N 皇后
N-Queens
题目详情
问题：N 皇后
考察：递归、数组
来源：Citadel
链接：https://www.jointaro.com/interviews/questions/n-queens/
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
解析
思路：按行回溯放置皇后，用三组集合记录已占用列、主对角线和副对角线。每行只尝试不冲突的列，放满 n 行时输出棋盘。
复杂度：最坏指数级，递归深度 O(n)，输出规模另计。