Write a recursive function: maximum(lst: list)--> int The function returns the maximum from a list of integers.

4) Recursive Analysis Homework • Unanswered The following algorithm takes an unsorted list of positive integers, along with two integers a and y. It returns the largest number, z, in the list such that either 2* = y or z9 = x is true. It returns 0 if no such z exists. The algorithm assumes that the list size, n, is a power of 2 with n > 1. 1 : integer xyMax(x, y, {a0,a1, ..., an-1}) 2 : if n == 1 3 : if (að у) or (až x) 4 return ao 5 : else 6 : return 0 7 : 8 : # process the left half 9 : 10 : m1 = xyMax(x,y,{a0,..., a4 J-1}) 11 : 12 : # process the right half 13 : m2 = xyMax(x,y,{a ;,.., an-1}) 14 : 15 : 16 : # find the largest 17 : 18 : max %3D тi 19 : if (m2 > max) 20 : 21 : 22 : max %3D тg return max 23 : end xyMax What is the recurrence relation that counts the number of comparisons for this algorithm? (The critical steps are at lines 2, 3, and 19.) What is a good big-O reference function for algorithm xyMax? (Hint: Which Master Theorem applies here?)

C++

Modify the recursive Fibonacci function to employ the memoization technique discussed in this chapter. The function creates a dictionary and then defines a nested recursive helper function named memoizedFib. You will need to create a dictionary to cache the sum of the fib function. The base case of the fib function is the same as before. However, before making any recursive calls, the helper function looks up the value for the function’s current argument in the dictionary (use the method get, with None as the default value). If the value exists, the function returns it and skips any recursive calls. Otherwise, after the helper function adds the results of its two recursive calls, it saves the sum in the dictionary with the current argument of the function as the key. Note: The program should output in the following format: n      fib(n) 2       1 4       3 8       21 16      987 32      2178309 ---------------------------------------------------------------------------------- def…