[30 pts.] Question 3: Complexity of Songs You may be familiar with the children's song "Old MacDonald Had a Farm." The first verse is Old MacDonald had a farm, E-I-E-1-O. And on that farm he had a cow, E-I-E-1-O With a moo-moo here and a moo-moo there, Here a moo, there a moo Everywhere a moo-moo, Old MacDonald had a farm, E-I-E-1-O. In successive verses, more animals are added, and the middle refrain gets longer and longer. For example, the second verse is: Old MacDonald had a farm, E-I-E-1-O. And on that farm he had a pig, E-I-E-I-O. With an oink-oink here and an oink-oink there, Here an oink, there an oink Everywhere an oink-oink, With a moo-moo here and a moo-moo there, Here a moo, there a moo Everywhere a moo-moo, Old MacDonald had a farm, E-I-E-1-O. [20 pts.] Question 3a Now, suppose that we consider singing the song "Old MacDonald Had a Farm" to be an algorithm, and we count singing one word as an operation. Then, perform an exact analysis for this algorithm. That is, what is the exact number of words sung in N verses? Explain how you arrived at this expression. You may assume that all animal names and animal sounds used in the song are one word each. Further, you should count hyphenated words (such as E-I-E-I-O and moo-moo) as one word [10 pts.] Question 3b Given your analysis from question (3a), and again assuming that we treat each word sung as one operation, what is the order of magnitude for the "Old MacDonald" algorithm