Problem 3. Given an array A[1 : n] of n positive integers (possibly with repetitions), your goal is to find whether there is a sub-array A[l : r] such that = n. i=l Example. Given A = up to n = 10. On the other hand, if the input array is A = [3, 2, 6, 8, 20, 2, 4] for n = 7, the answer is No since no sub-array of A adds up to n = 7. [13, 1, 2, 3, 4, 7, 2, 3, 8, 9] for n = 10, the answer is Yes since elements in A[2 : 5] add Hint: Observe that if - A[i] = n, then A[i] = E=1 A[i] – n; this may come handy!

write a computer program that produces the desired output from the given input. Input: Elements in a finite set SOutput: Elements in ℘(S)Algorithm: Use recursion.

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.

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

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.

An evil king has n bottles of wine, and a spy has just poisoned one of them. Unfortunately, they do not know which one it is. The poison is very deadly; just one drop diluted even a billion to one will still kill. Even so, it takes a full month for the poison to take effect. Design a scheme for determining exactly which one of the wine bottles was poisoned in just one month’s time while expending O(log n) taste testers.