Design an algorithm to find the maximum element in a list of n unique numbers. Give a trace for get.MAX(A,n), where A={1,5,2,9,4,3} and n=6. Design a recurrence relation for the algorithm and find its time complexity. Give a proof of correctness.

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Use a recursion tree to determine a good asymptotic upper bound on therecurrence T(n) = 3T(n/2) + n. Use the substitution method to prove your answer.

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