面试题 08.12.八皇后

代码思路：用三个set标记当前位置所在的行、主、次对角线方向上是否合法。

class Solution(object):
    def solveNQueens(self, n):
        """
        :type n: int
        :rtype: List[List[str]]
        """
        # 返回值
        res = []
        # 皇后
        queens = [-1] * n
        # 列
        columns = set()
        # 主对角线方向
        dia1 = set()
        # 次对角线方向
        dia2 = set()
        self.helper(queens, columns, dia1, dia2, res, n, 0)
        return res

    def helper(self, queens, columns, dia1, dia2, res, n, row):
        if row == n:
            path = self.drawPath(queens, n)
            res.append(path)
        else:
            for i in range(n):
                # if columns[i]: continue
                # d1 = row - i
                # if dia1[d1]: continue
                # d2 = row + i
                # if dia2[d2]: continue
                if i in columns or row - i in dia1 or row + i in dia2:
                    continue
                queens[row] = i
                columns.add(i)
                dia1.add(row - i)
                dia2.add(row + i)
                # 递归
                self.helper(queens, columns, dia1, dia2, res, n, row + 1)
                # 回退
                columns.remove(i)
                dia1.remove(row - i)
                dia2.remove(row + i)

    def drawPath(self, queens, n):
        path = []
        row = ["."] * n
        for i in range(n):
            row[queens[i]] = "Q"
            path.append("".join(row))
            row[queens[i]] = "."
        return path