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.

It is found that the number of primitive operations required by an algorithm is log n!, where n is the size of the input. What is its Big-Oh time complexity of the algorithm? Give the time complexity in terms of the closest function. Select one: O a. 0(2") Ob. O(n') O(log n) Od. O(n") e. None of the above

An algorithm was introduced for finding integers a, b for anym, n where m, n are positive such that am+bn = gcd(m, n). Implementthis algorithm as a Python program

Computer Algorithms Obtain the complexity of the program fragment below   for i <-- 1 to n do k <-- n while K > 1 do K <-- k/2 while (k) end-while end-for

The following Prefix_Average algorithm needs O(n-logn). def Prefix_Average(Seq):      sum = 0      length = len(Seq)      Avg = [0] * length      for i in range (length):              sum += Seq[i]              Avg[i] = sum / (i+1)      return  Avg True or False? Please solve it as soon as possible

If |V| = n and |E| = m, the running time complexity for Dijkstra's algorithm if implemented by an array is    Question 28 options:   O(n+m)   O(nm)   O(nlogm)   O(n^2)

What is time complexity ofCalc function Calc(n) if n==0 return 1 else k = Calc(n/2) return k*k end end A T(n) = θ (1) B. T(n) = θ (Lgn) C. T(n) = θ((Ign)^2) D. T(n) = θ(n)

Present an O(n) time algorithm to compute the coefficients of the polynomial (1 + x)^n. How much time is needed if you use the FFT algorithm to solve this problem?

Given the problem of basic multiplication: Input: Two n-digit nonnegative integers, x and y. Output: The product x - y e.g. 5 9 7 4 1 2 6 3 1 7 9 2 3 8 4 4 0 1 1 9 4 + 9. 7 4 7 5 4 5 1 6 2 What is the time complexity considering the number of primitive operations, i.e. additions and multiplications, performed? O(n*) O O(n) O None of the choices O(n) O(n")

Prove that if n is divisible by neither 2 nor 5, then there is a number m=11....11 (a string of 1s in base 10) which is divisible by n.