How does hierarchy dimension reduction work in Kylin

Question

Following picture is illustrating the effect of hierarchy dimension reduction.

It reduces the number of cuboid from 2^N to N+1

With this dimension reduction, I wonder how following queries could give correct answer?

1. select B, count(1) from X group by B
2. select C, count(1) from X group by C
3. select B,C,count(1) from X group by B,C

Answer 1

Looks I found the answer: => means equal to

group by A,B => group by A,B
group by B,C => group by C => group by A,B,C
group by A,C => group by C => group by A,B,C
group by A => group by A
group by B => group by A,B
group by C => group by A,B,C
group by B,C => group by A,B,C