The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm.  Algorithm Euclid(a,b) Require: a, b ≥ 0 Ensure: a = GCD(a, b)     while b ̸= 0 do         t ← b         b ← a mod b         a ← t end while return a We want to estimate its worst case running time using the big-Oh notation. Assuming the Euclidian division of two integers of n bits is executed in O(n^2), give a big-Oh notation of the worst-case running time of the algorithm Euclid.

hello im having this question in algorithm i need help with

Let A be an array of n integers: (a) Write a pseudo code for a divide-and-conquer algorithm that computes the MAX and MIN values in array A . (b) Write the recurrence for this algorithm. (c) Solve the recurrence using the substitution method.

Consider the problem of counting, in a given text, the number of substrings that start with an A and end with a B. For example, there are four such substrings in CABAAXBYA.a. Design a brute-force algorithm for this problem and determine its efficiency class.b. Design a more efficient algorithm for this problem with complexity O (n)

How did my textbook  get  2(n − 1) + 1 = 2n − 1 comparisons are used whenever this algorithm is applied:  (textbook solves the time complexity of finding the maximum element in a finite set using the following algorithm)  Algorithm below: procedure max(a1, a2,…, an: integers) max := a1 for i := 2 to n     if max < ai then max := ai return max{max is the largest element}

Write a recurrence for this algorithm and solve it to obtain a tight upper bound on the worst case runtime of this algorithm. You can use any method you like for solving this recurrence.

Below is pseudocode representing the Compute-Opt algorithm: Compute-Opt(j):    If j = 0 then        Return 0    Else        Return max(vj+Compute-Opt(p(j)), Compute-Opt(j − 1))    Endif Memoization of this algorithm does what to its running time? Group of answer choices It reduces the running time from exponential to linear. It reduces the running time from O(n2) to O(n). It reduces the running time from exponential to O(n log n). It doesn't significantly reduce the running time, but it enables the algorithm to utilize less space.

For part A, how what would the pseudo-code visually be when trying to visualize an efficient algorithm? As for Part B, what would determine the space and complexity?

Please help me solve the problem with step by step solution.

Consider array A of n numbers. We want to design a dynamic programming algorithm to find the maximum sum of consecutive numbers with at least one number. Clearly, if all numbers are positive, the maximum will be the sum of all the numbers. On the other hand, if all of them are negative, the maximum will be the largest negative number. The complexity of your dynamic programming algorithm must be O(n2). However, the running time of the most efficient algorithm is O(n). Design the most efficient algorithm you can and answer the following questions based on it. To get the full points you should design the O(n) algorithm. However, if you cannot do that, still answer the following questions based on your algorithm and you will get partial credit. Write the recursion that computes the optimal solution recursively based on the solu- (a) tion(s) to subproblem(s). Briefly explain how it computes the solution. Do not forget the base case(s) of your recursion.