answers with explaination . thank you 1. Suppose f(x) is a monotonically increas

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answers with explaination . thank you

1. Suppose f(x) is a monotonically increasing function. Which of the following approximates the summation? n+1 1+1 m-1 k-m m+1 k=m m-1 n+1 m nt k-m km m-1 2. Which of the following is solved heuristically by a greedy method? B. Finding the shortest paths from a designated source vertex in a sparse graph C. Minimum spanning tree D. 0/1 knapsack Which of the following is not true regarding dynamic programming? A. It is a form of exhaustive search B. It is a form of divide-and conquer 3. C. D. A cost function must be defined The backtrace may be based on recomputing the cost function 4. What is the definition of Hn? k=1 5. Which of the following functions is not im Q() O Type here to search

Explanation / Answer

Answer 1: definition of Hn

Given any sequence {an}

we have the following.

Therefore, by the definition option A is correct. m-1n-1f(x) <=k=m nf(k) <= m+1n+1f(x)

Answer 2:

Option A) Fractional knapsack

Explaination : Knapsack problems can be solved by heuristics in which a given set of items (each with quality and value) are grouped to have a maximum value while being below a certain quality limit. The heuristic algorithm for this problem is called the greedy approximation algorithm, which sorts the items based on the value per unit mass and adds the item with the highest v / m as long as there is still room left.

Answer 3:

Option A : It is a form of exhaustive search. This statement is not true about dynamic programming. Greedy approach is form of exhaustive search.

Answer 4:

Option A) (n)

EXplaination: In the average case analysis, we take all possible inputs and calculate the calculation time for all inputs. Add all calculated values and divide the total by the total number of inputs. We must predict the distribution of the case.

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