1. (5 pts)What is the largest possible number of internal (key) nodes in a red-black tree with black-height k (measured from root)? What is the smallest possible number?

2. (5 pts) A team of biologists keeps information about DNA structures in a balanced binary search tree (i.e. AVL, red/black, etc) using as key the specific weight (an integer) of the structure. The biologists routinely ask questions of the type: "Are there any structures in the tree with specific weight between a and b (inclusive)?" and they hope to get an answer as soon as possible. Design an efficient algorithm that, given integers a and b, returns true if there exists a key x in the tree such that a<=x<=b, and false if no such key exists in the tree. Describe your algorithm in pseudocode. What is the time complexity of your algorithm?