Analysis of Algorithm - Part 1 of 3: recursive definition Given the following function f, written in pseudocode similar to C or Java: void f(int n) { if (n==0) print("hello") else if (n==1) print ("hellohello") else { f(n-2) print("hellohellohello") f(n-2) } } Define the sequence h n = the number of hellos printed by f(n). Give a recursive definition of h n . This definition must include: All the initial conditions needed to define this sequence (do not give more or fewer than needed) A recurrence relation as a function of some of the elements of the sequence that precede h n The values of n for which this recurrence relation applies Explain this recursive definition. This explanation must include: an explanation of the recurrence relation an explanation of how you decided how many initial conditions were needed for this recursive definition Note that the explanations are the most important part of this question. Do not simply give answers for your mathematical formulas. Explain your reasoning! You may find it useful to begin working on the next question at the same time as this question particularly if you are finding this question challenging.