1. As we are walking through Scott Carpenter park one cold, wintry day, we stop to drink hot chocolate and observe some children building an igloo out of snow. These children are awesome, however, and as part of their igloo-building algorithm, they multiply two matrices of size n x n and then binary search through the result, along with a few other operations. The Force is strong in these younglings! In any event, the complexity of their resulting algorithm is given by the function f: (n)-8n3+12n* log (n2) -n log n (a) Find a tight big-O bound of the form g(n)for f, for some natural number p. What are the constants C and k from the big-O definition? (b) Find a tight big-S2 bound of the form g(n) for f, for some natumber p. What are the constants C and k from the big- definition? (c) Can we conclude that f is big-(np) for any natural number p