Problem 1, (20 p orithm, the most important measures are the average and time: A(n) and B(n). There is no need to pay attention to true alse e running t-case running time W[n) because that the worst case does not happen very Suppose you have a computer that requires 1 minute to solve problem instances of size n than the old one. Assume that T(nyen), the largest problem instance size that can be solved in the new computer within 1 minute is 10 100. Suppose you buy a new computer that runs 1000 times faster false true Given TUn), if T(n) E o(n') then it is always true that Se Tn)e one true false rray of presorted integers represents a worst-case scenario for q hen using the first item as the pivot. e Divide and conquer is usualily implemented with recursive method that soes true alse true false may also be solved ru als always produce optimal solution, its optimality streFalse ) Floyd's algorithm is a greedy algorithm that can be used to find the minimumals true false he problem by solving the sub-problems programming method is efficient t solution to problems where nstances are related imi lar to shortest path problem, the longest path problem ng Dynamic programming approach. formally proved. nning h) Greedy algorithms do not tree in a weighted directed graph. D Mergesort algorithm is an example of divide and conquer algorithm. Problem 2. (10 points) Deide the complexity category of the following running time functions with Big- O notations (using the lowest upper bound). Note that log n is a shorthand notation for log, n. Ranking these functions by growth rate in increasing order ("1 is the lowest growth rate, use the same number for the functions with the same growth rate). Rankin Big-O notation T n) n+1024"logn F1 F2 5r'+100n log(n) F4 100nlogn+ n'logn F61024 2 n 5+1024n log'n F9-+ 1024n"login F8 3+8n log n F10 100 logn