we are given a recurrence relation T(n) = T(n/2) +T(n/4) + n. what we must do is draw a tree and determine the appropriate quess for the answer.

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Adjacency matrix. Given a relation relation (as a numpy.array, see example below) and number of nodes n, define a function adjacency to construct the adjacency matrix A (as a numpy.array).You can assume that n is a positive integer and treat relation as a list of directed edges.   # Example from p112 of VMLSrelation = np.array([[1, 2], [1, 3], [2, 1], [2, 4], [3, 4], [4, 1]])n = 4 # Modify the function adjacency below with your answer for Q8def adjacency(relation, n):    A = None    ###########################    ### YOUR CODE HERE ########            ## REMOVE THIS LINE--------    raise NotImplementedError()    ## ------------------------    ###########################    return A

What is the recurrence relation of maximum subarray sum problem by using Divide and Conquer approach CHOOSE ANY ONE OPTION    1.T(n) = 7T(n/2) + n 2.T(n) = 8T(n/2) + n 3.T(n) = 2T(n/2) + n 4.T(n) = T(n/2) + n

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Solving recurrences Solve the following recurrence relations and give a Θbound for eachof them. Do not use the Master Theorem. You must use the recursion tree method. For each recurrence,state the branching factor, the height of the tree, the size of the subproblems at depth k, and the number of subproblems at depth k. You can draw the recursion tree to help find the solution, but do not include the tree in your submission as it will not be graded.(a) T (n) = 4T (n/3)+n(b) T (n) = 3T (n/3)+n(c) T (n) = 4T (n/4)+√n(d) T (n) = 16T (n/4)+n2(e) T (n) = 3T (n/4)+1

Define the subproblem as follows: Let M(i) be the maximum sum of all contiguous subarrays ending at position i. Clearly M(1) = A[1]. What is the recurrence relation for computing M(i)? Use this to give a more efficient algorithm to compute OPT.

25 f(n) = f(n/2) + 2 is a recurrence relation for the binary search problem true?

What is the complexity of the following recurrence: T'п) — 4T (п/2) +п, T(1) —D1 %3D

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n)=4T(n/2+2)+n. Use the substitution method to verify your answer.