Given the one$-$element array $[374]$ as input, your first algorithm should return $0,$

and your second algorithm should return $1.($The empty interval is still an interval!$)$ For the sake of analysis, assume that comparing, adding, or multiplying any pair of numbers takes O$(1)$ time.

$4.$ Draw the recursion tree for the Merge$-$Sort algorithm on an array of $16$ elements. Explain why memorization fails to speed up a good divide and conquer algorithm such as Merge$-$Sort.

$5.$ Solve maximum independent set $($in trees$)$ problem using a greedy approach and give the solution in pseudo code.