sql - 使用关系数据库解决密码算术难题

Question

假设你有一个密码算术难题:

发送+更多=金钱

目标是用数字 (0-9) 替换字母，以便进行加法运算。

我知道如何用数学方法解决这个问题，但我不确定如何使用关系数据库来解决这个问题。

如何设计架构来解决这个问题？

尝试解决此问题的 SQL 查询会是什么样子？

编辑:有一些限制:

1. 给定的字母应始终使用相同的数字。例如，如果你猜字母 E 是“5”，那么 E 在所有它出现的地方都应该得到值“5”发生。
2. 不同的字母应该有不同的数字，例如，您不能为两者分配“4”E 和 M。
3. 所有数字(单词)都不能有任何前导零

Answer 1

这回答了用户提出的其他问题。

SEND + MORE = MONEY，其中每个字符都有一个唯一的数字，并且没有单词以零开头。

select
    top 1
    S.num as S,
    E.num as E,
    N.num as N,
    D.num as D,
    M.num as M,
    O.num as O,
    R.num as R,
    Y.num as Y,
    (S.num * 1000 + E.num * 100 + N.num * 10 + D.num) as [SEND],
    (M.num * 1000 + O.num * 100 + R.num * 10 + E.num) as MORE,
    (S.num * 1000 + E.num * 100 + N.num * 10 + D.num) + (M.num * 1000 + O.num * 100 + R.num * 10 + E.num) as SEND_plus_MORE,
    (M.num * 10000 + O.num * 1000 + N.num * 100 + E.num * 10 + Y.num) as [MONEY]

from
    Digits as S
    join digits as E on E.num <> S.num
    join digits as N on N.num <> S.num and N.num <> E.num
    join digits as D on D.num <> S.num and D.num <> E.num and D.num <> N.num
    join digits as M on M.num <> S.num and M.num <> E.num and M.num <> N.num and M.num <> D.num
    join digits as O on O.num <> S.num and O.num <> E.num and O.num <> N.num and O.num <> D.num and O.num <> M.num
    join digits as R on R.num <> S.num and R.num <> E.num and R.num <> N.num and R.num <> D.num and R.num <> M.num and R.num <> O.num
    join digits as Y on Y.num <> S.num and Y.num <> E.num and Y.num <> N.num and Y.num <> D.num and Y.num <> M.num and Y.num <> O.num and Y.num <> R.num

where
    (S.num * 1000 + E.num * 100 + N.num * 10 + D.num)
    + (M.num * 1000 + O.num * 100 + R.num * 10 + E.num)
    = (M.num * 10000 + O.num * 1000 + N.num * 100 + E.num * 10 + Y.num)     
    and S.num <> 0 and M.num <> 0

我考虑过在 WHERE 子句中强制执行唯一数字，但我相信这最终会在检查 WHERE 子句之前处理太多排列。

由于我们只处理最多 10 位数字，因此出于速度考虑，我认为最好构建长 ON 子句。

这是没有疯狂 ON 子句的 FROM + WHERE 子句。这在我的服务器上运行速度慢很多。

from
    Digits as S
    cross join digits as E
    cross join digits as N
    cross join digits as D
    cross join digits as M
    cross join digits as O
    cross join digits as R
    cross join digits as Y

where
    (S.num * 1000 + E.num * 100 + N.num * 10 + D.num)
    + (M.num * 1000 + O.num * 100 + R.num * 10 + E.num)
    = (M.num * 10000 + O.num * 1000 + N.num * 100 + E.num * 10 + Y.num)     
    and S.num <> 0 and M.num <> 0

        and (select max(B.Count) from   
                (select COUNT(*) as Count from 
                    (select S.num, 's' as letter   -- the letters are included to make sure the unions do not merge equivalent rows
                    UNION select E.num, 'e'
                    UNION select N.num, 'n'
                    UNION select D.num, 'd'
                    UNION select M.num, 'm'
                    UNION select O.num, 'o'
                    UNION select R.num, 'r'
                    UNION select Y.num, 'y') as A
                    group by A.num
                ) as B
             ) = 1