Question
For this problem consider the problem of finding the minimum element in a list of integers. Minimum Integer in a List (MIN) Input: A [
For this problem consider the problem of finding the minimum element in a list of integers.
Minimum Integer in a List (MIN) Input: A[a...b] a list of integers. Output: A[i] for some a i b such that A[i] A[j] for all a j b,or if the list is empty.
Let M(A[a ...b]) represent the output of the MIN problem on input A[a ...b]. Let min(a,b) be
a simple function that returns the minimum of two elements. Let m = (a+b)/2 be the midpoint
between a and b. Let q = (a+b)/4 be the point at one quarter the distance from a to b, and let
t = (3(a+b))4 be the point at three quarters the distance from a to b.
A). Below is aself-reduction for the MIN problem. State are cursive algorithm using pseu- docode for finding the minimum element based on this self-reduction.
if a > b
M(A[a...b]) = Min(M(A[a...b1]),A[b]) if ab
B). Using the same reduction as part 1 now state are currence T(n) that expresses the worst case run time of the recursive algorithm. Find a similar recurrence in your notes and state the tight bound on T (n).
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