Please help with Algorithm question:

Let X be a set of n intervals on the real line. A subset of intervals Y C X is called a tiling path if the intervals in Y cover the intervals in X, that is, any real value that is contained in some interval in X is also contained in some interval in Y. The size of a ling cover is just the number of intervals. Describe and analyze an algorithm to compute the smallest tiling path of X as quickly as possible. Assume that your input consists of two arrays Xi[1,...,n] and Xn[1,..,n representing the left and right endpoints of the intervals in X. If you use a greedy algorithm, you must prove that it is correct A set of intervals. The seven shaded intervals form a tiling path