如何使用关系代数找到 MAX? [英] How can I find MAX with relational algebra?

问题描述

使用数据库，如何使用关系代数求 MAX?

Working with databases, how can I find MAX using relational algebra?

推荐答案

假设你有一个关系 A，有一个单一的属性 'a'(减少一个更复杂的关系，这是关系代数中的一个简单任务，我肯定你已经到了这一步)，所以现在你想在 A 中找到最大值.

Assuming you have a relation, A, with a single attribute, 'a' (reducing a more complex relation to this is a simple task in relational algebra, I'm sure you got this far), so now you want to find the maximum value in A.

一种方法是找到 A 与其自身的叉积，确保重命名 'a' 以便您的新关系具有具有不同名称的属性.例如:

One way to do it is to find the cross product of A with itself, be sure to rename 'a' so your new relation has attributes with distinct names. for example:

(将'a'重命名为'a1') X (将'a'重命名为'a2')

(rename 'a' as 'a1') X (rename 'a' as 'a2')

现在选择'a1' <'a2'，结果关系将具有除最大值之外的所有值.要获得最大值，只需找到原始关系之间的差异:

now select 'a1' < 'a2', the resulting relation will have all values except the maximum. To get the max simply find the difference between your original relation:

(A x A) - (select 'a1' < 'a2') ((rename 'a' as 'a1')(A) x (rename 'a' as 'a2')(A))

然后使用 project 运算符将其缩减为单列，正如 Tobi Lehman 在下面的评论中所建议的那样.

Then use the project operator to reduce down to a single column as Tobi Lehman suggests in the comment below.

用关系代数表示法写这个是(如果我没记错的话).注意最后的重命名(即 ρ)只是为了得到一个与原始关系同名的属性:

Writing this in relational algebra notation would be (if I remember correctly). Note the final rename (i.e. ρ) is just to end up with an attribute that has the same name as in the original relation:

ρ_a/a1(π_a1((A x A) - σ_{a1 (ρa1/a(A) x ρa2/a(A))))}

ρ_a/a1(π_a1((A x A) - σ_{a1 < a2} (ρ_a1/a(A) x ρ_a2/a(A))))

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