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.
Example 2:
Input: n = 1
Output: [["Q"]]
Explanation: There is only one way to place a single queen on a 1x1 board.
Examples
Example 1
Input: n = 4
Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
Explanation: There are exactly two distinct solutions for placing 4 queens on a 4x4 board without conflicts.
Example 2
Input: n = 1
Output: [["Q"]]
Explanation: A single queen on a 1x1 board is the only solution.
Constraints
- -1 <= n <= 9
Optimal Complexity
Time
O(n!)
Space
O(n^2)
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