This is a question mostly in the Algorithm field for Engineers. Could someone help me with it?

1. [Recurrences, 28 points Give the tightest asymptotic bounds you can for the following recurrences and provide a short explanation for your solution. a. T(n) = Tin-1) + n3 b. T(n) = 3T(n/2) + n, c, T(n)-2T(n/2) + e. Tn)-12T(n/)+n log n f. T(n) = Tin-1) + 10 log n, (assume T(1) = const) T)2Tn/2)+n/log n Recurrences II, 20 points each of the following functions, provide: - A recurence T(n) that desecribes the worst-case runtime of the function in terms of n as provided (i e. without any optimizations) The tightest asymptotic upper and lower bounds you can find for Ton) a. int A(int n) f nt STAM-0 for (i-0: ikn: i+) for j 0:j:+ sum += i * j % 5: relurn s b. int Blint n) f if(n == n/2) return else rerurn 12 B(n/20): c. int C(int if(n==0) return 1 if (C(n/2) >= 5) return C(n/2) 5 else relurn 5 EC330 Applied Algorithms and Data Structures for Engineers, Spring 2018 d. int Dint n) nt sm0: eturn for (int i0:ini SM eturn sum Dn/2