The Hungry Caterpillar You are a caterpillar on a tree G. Your tree has n branch points (or vertices), where fruits are located. Since you live in a tree, these points are connected in a tree-like manner. Upon arriving at a branch point, you will either encounter two branches leading out from the point, or no branches at all. As a hungry caterpillar, youd like to start from your home v, visit k branch points to eat fruit (where 1 k n), then return to your home v. For two connected points i, j, it costs `(i, j) energy for you to travel from branch point i to branch point j. You may visit vertices or edges more than once, and you may travel forward or backward across each branch. Give an algorithm to find the shortest possible closed walk that visits k distinct branch points, from a start and end point v. A four-part algorithm is required for this problem.

I need to find an algorithm and answer it within

1. main idea 2. pseudo code 3. Correctness 4. Runtime.

I don't seem to understand this problem.