Consider the following algorithm: function MYSTERY(A, n) /Input: Array A and integer n. A has size of least n if n <1 then return 0 else temp + 3 x A[n – 1]+ MYSTERY(A, n – 2) return temp a) Write down recurrence equations that describe the running time of he algorithm. Assume the base operation has a cost k.

CODING QUESTION. Euler's totient function, also known as phi-function φ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n): """Euler's totient function or Phi function. Time Complexity: O(sqrt(n)).""" result = n.

7. Suppose that you have two different algorithms for solving a problem. To solve a problem of size n, the first algorithm uses exactly n(log2 n) operations and the second algorithm uses exactly n3/2 operations. As n grows, which algorithm uses fewer operations?

a)The array A[0..n-2] contains n-1 integers in ascending order from 1 to n. (So an integer between 1 and n is missing.) Design an efficient algorithm to find the missing number. (The algorithm you designed should not be a Brute-force algorithm) b)Repeat (a) for an unordered sequence.

DESIGN YOUR OWN SETTING Devise your own setting for storing and searching the data in an array of non-negative integers redundantly. You may just describe the setting without having to give an explicit algorithm to explain the process by which data is stored. You should explain how hardware failures can be detected in your method. Once you have described the setting, make sure to include the following: Write a pseudocode function to describe an algorithm where the stored data can be searched for a value key: if the data is found, its location in the original array should be returned; -1 should be returned if the data is not found; -2 should be returned if there is a data storage error Include a short commentary explaining why your pseudocode works Describe the worst-case and best-case inputs to your search algorithm Derive the worst-case and best-case running times for the search algorithm Derive the Theta notation for the worst-case and best-case running times Maximum word count for...

Using recursion, write a function sum that takes a single argument n and computes the sum of all integers between 0 and n inclusive. Do not write this function using a while or for loop. Assume n is non-negative. def sum(n): """Using recursion, computes the sum of all integers between 1 and n, inclusive. Assume n is positive.>>> sum(1) 1>>> sum(5) # 1 + 2 + 3+ 4+ 5 15 "*** YOUR CODE HERE ***"

Java: Consider the following algorithm for searching in an unsorted array. If the size of the array is 1, then check if it contains the element to be searched. Otherwise, divide the array into two halves, and recursively search both halves. Which of (a)–(c) is false? The running time of this algorithm is O(N) The actual running time of this algorithm is likely to be better than sequential search. This is an example of a divide‐and‐conquer algorithm all of the above are true none of the above is true

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.

q16