Consider a segment tree with range $[0,...,$k$],$ where k is an integer.

$($a$)(7)$ Describe how a horizontal line segment is inserted into a segment tree. What is the time

complexity? Show how you derive it$.$ Assume that the two endpoints of the horizontal line

segment are integers within the range $[0,...,$k$]$ and each leaf node of the segment tree covers an

integer range.

$($b$)(7)$ If a segment tree contains n horizontal line segments, describe how to report all horizontal

line segments that intersect a given vertical line. What is the time complexity? Show how you

derive it$.$