How to find out the dependency paths?

Question

For example, there are packages and their dependencies:

a -> b (a require b)
b -> c & d
x -> a
y -> x
z -> x
z -> x & y

Now, give c and z, there are two dependency paths:

z -> x -> a -> b -> c
z -> y -> x -> a -> b -> c

The question is how to find out the dependency paths between two specific Debian packages?

P.S. The idea behind is to draw the dependency graph for a given set of packages, include the intermediate ones missing in the chain.

Answer 1

Your overall problem might already be solved by using apt-cache dotty.

If you want to implement it yourself, use some graph algorithm to find a path. Or check the source code of apt-cache. ;-)