tput This exercise uses sub-algorithms. Trace it for when input value is 6 and complete the trace tables. Also note that there are two variables name num, one in the main algorithm and another in the sub-algorithm. They are not related. Assume input is a positive integer. Write pre- post-conditions for each of these algorithms (the main one and the sub-algorithm). Note that the prime sub-algorithm is similar to the algorithm in Ex 1) but instead of reading input and producing outputs, it has a parameter num, and it returns the result. Also note that the =true is in gray color, which means it can be ignored. Note that since the sub-program is called several times, it's better that you use separate trace tables, one for each call, as shown below. num i←2 start i←i + 1 i T prime(i) = true T i≤ num end F prime(num) start flag ← true d-2 flag = true and d≤ num/2 T num mod d=0 LT flag ←false d

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Question 1 Suppose a large group of people in a room were all born in the same year. Consider the following three algorithms, which are each intended to identify the people in the room who have the earliest birthday based on just the month and day. For example, a person born on February 10 is considered to have an earlier birthday than a person born on March 5. Which of the three algorithms will identify the correct people? I. All the people in the room stand up. All standing people form pairs where possible, leaving at most one person not part of a pair. For each pair, the person with the earlier birthday remains standing, while the other person in the pair sits down. If there is a tie, both people sit down. Any individual not part of a pair remains standing. Continue doing this until only one person remains standing. That person has the earliest birthday. II. All the people in the room stand up. All standing people form pairs with another standing person that they have not previously…

Determine the expected case running time of the algorithm. Fully justify your solution. Determine the best case running time of the algorithm and state what condition must be true forit to occur. No justification is needed! Determine the worst case running time of the algorithm and state what condition must be true forit to occur. No justification is needed!

Algorithm

A binary searching algorithm has logarithmic ?(log?) performance. It takes a second to find an item in a list of 10,000 entries. How long do you expect it to take to find an item in a list of 50,000,000 entries? How did you arrive at your answer?

Construct a trace table to trace the action of the algorithm below for the input variables given. a := 53, d := 11 r:= a, q := 0 while (r 2 d) r:=r- d 9 := q + 1 end while iteration 1 2 3 a 53 d 11 53

Analysis of Algorithm: The number of operations executed by algorithms A and B is 40n2 and 2n3, respectively. Determine a n0 such that A is better than B for n >= n0

No plagarism please! Correct and detailed answer will be Upvoted else downvoted. Thank you!