Analyse the below algorithm acc average-case efficiencies in terms асс Algo1(A[0..n-1], k) i=0 while i
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A: time complexity of the examples are shown below in step2.
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A: I would show the answer of first question only. Please post second question separately.
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- Determine the big-O worst-case runtime for each algorithm. for (k = 0; k < N; k++) for (i = 0; i < N; i++) { for (j = 0; j < N; j++) { if (Arr[i] < Arr[j] && Arr[i]<Arr[k]) { ++count } else { ++count } } }Conceptual Question: How do you find the Big Oh, Big Omega, and Big Theta of an Algorithm? What do each of them mean? Can you provide an example for solving for each with some algorithm? Like... (Java) for (i = 1; i < n; i++) { j = i; while ((j > 0) && (s[j] < s[j-1])) { temp = s[j]; s[j] = s[j-1]; s[j-1] = temp; } j--; } And what about if Algorithm is recurssive like... public int runBinarySearchRecursively(int[] sortedArray, int key, int low, int high) { int middle = (low + high) / 2; if (high < low) { return -1; } if (key == sortedArray[middle]) { return middle; } else if (key < sortedArray[middle]) { return runBinarySearchRecursively(sortedArray, key, low, middle - 1); } else { return runBinarySearchRecursively(sortedArray, key, middle + 1, high); } }Give a Θ(lg n) algorithm that computes the remainder when xn is divided byp. For simplicity, you may assume that n is a power of 2. That is, n = 2k forsome positive integer k.
- Give an example of an algorithm that is O(1), an algorithm that is O(n) and an algorithm that is O(n2). Discuss the difference between them.Please explain What is the big-O complexity of the following algorithm? void mystery(int* a, int n){ for (int i = 0; i < n; i++) { for (int j = 0; j < n - 1; j++) { if (a[j] > a[j + 1]) { swap(&a[j], &a[j + 1]); } } }} Group of answer choices a. O(n*n) b. (O(n*log(n)) c. O(n) d. O(n!)Hello, this algorithm does not seem O(N) to me. Can an algorithm be written O(N) in this problem?
- When the order of growth of the running time of an algorithm is N log N, the doubling test will lead to the hypothesis that the running time is ~ a N for a constant a. Isn’tthat a problem?Give an O(n^2)-time algorithm to nd the longest monotonically increasing subsequence of a sequence of n numbers.Illustrate your algorithm on the sequence:8, 3, 7, 5, 9, 3, 4, 1, 9, 2, 6.The time complexity equation of merger-sort is T(n) = 2* T(n/2) + n, where T(1) = C and C is a constant. Solve this equation by giving detailed steps. If you have an equation like the following T(n) = 3* T(n/3) + n, where T(1)=T(2)=C, what would be T(n)?
- Consider a divide-and-conquer algorithm that calculates the sum of all elements in a set of n numbers by dividing the set into two sets of n/2 numbers each, finding the sum of each of the two subsets recursively, and then adding the result. What is the recurrence relation for the number of operations required for this algorithm? Answer is f(n) = 2 f(n/2) + 1. Please show why this is the case.Consider the following problem: given a list of integers N and an individual integer n, is there any element of N that is a factor of n? (1) There is a semi-decision procedure for the problem. If your answer is true, try to describe the procedure in English or pseudocode for learning purposes. Group of answer choices True FalseCorrect answer will be upvoted else downvoted. Computer science. Allow us to signify by d(n) the amount of all divisors of the number n, for example d(n)=∑k|nk. For instance, d(1)=1, d(4)=1+2+4=7, d(6)=1+2+3+6=12. For a given number c, track down the base n to such an extent that d(n)=c. Input The principal line contains one integer t (1≤t≤104). Then, at that point, t experiments follow. Each experiment is characterized by one integer c (1≤c≤107). Output For each experiment, output: "- 1" in case there is no such n that d(n)=c; n, in any case.