For this item consider the problem of finding the minimum even element in a list of integers.

Minimum Even Integer in a List (MINEVEN Input Ala...b] a list of integers. Output: Alil for some asis b such that Alil is even and Alils Aljl for all asjsb such that Aljl is even, or oo if the list contains no even element. Let ME(Ala...b) represent the output of the MINEVEN problem on input Ala...b. Let ath minta, b) be a simple function that returns the minimum of any two elements. Let m = be the midpoint between a and b. (2 points)1. Below is a self-reduction for the MINEVEN problem. State a recursive algorithm using pseudocode for finding the minimum even element based on this self-reduction. if a>b if a s b and Alal is odd ME(Ala b)- ME(Ala +1...bl) min(Alal,ME(A[a+1...bl)) ifa s b and A[al is even Using the same reduction as part 1 now state a recurrence T(n) that expresses the worst case run time of the recursive algorithm. Find a similar recurrence in your notes and state the tight (Big Theta) bound on T(n) (3 points) 2