Problem $1-3($Matching Numbers$)$

$16+3$ points

You are given a set of $n$ points $x_1,$dots,$x_n$ and a set of $n$ segments $[a_1,b_1]dots[a_n,b_n]$ on a line, where $x_i,a_i,b_i$ are all integers. We want to output $k_1,k_2$dots,$k_n,$ where $k_i$ is the number of segments that contain $x_i.$ More formally, let $x[1,$dots,$n]$ be the array storing the points. Moreover, let $I[1,$dots,$n]$ denote an array storing the segments such that each entry $I[i]$ stores two values $I[i].$left and $I[i].$right. We want to write an algorithm that computes $K[1,$dots,$n]$ with $K[i]$ being the number of segments containing the point $x[i].$ In the following, assume that all the points, starting points, and endpoints are distinct.

${?}^1$ I.e$.,$ function of the form $a^n{n}^{b}lo{g}^{c}n$ for constants $a1$ and $b,c0.$

${?}^2$ This way even if you got part $($a$)$ wrong, you can still have correct solution to part $($b$).$

PS $1,$ Page $1$