[LeetCode] 52. N-QueensII_Hard tag: DFS, backtracking

The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle.

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:

Input: 4
Output: [
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.

这个题目就是在的基础上将具体方案变成了方案总数，我们只需要返回len(ans)即可。（同时还可以将drawPuzzle这个函数省略掉）

时间复杂度 = 方案总数 * 构造方案所需时间

O( n ! * n)

Code:

class Solution:
    def nQueens2(self, n):
        if n < 1: return 0
        ans, nums = [], list(range(n))
        self.search(ans, [], nums)
        return len(ans)
    
    def search(self, ans, temp, nums):
        if not nums:
            ans.append(temp)
        else:
            if self.isValid(temp, nums[i]):
                self.search(ans, temp + [nums[i]], nums[:i] + nums[i + 1:])
    
    def isValid(self, temp, col):    
        row = len(temp)
        for r, c in enumerate(temp):
            if r + c == row + col or r - c == row - col:
                return False
        return True