Compute the time complexity for the following algorithm Algorithm ABC2(X,p,m) { if (I==m) then print(X[1:m]) else { for i = p to m do temp = X[p]; X[p] = X[i]; X[i] = temp; ABC2(X, p+1, m); temp = X[p]; %3D X[p] = X[i]; X[i] = temp; %3D
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- For relatively small values of n, algorithms with larger orders can be more efficient than algorithms with smaller orders. Use a graphing calculator or computer to answer this question. For what values of n is an algorithm that requires n operations more efficient than an algorithm that requires [50 log2(n)] operations? (Assume n is an integer such that n > 1.) n?Select the asymptotic worst-case time complexity of the following algorithm:AlgorithmInput: a1, a2, ..., an, a sequence of numbersn, the length of the sequencex, a numberOutput: ??For i = 1 to n-1For j = i+1 to nFor k = 1 to nIf ((ai)^2 + (aj)^2 = (ak)^2) Return( "True" )End-forEnd-forEnd-forReturn( "False" )a. ?(1)b. ?(?)c. ?(?2)d. ?(?3)The algorithm consists of the following steps.1. Input: A weighted graph G = (V, E, w)2. Output: A maximal weighted matching M of G3. M ← Ø4. E ← E5. V ← V6. while E = Ø7. select at random any v ∈ V8. let e ∈ E be the heaviest edge incident to v9. M ← M ∪ e10. V ← V {v}11. E ← E \ {e and all adjacent edges to e}make two ways of implementing this algorithm in Python. don't copy bartleby old answer its wrong need correct ans otherwise you will get downvote
- For each, draw the recursion tree, find the height of the tree, the running time of each layer, and the sum of running times. Then use this info to find the explicit answer for T(n). a. T(n) = 2T(n/4) + √ n (n is a power of 4 (n = 4^k) for some positive integer k) b. T(n) = 9T(n/3) + n^2 (n is a power of 3 (n = 3^k) for some positive integer k) c. T(n) = T(n/2) + 1 (n is a power of 2 (n = 2^k) for some positive integer k)Modeling the spread of a virus like COVID-19 using recursion. Let N = total population (assumed constant, disregarding deaths, births, immigration, and emigration). S n = number who are susceptible to the disease at time n (n is in weeks). I n = number who are infected (and contagious) at time n. R n = number who are recovered (and not contagiuous) at time n. The total population is divided between these three groups: N = S n + I n + R n There are several hidden assumptions here that may or may not apply to COVID-19, such as a recovered person is assumed to not be able to get the disease a second time, at least within the time window being examined. On week 0 (the start), you assume a certain small number of people have the infection (just to get things going). Everyone else is initially susceptible, and no one is recovered. There are two constants of interest: Let period = time period that it takes for an infected person to recover (recover meaning they become not infectious to…Exercise on Big-Oh Analysis. Answer True or False whether a function with growth rate is a member of the set of algorithms that grow with a certain complexity. Draw also the graph. n3/2 = O (n2); if n = 500 4n2+5n+2 = Ω (n2); if n = 150 2n3+8n2+6n+7 = ω (2n); if n = 500 (n+1)(n-1)/ 3 = o (logn); if n = 200 5n + 3 = O (nlogn); if n = 1000 int[] arr = {2,4,6,8,10,12,14,16}; for(int i= 0; i<arr.length; i++){ System.out.println(arr[i]); } = o (n) 7. for(int row= 1; row<=5; row++){ for(int col=1; col<=3; col++){ System.out.print(“*”); } System.out.println(); } = Ω (n2) 8. 2n = ω (n); if n = 20 9. 6n2+2n+5 = O (n!); if n = 50 10. 2n + 10 = ϴ (nlogn); if n = 200
- Computer Science Find the correct asymptotic complexity of an algorithm with runtime T(n) and step-by-step workings where T(x) = O(n) + T((2*x)/8) Assume x and n are the same. If it is different, how will the working be like?The given time complexity is: m T(m-1) + ca > 1 cb = 0 expanding using substitution: m T(m-1) + ca m[(m-1) T(m-2) + ca]+ ca m(m-1) T(m-2) + mca + ca m(m-1) [(m-2) T(m-3) + ca] + mca + ca m(m-1)(m-2) T(m-3) + m(m-1)ca + mca + ca what is the time complexity? form an expression for adding all the caSuppose a Genetic Algorithm uses chromosomes of the form x=abcdef with a fixed length of six genes.Each gene can be any digit between 0 and 9 . Let the fitness of individual x be calculated as : f(x) =(a+b)-(c+d)-(e+f) And let the initial population consist of four individuals x1, ... ,x4 with the following chromosomes : x1 = 3 5 3 2 6 5, x2 = 9 8 0 1 2 2, x3 = 1 2 2 1 2 3, x4 = 7 9 2 3 1 1 1. 1.Evaluate the fitness of each individual, showing all your workings, and arrange them in order with the fittest first and the least fit last. 2. calculate the average fitness. 3. Perform the following crossover operations:a- Cross the fittest two individuals using one point crossover at the middle point.b- Cross the second and third fittest individuals using a two point crossover (points b and e). Suppose the new population consists of the four offspring individuals received by the crossover operations in the above question. Evaluate the fitness of the new population, showing all your…
- Which one is the key thing in backtracking? Insertion Recursion Submission In what manner is a state-space tree for a backtracking algorithm constructed? Depth-first search Breadth-first search Twice around the tree Nearest neighbour first What does the following function do? int fun(int x, int y) { if (y == 0) return 0; return (x + fun(x, y-1)); } x + y x + x*y x*y xy Consider the following recursive function fun(x, y). What is the value of fun(4, 3) int fun(int x, int y) { if (x == 0) return y; return fun(x - 1, x + y); } 10 9 13 12 Predict output of following program 16 4 Runtime Error 8 Assume you have the following backtracking based sorting algorithm:bool Backtracking_Sort(sorted_list, unsorted_list, index, length) { if (index == length) { return true; } Potential_values = []; If (index != 0) {Potential_values = get_larger_unused_values(sorted_list, unsorted_list, index);} else { Potential_values = copy(unsorted_list);}…There is a cube and an ant is performing a random walk on its vertices,every step it will start from one vertex and walk to another along the connected edge, it willrandomly select any of the 3 adjoining vertices with equal probability. If it starts at one vertex,what is the expected number of steps it needs to reach the diagonally opposite vertex? Write a c++ program for the sameGive 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.