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 − 1          for j from n to i + 1              if 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!

(c) What is the minimum number of comparisons for sorting an array of length n using the selection sort algorithm and when does it happen (under what conditions)? Minimum Number of Comparisons for When does it happen? Selection Sort | (d) What is the average number of comparisons for unsuccessful sequential search in a sorted array of length n? Explain why. Average Number of Comparisons for Unsuccessful Sequential Search Why? (e) What is the maximum number of comparisons for unsuccessful binary search in a sorted array of length n and when does it happen (under what conditions)? Maximum Number of Comparisons for Unsuccessful Binary Search When does it happen?

python # Initialize a 6x6 matrix with all elements as 0 matrix = [[0 for _ in range(6)] for _ in range(6)] # Fill in the matrix for i in range(6): # Iterate over rows for j in range(6): # Iterate over columns if i > j: matrix[i][j] = 3*j - 4*i else: matrix[i][j] = 0 # Print the matrix for row in matrix: print(row)