In class, we discussed an algorithm which allows us to query an interval i in a search tree S, and we receive an interval in S which overlaps with i if one exists. Using the algorithm discussed in class as a sub procedure, give an algorithm which returns every interval in S which overlaps with i. Suppose there are k such intervals. What is the worst case running time of your algorithm in terms of k and n

The algorithm is expressed as S:

Count = array of k + 1 zero

For s in input do

count {key (s) } + = 1

total = 0

For i in 0, 1, ... k do

count (i), total = total, count (i) + total

Output = array of the sum length input for s in input do

Output {count (key (s) } = s

count {key (s) } + = 1

return output

b) The total space usage of the algorithm can be an impediment for maximum key values that are significantly smaller.