Consider the following algorithm and answer the questions. ALGORITHM X(A[0..n − 1]) // Input: A contains n real numbers for i ← 0 to n − 2 do for j ← i + 1 to n − 1 do if A[j] > A[i] swap A[i] and A[j] 1. What does this algorithm compute? 2. What is the input size? 3. What is the basic operation? 4. How many times is the basic operation executed? (Set up a sum, and simplify the sum, to find the function expressing the number of repetitions of the basic operation.) 5. What is the efficiency class of this algorithm?

Subject - Design & Anal algorithms Please complete all the questions together.  Thank you in Advance. Consider the following pseudocode for bubblesort:bubblesort(A, n)for i from 1 to n − 1for j from n to i + 1if A[j] < A[j − 1]swap(A[j], A[j − 1])(a) What is the loop invariant for bubblesort?(b) State briefly a proof of correctness.(c) Derive concisely the worst-case running time of bubblesort as a function of the input array sizen? Show your work!(d) Derive concisely the best-case running time as a function of n. Show your work!

Question 1. The input is an array a[1],. ,..., a[n] of size n containing natural numbers between 1 and n. Describe an O(n) algorithm that determines if the array contains 2 consecutive integers.

Consider the algorithm given below.    ALGORITHM MinDistance(A[0..n − 1])    //Input: Array A[0..n − 1] of numbers    //Output: Minimum distance between two of its elements        dmin←∞         for i ←0 to n − 1 do                for j ←0 to n − 1 do                         if i != j and |A[i]− A[j ]| < dmin                                  dmin ←|A[i]− A[j ]|      return dminif  n = 20, and the list is sorted in descending order, then the loop  " or i ←0 to n − 1 do " will be executed ______ times.