Lets say you have graph with same weighted bidirectional edges.
A <-> B <-> C <-> D <-> E
|                       |
|                       |
*---------F-------------*

Input is path between 2 nodes. eg You can travel from A to E with path A->B->C->D->E.
Compressed path of given path is ans so that your input path remains same ie you must travel along given path only but you can skip few nodes in representation.
case 1
eg. A -> C -> E
For going from A to C path is A -> B -> C and from C to E is C -> D -> E.

case 2
but A -> E is invalid because you can go from A to E with path A -> F -> E 

case 3
A -> D -> E  is also invalid because A to D can be A -> F -> E -> D and then from D to E with  D -> E which is now different from input path.

You have been provided with function which takes input as 2 nodes and returns shortest possible path.
You can assume it works fine and returns optimal answer.

Given input path find its most optimal valid compressed version.