Rabbit Jerry has n events added to his calendar. Given a new event e, he needs to find out whether e conflicts with any of these n events. Each event ei is defined by its start time and finish time [si, fi], inclusive, where si fi. Jerry wants conflict check to be faster than linear time. Assume the following C struct for events. struct Event { int start; int finish; }; (1) [5 pts] To make conflict check faster than linear time, Jerry uses an interval tree to maintain the list of n events. Please briefly describe the interval tree. Also define the C struct for the tree node. Interval tree: It is a balanced BST (i.e., RBT) where each node uses the start time of an interval as the key. In addition to the interval info, each node stores max finish time of all intervals stored on the subtree rooted at this node. struct Node { //fill in the data members here Event ev; int max_time; Node* left; Node* right; }; 4 (2) [10 pts] Based on the data structure described in (1), write C code to implement an algorithm that checks whether an event e conflicts with