The Catalan numbers are a sequence from combinatorics which count (among many other things) the total number of ways to parenthesize an expression. For our purposes, the most important feature of the Catalan numbers Cn are that they satisfy the recurrence n- with a base case of C(0) 1. Answer the following about developing algorithms to compute the Catalan numbers 1. Give a small example demonstrating why dynamic programming is useful for computing these numbers. 2. What implementation would you recommend for a data structure in a ynamic programming algorithm for the Catalan numbers! 3. Give pseudocode for a memoized dynamic programming algorithm for the Catalan numbers