Study Plan For Algorithms - Part26

1. N 皇后
给定一个整数 n ，返回所有不同的 n 皇后问题 的解决方案，方案中 'Q' 和 '.' 分别代表了皇后和空位。

class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        def is_valid(board, row, col):
            for i in range(row):
                if board[i][col] == 'Q':
                    return False
                if col - (row - i) >= 0 and board[i][col - (row - i)] == 'Q':
                    return False
                if col + (row - i) < n and board[i][col + (row - i)] == 'Q':
                    return False
            return True

        def backtrack(board, row):
            if row == n:
                res.append([''.join(row) for row in board])
                return
            for col in range(n):
                if is_valid(board, row, col):
                    board[row][col] = 'Q'
                    backtrack(board, row + 1)
                    board[row][col] = '.'

        board = [['.' for _ in range(n)] for _ in range(n)]
        res = []
        backtrack(board, 0)
        return res

2. N 皇后 II
给定一个整数 n ，返回 n 皇后问题 不同的解决方案的数量。

class Solution:
    def totalNQueens(self, n: int) -> int:
        def is_valid(board, row, col):
            for i in range(row):
                if board[i][col] == 'Q':
                    return False
                if col - (row - i) >= 0 and board[i][col - (row - i)] == 'Q':
                    return False
                if col + (row - i) < n and board[i][col + (row - i)] == 'Q':
                    return False
            return True

        def backtrack(board, row):
            if row == n:
                return 1
            count = 0
            for col in range(n):
                if is_valid(board, row, col):
                    board[row][col] = 'Q'
                    count += backtrack(board, row + 1)
                    board[row][col] = '.'
            return count

        board = [['.' for _ in range(n)] for _ in range(n)]
        return backtrack(board, 0)