51. N-Queens

最新推荐文章于 2020-09-03 08:53:08 发布

niunc

最新推荐文章于 2020-09-03 08:53:08 发布

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分类专栏： LeetCode

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https://leetcode.com/problems/n-queens/description/

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.

class Solution(object):
    def isValid(self, board, row, col):
        if board[row][col] == 'Q':
            return False
        n = len(board)
        for i in range(n):
            if board[i][col] == 'Q':
                return False
            if board[row][i] == 'Q':
                return False
        i = 1
        while row + i < n or row - i >= 0 or col + i < n or col - i >= 0:
            if row + i < n and col + i < n and board[row + i][col + i] == 'Q':
                return False
            if row + i < n and col - i >= 0 and board[row + i][col - i] == 'Q':
                return False
            if row - i >= 0 and col + i < n and board[row - i][col + i] == 'Q':
                return False
            if row - i >= 0 and col - i >= 0 and board[row - i][col - i] == 'Q':
                return False
            i += 1
        return True

    def solveNQueens(self, n):
        """
        :type n: int
        :rtype: List[List[str]]
        """
        self.res = []
        board = [['.'] * n for _ in range(n)]
        self.solveBoard(board, 0)
        return self.res


    def solveBoard(self, board, col):
        n = len(board)
        if col == n:
            self.res.append([reduce(lambda a, b: a + b, row) for row in board])
            return
        for i in range(n):
            if self.isValid(board, i, col):
                board[i][col] = 'Q'
                self.solveBoard(board, col + 1)
                board[i][col] = '.'