Design algorithm for maximum sum problem using dynamic programming approach. For example, given the sequence 3, -5, 4, -3, 10, the output is 11 (4-3+10). Present your algorithm in pseudo code. Trace your algorithm and show how it works on a small example, show the step-by-step process and the final result. Analyze the time complexity of the algorithm using order notation.

Consider a system of three independent, periodic real-time tasks: T1= (4, 3), T2 = (12,7), and T3 = (8, 5). Construct the schedule for these tasks in the interval [0, 24) with q=1 on twoprocessors with PF. Note that there are many PFair algorithms, while PF is one of them. PF prioritize subtasks by deadlines, and break ties by inspecting future subtask deadlines. Also, if a currently-executing job ties with a newly- released job, then continue executing the currently-executing job; break any other ties by task ID (T1 = highest, T3 = lowest). a. Show all sub jobs’ releases and deadlines for (the first job of) each task. Note that q=1 so each sub job should have execution requirement of 1b. Show the PF schedule.c. Will this task set be schedulable with q=2? Please explain.

Find The Time Complexity and The Space Complexity

Consider the following functions as time complexities of some algorithms. (a) First write the worst-case runtime of each algorithm in Big-O notation. (b) Then arrange functions from low to high (Consider their Big-O notations as you arrange them; as n grows, the function that grows slower should come sooner than the one that grows faster). (c) Arbitrary, select TWO of arrangements in part (b) and for each one of them justify why you have chosen such an ordering for the corresponding function. Provide formal proof. For example if fl<=f2<= f3<= f4<=f5 you may choose to formally justify why (1) fl<=f2 and why (2) f4<=f5 . fI(n)=n², f2(n)=210 nlogn, f3(n)=3", f4(n)=n, f5(n)=1, f6(n)=5*logn, f7(n)= n", f8(n)=4 n*n, f9(n)=2log(n³)