.add(i + cur)
                self.right_down.add(i - cur)
                self.cols.add(i)
                self.dfs(cur + 1, n)
                self.left_down.remove(i + cur)
                self.right_down.remove(i - cur)
                self.cols.remove(i)

    def totalNQueens(self, n: int) -> int:
        self.dfs(0, n)
        return self.res

# leetcode submit region end(Prohibit modification and deletion)

if __name__ == '__main__':
    so = Solution()
    res = so.totalNQueens(4)
    print(res)

1.1 解题思路

• left-down 横纵坐标的求和为定值。
• right-down 横纵坐标相减为定值。