Problem $6.(20$ points$)$

During the annual balloon festival, Bob is trying to burst the most balloons with the

least number of arrows. The balloons are taped on a horizontal line, and each balloon

is represented by a closed interval along the $x-$axis. You are given an array of balloons

represented as intervals $[x_{\text{s}\text{t}\text{a}\text{r}\text{t}},x_{\text{e}\text{n}\text{d}}],$ where each interval indicates the horizontal diameter

of the balloon. The goal is to determine the minimum number of arrows that must be shot

on the $x-$axis to burst all the balloons. An arrow can burst a balloon if it is shot within the

interval that represents that balloon. A single arrow will burst all balloons in its path.

For instance, consider the array of balloon interyals $\left[\begin{array}{cc}10& 16\\ 2& 8\\ 1& 6\\ 7& 12\end{array}\right].$ Bob can

burst all the balloons with just two arrows:

An arrow shot at $x=6$ will burst the balloons $2,8$ and $1,6.$

An arrow shot at $x=11$ will burst the balloons $10,16$ and $7,12.$

Given an array interval s of balloon intervals, design an algorithm MINARROWS$($intervals$)$

in pseudocode that returns the minimum number of arrows required to burst all the bal$-$

loons. Briefly explain your algorithm and state the time complexity in Big$-$O notation. You

may call an external function SORT$(A)$ that sorts an array $A$ of $n$ intervals by their end

points in ascending order in time $O(nlogn).$ For full credit, your algorithm should have a

time complexity of $O(NlogN),$ where $N$ is the number of intervals; however, partial credit

will be given for slower solutions. Can someone explain the different elements that this code would need to have to receive full credit, and how Big$-$O notation works